diff --git a/.all-contributorsrc b/.all-contributorsrc
new file mode 100644
index 0000000000..18990490d9
--- /dev/null
+++ b/.all-contributorsrc
@@ -0,0 +1,283 @@
+{
+  "files": [
+    "README.md"
+  ],
+  "imageSize": 100,
+  "commit": false,
+  "contributors": [
+    {
+      "login": "tinosulzer",
+      "name": "Valentin Sulzer",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/20817509?v=4",
+      "profile": "https://sites.google.com/view/valentinsulzer",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "maintenance",
+        "review",
+        "test",
+        "tutorial",
+        "blog"
+      ]
+    },
+    {
+      "login": "rtimms",
+      "name": "Robert Timms",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/43040151?v=4",
+      "profile": "http://www.robertwtimms.com",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "maintenance",
+        "review",
+        "test",
+        "tutorial"
+      ]
+    },
+    {
+      "login": "Scottmar93",
+      "name": "Scott Marquis",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/22661308?v=4",
+      "profile": "https://github.com/Scottmar93",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "maintenance",
+        "review",
+        "test",
+        "tutorial"
+      ]
+    },
+    {
+      "login": "martinjrobins",
+      "name": "Martin Robinson",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/1148404?v=4",
+      "profile": "https://github.com/martinjrobins",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "review",
+        "test"
+      ]
+    },
+    {
+      "login": "ferranbrosa",
+      "name": "Ferran Brosa Planella",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/28443643?v=4",
+      "profile": "https://www.brosaplanella.com",
+      "contributions": [
+        "review",
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "maintenance",
+        "test",
+        "tutorial",
+        "blog"
+      ]
+    },
+    {
+      "login": "TomTranter",
+      "name": "Tom Tranter",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/7068741?v=4",
+      "profile": "https://github.com/TomTranter",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "review",
+        "test"
+      ]
+    },
+    {
+      "login": "tlestang",
+      "name": "Thibault Lestang",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/13448239?v=4",
+      "profile": "http://tlestang.github.io",
+      "contributions": [
+        "bug",
+        "code",
+        "doc",
+        "example",
+        "ideas",
+        "review",
+        "test",
+        "infra"
+      ]
+    },
+    {
+      "login": "dalonsoa",
+      "name": "Diego",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/6095790?v=4",
+      "profile": "https://www.imperial.ac.uk/admin-services/ict/self-service/research-support/rcs/research-software-engineering/",
+      "contributions": [
+        "bug",
+        "review",
+        "code",
+        "infra"
+      ]
+    },
+    {
+      "login": "felipe-salinas",
+      "name": "felipe-salinas",
+      "avatar_url": "https://avatars2.githubusercontent.com/u/64426781?v=4",
+      "profile": "https://github.com/felipe-salinas",
+      "contributions": [
+        "code",
+        "test"
+      ]
+    },
+    {
+      "login": "suhaklee",
+      "name": "suhaklee",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/57151989?v=4",
+      "profile": "https://github.com/suhaklee",
+      "contributions": [
+        "code",
+        "test"
+      ]
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+    {
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+      "name": "viviantran27",
+      "avatar_url": "https://avatars0.githubusercontent.com/u/6379429?v=4",
+      "profile": "https://github.com/viviantran27",
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+        "code",
+        "test"
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+    {
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+      "name": "gyouhoc",
+      "avatar_url": "https://avatars0.githubusercontent.com/u/60714526?v=4",
+      "profile": "https://github.com/gyouhoc",
+      "contributions": [
+        "bug",
+        "code",
+        "test"
+      ]
+    },
+    {
+      "login": "YannickNoelStephanKuhn",
+      "name": "Yannick Kuhn",
+      "avatar_url": "https://avatars0.githubusercontent.com/u/62429912?v=4",
+      "profile": "https://github.com/YannickNoelStephanKuhn",
+      "contributions": [
+        "code",
+        "test"
+      ]
+    },
+    {
+      "login": "jedgedrudd",
+      "name": "Jacqueline Edge",
+      "avatar_url": "https://avatars2.githubusercontent.com/u/39409226?v=4",
+      "profile": "http://batterymodel.co.uk",
+      "contributions": [
+        "ideas",
+        "eventOrganizing",
+        "fundingFinding"
+      ]
+    },
+    {
+      "login": "fcooper8472",
+      "name": "Fergus Cooper",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/3770306?v=4",
+      "profile": "https://www.rse.ox.ac.uk/",
+      "contributions": [
+        "code",
+        "test"
+      ]
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+    {
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+      "name": "jonchapman1",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/28925818?v=4",
+      "profile": "https://github.com/jonchapman1",
+      "contributions": [
+        "ideas",
+        "fundingFinding"
+      ]
+    },
+    {
+      "login": "colinplease",
+      "name": "Colin Please",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/44977104?v=4",
+      "profile": "https://github.com/colinplease",
+      "contributions": [
+        "ideas",
+        "fundingFinding"
+      ]
+    },
+    {
+      "login": "FaradayInstitution",
+      "name": "Faraday Institution",
+      "avatar_url": "https://avatars2.githubusercontent.com/u/42166506?v=4",
+      "profile": "https://faraday.ac.uk",
+      "contributions": [
+        "financial"
+      ]
+    },
+    {
+      "login": "bessman",
+      "name": "Alexander Bessman",
+      "avatar_url": "https://avatars3.githubusercontent.com/u/1999462?v=4",
+      "profile": "https://github.com/bessman",
+      "contributions": [
+        "bug",
+        "example"
+      ]
+    },
+    {
+      "login": "dalbamont",
+      "name": "dalbamont",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/19659095?v=4",
+      "profile": "https://github.com/dalbamont",
+      "contributions": [
+        "code"
+      ]
+    },
+    {
+      "login": "anandmy",
+      "name": "Anand Mohan Yadav",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/34894671?v=4",
+      "profile": "https://github.com/anandmy",
+      "contributions": [
+        "doc"
+      ]
+    },
+    {
+      "login": "weilongai",
+      "name": "WEILONG AI",
+      "avatar_url": "https://avatars1.githubusercontent.com/u/41424174?v=4",
+      "profile": "https://github.com/weilongai",
+      "contributions": [
+        "code",
+        "example",
+        "test"
+      ]
+    }
+  ],
+  "contributorsPerLine": 7,
+  "projectName": "PyBaMM",
+  "projectOwner": "pybamm-team",
+  "repoType": "github",
+  "repoHost": "https://github.com",
+  "skipCi": true
+}
diff --git a/.github/release_checklist.md b/.github/release_checklist.md
index 339237deca..434859657a 100644
--- a/.github/release_checklist.md
+++ b/.github/release_checklist.md
@@ -1,4 +1,4 @@
-- Increment version number in `version`
-- Increment version number in `docs/conf.py`
-- Update CHANGELOG.md with a summary of the release
-- Update (and pin) jax and jaxlib to latest version and fix any bugs that arise
\ No newline at end of file
+- Increment version number in `version`	
+- Increment version number in `docs/conf.py`	
+- Update CHANGELOG.md with a summary of the release	
+- Update (and pin) jax and jaxlib to latest version and fix any bugs that arise	
diff --git a/.github/workflows/build_wheels_and_publish.yml b/.github/workflows/build_wheels_and_publish.yml
index d320bcbe16..c4f04734dc 100644
--- a/.github/workflows/build_wheels_and_publish.yml
+++ b/.github/workflows/build_wheels_and_publish.yml
@@ -37,10 +37,6 @@ jobs:
     - name: Install build-time deps for MacOS
       if: matrix.os == 'macos-latest'
       run: |
-        # Temporary fix for https://github.com/actions/virtual-environments/issues/1811
-        brew untap local/homebrew-openssl
-        brew untap local/homebrew-python2
-        # End of fix
         brew update
         brew install graphviz
         brew install sundials
diff --git a/.github/workflows/test_on_push.yml b/.github/workflows/test_on_push.yml
index 21ee6c3bf5..7fb0962cd1 100644
--- a/.github/workflows/test_on_push.yml
+++ b/.github/workflows/test_on_push.yml
@@ -50,10 +50,6 @@ jobs:
     - name: Install MacOS system dependencies
       if: matrix.os == 'macos-latest'
       run: |
-        # Temporary fix for https://github.com/actions/virtual-environments/issues/1811
-        brew untap local/homebrew-openssl
-        brew untap local/homebrew-python2
-        # End of fix
         brew update
         brew install graphviz
         brew install openblas
@@ -87,8 +83,8 @@ jobs:
       if: matrix.os != 'windows-latest'
       run: tox -e examples
         
-    - name: Instal and run coverage
-      if: success() && (matrix.os == 'unbuntu-latest' && matrix.python-version == 3.7)
+    - name: Install and run coverage
+      if: success() && (matrix.os == 'ubuntu-latest' && matrix.python-version == 3.7)
       run: tox -e coverage
 
     - name: Upload coverage report
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1c588edab5..0ea3d2e92f 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,41 @@
+# [v0.3.0](https://github.com/pybamm-team/PyBaMM)
+
+This release introduces a new aging model for particle swelling and cracking, a new reduced-order model (TSPMe), and a parameter set for A123 LFP cells. Additionally, there have been several backend optimizations to speed up model creation and solving, and other minor features and bug fixes.
+
+## Features
+
+-   Added a submodel for particle swelling and cracking ([#1232](https://github.com/pybamm-team/PyBaMM/pull/1232))
+-   Added a notebook on how to speed up the solver and handle instabilities ([#1223](https://github.com/pybamm-team/PyBaMM/pull/1223))
+-   Improve string printing of `BinaryOperator`, `Function`, and `Concatenation` objects ([#1223](https://github.com/pybamm-team/PyBaMM/pull/1223))
+-   Added `Solution.integration_time`, which is the time taken just by the integration subroutine, without extra setups ([#1223](https://github.com/pybamm-team/PyBaMM/pull/1223))
+-   Added parameter set for an A123 LFP cell ([#1209](https://github.com/pybamm-team/PyBaMM/pull/1209))
+-   Added variables related to equivalent circuit models ([#1204](https://github.com/pybamm-team/PyBaMM/pull/1204))
+-   Added the `Integrated` electrolyte conductivity submodel ([#1188](https://github.com/pybamm-team/PyBaMM/pull/1188))
+-   Added an example script to check conservation of lithium ([#1186](https://github.com/pybamm-team/PyBaMM/pull/1186))
+-   Added `erf` and `erfc` functions ([#1184](https://github.com/pybamm-team/PyBaMM/pull/1184))
+
+## Optimizations
+
+-   Add (optional) smooth approximations for the `Minimum`, `Maximum`, `Heaviside`, and `AbsoluteValue` operators ([#1223](https://github.com/pybamm-team/PyBaMM/pull/1223))
+-   Avoid unnecessary repeated computations in the solvers ([#1222](https://github.com/pybamm-team/PyBaMM/pull/1222))
+-   Rewrite `Symbol.is_constant` to be more efficient ([#1222](https://github.com/pybamm-team/PyBaMM/pull/1222))
+-   Cache shape and size calculations ([#1222](https://github.com/pybamm-team/PyBaMM/pull/1222))
+-   Only instantiate the geometric, electrical and thermal parameter classes once ([#1222](https://github.com/pybamm-team/PyBaMM/pull/1222))
+
+## Bug fixes
+
+-   Quickplot now works when timescale or lengthscale is a function of an input parameter ([#1234](https://github.com/pybamm-team/PyBaMM/pull/1234))
+-   Fix bug that was slowing down creation of the EC reaction SEI submodel ([#1227](https://github.com/pybamm-team/PyBaMM/pull/1227))
+-   Add missing separator thermal parameters for the Ecker parameter set ([#1226](https://github.com/pybamm-team/PyBaMM/pull/1226))
+-   Make sure simulation solves when evaluated timescale is a function of an input parameter ([#1218](https://github.com/pybamm-team/PyBaMM/pull/1218))
+-   Raise error if saving to MATLAB with variable names that MATLAB can't read, and give option of providing alternative variable names ([#1206](https://github.com/pybamm-team/PyBaMM/pull/1206))
+-   Raise error if the boundary condition at the origin in a spherical domain is other than no-flux ([#1175](https://github.com/pybamm-team/PyBaMM/pull/1175))
+-   Fix boundary conditions at r = 0 for Creating Models notebooks ([#1173](https://github.com/pybamm-team/PyBaMM/pull/1173))
+
+## Breaking changes
+
+-    The parameters "Positive/Negative particle distribution in x" and "Positive/Negative surface area per unit volume distribution in x" have been deprecated. Instead, users can provide "Positive/Negative particle radius [m]" and "Positive/Negative surface area per unit volume [m-1]" directly as functions of through-cell position (x [m]) ([#1237](https://github.com/pybamm-team/PyBaMM/pull/1237)) 
+
 # [v0.2.4](https://github.com/pybamm-team/PyBaMM/tree/v0.2.4) - 2020-09-07
 
 This release adds new operators for more complex models, some basic sensitivity analysis, and a spectral volumes spatial method, as well as some small bug fixes.
diff --git a/MANIFEST.in b/MANIFEST.in
index c40770432c..c2f9cd7db7 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -28,6 +28,8 @@ include pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/paramet
 include pybamm/input/parameters/lithium-ion/separators/separator_Kim2011/parameters.csv
 include pybamm/input/parameters/lithium-ion/separators/separator_Chen2020/parameters.csv
 include pybamm/input/parameters/lithium-ion/separators/separator_Marquis2019/parameters.csv
+include pybamm/input/parameters/lithium-ion/mechanicals/lico2_graphite_Ai2020/parameters.csv
+include pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020.csv
 include pybamm/input/parameters/lead-acid/anodes/lead_Sulzer2019/lead_ocp_Bode1977.py
 include pybamm/input/parameters/lead-acid/cathodes/lead_dioxide_Sulzer2019/lead_dioxide_ocp_Bode1977.py
 include pybamm/input/parameters/lead-acid/electrolytes/sulfuric_acid_Sulzer2019/diffusivity_Gu1997.py
@@ -82,6 +84,7 @@ include pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/README.
 include pybamm/input/parameters/lithium-ion/separators/separator_Kim2011/README.md
 include pybamm/input/parameters/lithium-ion/separators/separator_Chen2020/README.md
 include pybamm/input/parameters/lithium-ion/separators/separator_Marquis2019/README.md
+include pybamm/input/parameters/lithium-ion/mechanicals/lico2_graphite_Ai2020/README.md
 include pybamm/version
 include pybamm/CITATIONS.txt
 include CMakeBuild.py
\ No newline at end of file
diff --git a/README.md b/README.md
index ef339a4cee..d35b5c8291 100644
--- a/README.md
+++ b/README.md
@@ -5,6 +5,9 @@
 [![codecov](https://codecov.io/gh/pybamm-team/PyBaMM/branch/master/graph/badge.svg)](https://codecov.io/gh/pybamm-team/PyBaMM)
 [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/pybamm-team/PyBaMM/blob/master/)
 [![black_code_style](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/ambv/black)
+<!-- ALL-CONTRIBUTORS-BADGE:START - Do not remove or modify this section -->
+[![All Contributors](https://img.shields.io/badge/all_contributors-22-orange.svg?style=flat-square)](#contributors-)
+<!-- ALL-CONTRIBUTORS-BADGE:END -->
 
 PyBaMM (Python Battery Mathematical Modelling) solves physics-based electrochemical DAE models by using state-of-the-art automatic differentiation and numerical solvers. The Doyle-Fuller-Newman model can be solved in under 0.1 seconds, while the reduced-order Single Particle Model and Single Particle Model with electrolyte can be solved in just a few milliseconds. Additional physics can easily be included such as thermal effects, fast particle diffusion, 3D effects, and more. All models are implemented in a flexible manner, and a wide range of models and parameter sets (NCA, NMC, LiCoO2, ...) are available. There is also functionality to simulate any set of experimental instructions, such as CCCV or GITT, or specify drive cycles.
 
@@ -101,3 +104,49 @@ If you'd like to help us develop PyBaMM by adding new methods, writing documenta
 ## Licensing
 
 PyBaMM is fully open source. For more information about its license, see [LICENSE](./LICENSE.txt).
+
+## Contributors ✨
+
+Thanks goes to these wonderful people ([emoji key](https://allcontributors.org/docs/en/emoji-key)):
+
+<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
+<!-- prettier-ignore-start -->
+<!-- markdownlint-disable -->
+<table>
+  <tr>
+    <td align="center"><a href="https://sites.google.com/view/valentinsulzer"><img src="https://avatars3.githubusercontent.com/u/20817509?v=4" width="100px;" alt=""/><br /><sub><b>Valentin Sulzer</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Atinosulzer" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tinosulzer" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tinosulzer" title="Documentation">📖</a> <a href="#example-tinosulzer" title="Examples">💡</a> <a href="#ideas-tinosulzer" title="Ideas, Planning, & Feedback">🤔</a> <a href="#maintenance-tinosulzer" title="Maintenance">🚧</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Atinosulzer" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tinosulzer" title="Tests">⚠️</a> <a href="#tutorial-tinosulzer" title="Tutorials">✅</a> <a href="#blog-tinosulzer" title="Blogposts">📝</a></td>
+    <td align="center"><a href="http://www.robertwtimms.com"><img src="https://avatars1.githubusercontent.com/u/43040151?v=4" width="100px;" alt=""/><br /><sub><b>Robert Timms</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Artimms" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=rtimms" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=rtimms" title="Documentation">📖</a> <a href="#example-rtimms" title="Examples">💡</a> <a href="#ideas-rtimms" title="Ideas, Planning, & Feedback">🤔</a> <a href="#maintenance-rtimms" title="Maintenance">🚧</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Artimms" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=rtimms" title="Tests">⚠️</a> <a href="#tutorial-rtimms" title="Tutorials">✅</a></td>
+    <td align="center"><a href="https://github.com/Scottmar93"><img src="https://avatars1.githubusercontent.com/u/22661308?v=4" width="100px;" alt=""/><br /><sub><b>Scott Marquis</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3AScottmar93" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=Scottmar93" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=Scottmar93" title="Documentation">📖</a> <a href="#example-Scottmar93" title="Examples">💡</a> <a href="#ideas-Scottmar93" title="Ideas, Planning, & Feedback">🤔</a> <a href="#maintenance-Scottmar93" title="Maintenance">🚧</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3AScottmar93" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=Scottmar93" title="Tests">⚠️</a> <a href="#tutorial-Scottmar93" title="Tutorials">✅</a></td>
+    <td align="center"><a href="https://github.com/martinjrobins"><img src="https://avatars3.githubusercontent.com/u/1148404?v=4" width="100px;" alt=""/><br /><sub><b>Martin Robinson</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Amartinjrobins" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=martinjrobins" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=martinjrobins" title="Documentation">📖</a> <a href="#example-martinjrobins" title="Examples">💡</a> <a href="#ideas-martinjrobins" title="Ideas, Planning, & Feedback">🤔</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Amartinjrobins" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=martinjrobins" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://www.brosaplanella.com"><img src="https://avatars3.githubusercontent.com/u/28443643?v=4" width="100px;" alt=""/><br /><sub><b>Ferran Brosa Planella</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Aferranbrosa" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Aferranbrosa" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=ferranbrosa" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=ferranbrosa" title="Documentation">📖</a> <a href="#example-ferranbrosa" title="Examples">💡</a> <a href="#ideas-ferranbrosa" title="Ideas, Planning, & Feedback">🤔</a> <a href="#maintenance-ferranbrosa" title="Maintenance">🚧</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=ferranbrosa" title="Tests">⚠️</a> <a href="#tutorial-ferranbrosa" title="Tutorials">✅</a> <a href="#blog-ferranbrosa" title="Blogposts">📝</a></td>
+    <td align="center"><a href="https://github.com/TomTranter"><img src="https://avatars3.githubusercontent.com/u/7068741?v=4" width="100px;" alt=""/><br /><sub><b>Tom Tranter</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3ATomTranter" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=TomTranter" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=TomTranter" title="Documentation">📖</a> <a href="#example-TomTranter" title="Examples">💡</a> <a href="#ideas-TomTranter" title="Ideas, Planning, & Feedback">🤔</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3ATomTranter" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=TomTranter" title="Tests">⚠️</a></td>
+    <td align="center"><a href="http://tlestang.github.io"><img src="https://avatars3.githubusercontent.com/u/13448239?v=4" width="100px;" alt=""/><br /><sub><b>Thibault Lestang</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Atlestang" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tlestang" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tlestang" title="Documentation">📖</a> <a href="#example-tlestang" title="Examples">💡</a> <a href="#ideas-tlestang" title="Ideas, Planning, & Feedback">🤔</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Atlestang" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=tlestang" title="Tests">⚠️</a> <a href="#infra-tlestang" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a></td>
+  </tr>
+  <tr>
+    <td align="center"><a href="https://www.imperial.ac.uk/admin-services/ict/self-service/research-support/rcs/research-software-engineering/"><img src="https://avatars1.githubusercontent.com/u/6095790?v=4" width="100px;" alt=""/><br /><sub><b>Diego</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Adalonsoa" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/pulls?q=is%3Apr+reviewed-by%3Adalonsoa" title="Reviewed Pull Requests">👀</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=dalonsoa" title="Code">💻</a> <a href="#infra-dalonsoa" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a></td>
+    <td align="center"><a href="https://github.com/felipe-salinas"><img src="https://avatars2.githubusercontent.com/u/64426781?v=4" width="100px;" alt=""/><br /><sub><b>felipe-salinas</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=felipe-salinas" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=felipe-salinas" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://github.com/suhaklee"><img src="https://avatars3.githubusercontent.com/u/57151989?v=4" width="100px;" alt=""/><br /><sub><b>suhaklee</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=suhaklee" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=suhaklee" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://github.com/viviantran27"><img src="https://avatars0.githubusercontent.com/u/6379429?v=4" width="100px;" alt=""/><br /><sub><b>viviantran27</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=viviantran27" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=viviantran27" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://github.com/gyouhoc"><img src="https://avatars0.githubusercontent.com/u/60714526?v=4" width="100px;" alt=""/><br /><sub><b>gyouhoc</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Agyouhoc" title="Bug reports">🐛</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=gyouhoc" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=gyouhoc" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://github.com/YannickNoelStephanKuhn"><img src="https://avatars0.githubusercontent.com/u/62429912?v=4" width="100px;" alt=""/><br /><sub><b>Yannick Kuhn</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=YannickNoelStephanKuhn" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=YannickNoelStephanKuhn" title="Tests">⚠️</a></td>
+    <td align="center"><a href="http://batterymodel.co.uk"><img src="https://avatars2.githubusercontent.com/u/39409226?v=4" width="100px;" alt=""/><br /><sub><b>Jacqueline Edge</b></sub></a><br /><a href="#ideas-jedgedrudd" title="Ideas, Planning, & Feedback">🤔</a> <a href="#eventOrganizing-jedgedrudd" title="Event Organizing">📋</a> <a href="#fundingFinding-jedgedrudd" title="Funding Finding">🔍</a></td>
+  </tr>
+  <tr>
+    <td align="center"><a href="https://www.rse.ox.ac.uk/"><img src="https://avatars3.githubusercontent.com/u/3770306?v=4" width="100px;" alt=""/><br /><sub><b>Fergus Cooper</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=fcooper8472" title="Code">💻</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=fcooper8472" title="Tests">⚠️</a></td>
+    <td align="center"><a href="https://github.com/jonchapman1"><img src="https://avatars1.githubusercontent.com/u/28925818?v=4" width="100px;" alt=""/><br /><sub><b>jonchapman1</b></sub></a><br /><a href="#ideas-jonchapman1" title="Ideas, Planning, & Feedback">🤔</a> <a href="#fundingFinding-jonchapman1" title="Funding Finding">🔍</a></td>
+    <td align="center"><a href="https://github.com/colinplease"><img src="https://avatars3.githubusercontent.com/u/44977104?v=4" width="100px;" alt=""/><br /><sub><b>Colin Please</b></sub></a><br /><a href="#ideas-colinplease" title="Ideas, Planning, & Feedback">🤔</a> <a href="#fundingFinding-colinplease" title="Funding Finding">🔍</a></td>
+    <td align="center"><a href="https://faraday.ac.uk"><img src="https://avatars2.githubusercontent.com/u/42166506?v=4" width="100px;" alt=""/><br /><sub><b>Faraday Institution</b></sub></a><br /><a href="#financial-FaradayInstitution" title="Financial">💵</a></td>
+    <td align="center"><a href="https://github.com/bessman"><img src="https://avatars3.githubusercontent.com/u/1999462?v=4" width="100px;" alt=""/><br /><sub><b>Alexander Bessman</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/issues?q=author%3Abessman" title="Bug reports">🐛</a> <a href="#example-bessman" title="Examples">💡</a></td>
+    <td align="center"><a href="https://github.com/dalbamont"><img src="https://avatars1.githubusercontent.com/u/19659095?v=4" width="100px;" alt=""/><br /><sub><b>dalbamont</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=dalbamont" title="Code">💻</a></td>
+    <td align="center"><a href="https://github.com/anandmy"><img src="https://avatars1.githubusercontent.com/u/34894671?v=4" width="100px;" alt=""/><br /><sub><b>Anand Mohan Yadav</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=anandmy" title="Documentation">📖</a></td>
+  </tr>
+  <tr>
+    <td align="center"><a href="https://github.com/weilongai"><img src="https://avatars1.githubusercontent.com/u/41424174?v=4" width="100px;" alt=""/><br /><sub><b>WEILONG AI</b></sub></a><br /><a href="https://github.com/pybamm-team/PyBaMM/commits?author=weilongai" title="Code">💻</a> <a href="#example-weilongai" title="Examples">💡</a> <a href="https://github.com/pybamm-team/PyBaMM/commits?author=weilongai" title="Tests">⚠️</a></td>
+  </tr>
+</table>
+
+<!-- markdownlint-enable -->
+<!-- prettier-ignore-end -->
+<!-- ALL-CONTRIBUTORS-LIST:END -->
+
+This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome!
\ No newline at end of file
diff --git a/docs/conf.py b/docs/conf.py
index dc22f6d6b0..0bacae7c03 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -26,9 +26,9 @@
 author = "The PyBaMM Team"
 
 # The short X.Y version
-version = "0.2"
+version = "0.3"
 # The full version, including alpha/beta/rc tags
-release = "0.2.4"
+release = "0.3.0-beta"
 
 
 # -- General configuration ---------------------------------------------------
diff --git a/docs/install/install-from-source.rst b/docs/install/install-from-source.rst
index 261515c1e0..f8156a075a 100644
--- a/docs/install/install-from-source.rst
+++ b/docs/install/install-from-source.rst
@@ -128,7 +128,7 @@ Using Tox (recommended)
 	  python -m tox -e windows-dev # (Windows)
 
 
-This creates a virtual environment ``.tox/dev`` inside the ``PyBaMM/`` directory.
+This creates a virtual environment ``.tox/dev`` (or ``windows-dev``) inside the ``PyBaMM/`` directory.
 It comes ready with PyBaMM and some useful development tools like `flake8 <https://flake8.pycqa.org/en/latest/>`_ and `black <https://black.readthedocs.io/en/stable/>`_.
 
 You can now activate the environment with
@@ -137,7 +137,7 @@ You can now activate the environment with
 
 	  source .tox/dev/bin/activate # (GNU/Linux and MacOS)
 	  #
-	  .tox\dev\Scripts\activate.bat # (Windows)
+	  .tox\windows-dev\Scripts\activate.bat # (Windows)
 
 and run the tests to check your installation.
 
diff --git a/docs/source/expression_tree/binary_operator.rst b/docs/source/expression_tree/binary_operator.rst
index 39e819bfb0..971bdd26f4 100644
--- a/docs/source/expression_tree/binary_operator.rst
+++ b/docs/source/expression_tree/binary_operator.rst
@@ -47,4 +47,10 @@ Binary Operators
 
 .. autofunction:: pybamm.maximum
 
+.. autofunction:: pybamm.softminus
+
+.. autofunction:: pybamm.softplus
+
+.. autofunction:: pybamm.sigmoid
+
 .. autofunction:: pybamm.source
diff --git a/docs/source/expression_tree/unary_operator.rst b/docs/source/expression_tree/unary_operator.rst
index 3fe0627da1..d09ebd1649 100644
--- a/docs/source/expression_tree/unary_operator.rst
+++ b/docs/source/expression_tree/unary_operator.rst
@@ -87,6 +87,8 @@ Unary Operators
 
 .. autofunction:: pybamm.boundary_value
 
+.. autofunction:: pybamm.smooth_absolute_value
+
 .. autofunction:: pybamm.sign
 
 .. autofunction:: pybamm.upwind
diff --git a/docs/source/models/submodels/electrolyte_conductivity/index.rst b/docs/source/models/submodels/electrolyte_conductivity/index.rst
index 8d0be2223a..a723c32aab 100644
--- a/docs/source/models/submodels/electrolyte_conductivity/index.rst
+++ b/docs/source/models/submodels/electrolyte_conductivity/index.rst
@@ -7,5 +7,6 @@ Electrolyte Conductivity
     base_electrolyte_conductivity
     leading_order_conductivity
     composite_conductivity
+    integrated_conductivity
     full_conductivity
     surface_form/index
diff --git a/docs/source/models/submodels/electrolyte_conductivity/integrated_conductivity.rst b/docs/source/models/submodels/electrolyte_conductivity/integrated_conductivity.rst
new file mode 100644
index 0000000000..469e3e7dcb
--- /dev/null
+++ b/docs/source/models/submodels/electrolyte_conductivity/integrated_conductivity.rst
@@ -0,0 +1,5 @@
+Integrated Model
+================
+
+.. autoclass:: pybamm.electrolyte_conductivity.Integrated
+    :members:
diff --git a/docs/source/models/submodels/index.rst b/docs/source/models/submodels/index.rst
index a72bfa243f..c6624b516c 100644
--- a/docs/source/models/submodels/index.rst
+++ b/docs/source/models/submodels/index.rst
@@ -14,6 +14,7 @@ Submodels
     interface/index
     oxygen_diffusion/index
     particle/index
+    particle_cracking/index
     porosity/index
     thermal/index
     tortuosity/index
diff --git a/docs/source/models/submodels/particle_cracking/base_cracking.rst b/docs/source/models/submodels/particle_cracking/base_cracking.rst
new file mode 100644
index 0000000000..9cdc3343d6
--- /dev/null
+++ b/docs/source/models/submodels/particle_cracking/base_cracking.rst
@@ -0,0 +1,5 @@
+Base Particle Cracking Model
+============================
+
+.. autoclass:: pybamm.particle_cracking.BaseCracking
+    :members:
diff --git a/docs/source/models/submodels/particle_cracking/crack_propagation.rst b/docs/source/models/submodels/particle_cracking/crack_propagation.rst
new file mode 100644
index 0000000000..82b395df88
--- /dev/null
+++ b/docs/source/models/submodels/particle_cracking/crack_propagation.rst
@@ -0,0 +1,5 @@
+Crack Propagation Model
+=======================
+
+.. autoclass:: pybamm.particle_cracking.CrackPropagation
+    :members:
diff --git a/docs/source/models/submodels/particle_cracking/index.rst b/docs/source/models/submodels/particle_cracking/index.rst
new file mode 100644
index 0000000000..872921c628
--- /dev/null
+++ b/docs/source/models/submodels/particle_cracking/index.rst
@@ -0,0 +1,9 @@
+Particle Cracking
+=================
+
+.. toctree::
+  :maxdepth: 1
+
+  base_cracking
+  crack_propagation
+  no_cracking
diff --git a/docs/source/models/submodels/particle_cracking/no_cracking.rst b/docs/source/models/submodels/particle_cracking/no_cracking.rst
new file mode 100644
index 0000000000..171713a975
--- /dev/null
+++ b/docs/source/models/submodels/particle_cracking/no_cracking.rst
@@ -0,0 +1,5 @@
+No Cracking Model
+=================
+
+.. autoclass:: pybamm.particle_cracking.NoCracking
+    :members:
diff --git a/docs/source/spatial_methods/index.rst b/docs/source/spatial_methods/index.rst
index 8bb4f0eee0..060eb91c02 100644
--- a/docs/source/spatial_methods/index.rst
+++ b/docs/source/spatial_methods/index.rst
@@ -6,5 +6,6 @@ Discretisation and spatial methods
   discretisation
   spatial_method
   finite_volume
+  spectral_volume
   scikit_finite_element
   zero_dimensional_method
diff --git a/docs/source/spatial_methods/spectral_volume.rst b/docs/source/spatial_methods/spectral_volume.rst
new file mode 100644
index 0000000000..30b7f475a3
--- /dev/null
+++ b/docs/source/spatial_methods/spectral_volume.rst
@@ -0,0 +1,5 @@
+Spectral Volume
+===============
+
+.. autoclass:: pybamm.SpectralVolume
+    :members:
diff --git a/examples/notebooks/Creating Models/2-a-pde-model.ipynb b/examples/notebooks/Creating Models/2-a-pde-model.ipynb
index 3f84c4904d..ac441e5c92 100644
--- a/examples/notebooks/Creating Models/2-a-pde-model.ipynb	
+++ b/examples/notebooks/Creating Models/2-a-pde-model.ipynb	
@@ -107,7 +107,7 @@
     "# boundary conditions\n",
     "lbc = pybamm.Scalar(0)\n",
     "rbc = pybamm.Scalar(2)\n",
-    "model.boundary_conditions = {c: {\"left\": (lbc, \"Dirichlet\"), \"right\": (rbc, \"Neumann\")}}"
+    "model.boundary_conditions = {c: {\"left\": (lbc, \"Neumann\"), \"right\": (rbc, \"Neumann\")}}"
    ]
   },
   {
diff --git a/examples/notebooks/Creating Models/3-negative-particle-problem.ipynb b/examples/notebooks/Creating Models/3-negative-particle-problem.ipynb
index 8c9a2f4cd9..145df5985b 100644
--- a/examples/notebooks/Creating Models/3-negative-particle-problem.ipynb	
+++ b/examples/notebooks/Creating Models/3-negative-particle-problem.ipynb	
@@ -105,7 +105,7 @@
     "# boundary conditions \n",
     "lbc = pybamm.Scalar(0)\n",
     "rbc = -j / F / D\n",
-    "model.boundary_conditions = {c: {\"left\": (lbc, \"Dirichlet\"), \"right\": (rbc, \"Neumann\")}}\n",
+    "model.boundary_conditions = {c: {\"left\": (lbc, \"Neumann\"), \"right\": (rbc, \"Neumann\")}}\n",
     "\n",
     "# initial conditions \n",
     "model.initial_conditions = {c: c0}"
diff --git a/examples/notebooks/Creating Models/4-comparing-full-and-reduced-order-models.ipynb b/examples/notebooks/Creating Models/4-comparing-full-and-reduced-order-models.ipynb
index a69f26b2d1..57ba2a76e1 100644
--- a/examples/notebooks/Creating Models/4-comparing-full-and-reduced-order-models.ipynb	
+++ b/examples/notebooks/Creating Models/4-comparing-full-and-reduced-order-models.ipynb	
@@ -140,7 +140,7 @@
     "# boundary conditions (only required for full model)\n",
     "lbc = pybamm.Scalar(0)\n",
     "rbc = -j / F / D\n",
-    "full_model.boundary_conditions = {c: {\"left\": (lbc, \"Dirichlet\"), \"right\": (rbc, \"Neumann\")}}"
+    "full_model.boundary_conditions = {c: {\"left\": (lbc, \"Neumann\"), \"right\": (rbc, \"Neumann\")}}"
    ]
   },
   {
@@ -391,7 +391,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.7.7"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/Getting Started/Tutorial 1 - How to run a model.ipynb b/examples/notebooks/Getting Started/Tutorial 1 - How to run a model.ipynb
index 38d4d4ea53..974a089de3 100644
--- a/examples/notebooks/Getting Started/Tutorial 1 - How to run a model.ipynb	
+++ b/examples/notebooks/Getting Started/Tutorial 1 - How to run a model.ipynb	
@@ -83,7 +83,7 @@
     {
      "data": {
       "text/plain": [
-       "<pybamm.solvers.solution.Solution at 0x7f09715ea9b0>"
+       "<pybamm.solvers.solution.Solution at 0x7f20b554f650>"
       ]
      },
      "execution_count": 4,
@@ -110,7 +110,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "06ae219fb8b94fa3aad3b8907a41ed27",
+       "model_id": "2b323f5e668d4135834681aac97571ce",
        "version_major": 2,
        "version_minor": 0
       },
@@ -152,7 +152,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/Getting Started/Tutorial 5 - Run experiments.ipynb b/examples/notebooks/Getting Started/Tutorial 5 - Run experiments.ipynb
index 082e9accc4..d14cac014d 100644
--- a/examples/notebooks/Getting Started/Tutorial 5 - Run experiments.ipynb	
+++ b/examples/notebooks/Getting Started/Tutorial 5 - Run experiments.ipynb	
@@ -206,7 +206,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/Getting Started/Tutorial 6 - Managing simulation outputs.ipynb b/examples/notebooks/Getting Started/Tutorial 6 - Managing simulation outputs.ipynb
index 565726a863..a343548e53 100644
--- a/examples/notebooks/Getting Started/Tutorial 6 - Managing simulation outputs.ipynb	
+++ b/examples/notebooks/Getting Started/Tutorial 6 - Managing simulation outputs.ipynb	
@@ -22,21 +22,23 @@
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
+     "name": "stdout",
      "text": [
+      "\u001b[33mWARNING: You are using pip version 20.2.1; however, version 20.2.4 is available.\n",
+      "You should consider upgrading via the '/Users/vsulzer/Documents/Energy_storage/PyBaMM/.tox/dev/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
       "Note: you may need to restart the kernel to use updated packages.\n"
      ]
     },
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<pybamm.solvers.solution.Solution at 0x7f39e107d1d0>"
+       "<pybamm.solvers.solution.Solution at 0x1467c6820>"
       ]
      },
-     "execution_count": 1,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 1
     }
    ],
    "source": [
@@ -100,6 +102,7 @@
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([3.77047806, 3.75305163, 3.74567013, 3.74038819, 3.73581198,\n",
@@ -124,9 +127,8 @@
        "       3.45439366, 3.41299183, 3.35578872, 3.27680073, 3.16842637])"
       ]
      },
-     "execution_count": 4,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 4
     }
    ],
    "source": [
@@ -146,6 +148,7 @@
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([   0.        ,   36.36363636,   72.72727273,  109.09090909,\n",
@@ -175,9 +178,8 @@
        "       3490.90909091, 3527.27272727, 3563.63636364, 3600.        ])"
       ]
      },
-     "execution_count": 5,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 5
     }
    ],
    "source": [
@@ -197,14 +199,14 @@
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([3.72947891, 3.70860034, 3.67810702, 3.65400558])"
       ]
      },
-     "execution_count": 6,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 6
     }
    ],
    "source": [
@@ -263,18 +265,16 @@
    "metadata": {},
    "outputs": [
     {
+     "output_type": "display_data",
      "data": {
+      "text/plain": "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…",
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "7e116fdff90e40b28b3f13b79f3e7347",
        "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
-      ]
+       "version_minor": 0,
+       "model_id": "0b4ebac3fdd947218f9444b2b381cf04"
+      }
      },
-     "metadata": {},
-     "output_type": "display_data"
+     "metadata": {}
     }
    ],
    "source": [
@@ -311,28 +311,26 @@
    "metadata": {},
    "outputs": [
     {
+     "output_type": "display_data",
      "data": {
+      "text/plain": "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…",
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "cb9640519af3475b9b921b8523c01020",
        "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
-      ]
+       "version_minor": 0,
+       "model_id": "f4a1b65b2bf945099197135c5598084b"
+      }
      },
-     "metadata": {},
-     "output_type": "display_data"
+     "metadata": {}
     },
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<pybamm.plotting.quick_plot.QuickPlot at 0x7f39dc81a0b8>"
+       "<pybamm.plotting.quick_plot.QuickPlot at 0x14be13b80>"
       ]
      },
-     "execution_count": 11,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 11
     }
    ],
    "source": [
@@ -370,7 +368,9 @@
    "outputs": [],
    "source": [
     "sol.save_data(\"sol_data.csv\", [\"Current [A]\", \"Terminal voltage [V]\"], to_format=\"csv\")\n",
-    "sol.save_data(\"sol_data.mat\", [\"Current [A]\", \"Terminal voltage [V]\"], to_format=\"matlab\")"
+    "# matlab needs names without spaces\n",
+    "sol.save_data(\"sol_data.mat\", [\"Current [A]\", \"Terminal voltage [V]\"], to_format=\"matlab\",\n",
+    "              short_names={\"Current [A]\": \"I\", \"Terminal voltage [V]\": \"V\"})"
    ]
   },
   {
@@ -425,9 +425,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.8.5-final"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}
\ No newline at end of file
diff --git a/examples/notebooks/Getting Started/Tutorial 7 - Model options.ipynb b/examples/notebooks/Getting Started/Tutorial 7 - Model options.ipynb
index 9447f4838d..611aa4a0db 100644
--- a/examples/notebooks/Getting Started/Tutorial 7 - Model options.ipynb	
+++ b/examples/notebooks/Getting Started/Tutorial 7 - Model options.ipynb	
@@ -140,7 +140,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/Getting Started/Tutorial 9 - Changing the mesh.ipynb b/examples/notebooks/Getting Started/Tutorial 9 - Changing the mesh.ipynb
index 3b8cacddde..bca6b8232d 100644
--- a/examples/notebooks/Getting Started/Tutorial 9 - Changing the mesh.ipynb	
+++ b/examples/notebooks/Getting Started/Tutorial 9 - Changing the mesh.ipynb	
@@ -288,7 +288,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/Validating_mechanical_models_Enertech_DFN.ipynb b/examples/notebooks/Validating_mechanical_models_Enertech_DFN.ipynb
new file mode 100644
index 0000000000..e08791ca8e
--- /dev/null
+++ b/examples/notebooks/Validating_mechanical_models_Enertech_DFN.ipynb
@@ -0,0 +1,322 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Test the parameter set of the Enertech cells\n",
+    "In this notebook, we show how to use pybamm to reproduce the experimental results for the Enertech cells (LCO-G). To see all of the models and submodels available in PyBaMM, please take a look at the documentation [here](https://pybamm.readthedocs.io/en/latest/source/models/index.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
+    "import pybamm\n",
+    "import os\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "os.chdir(pybamm.__path__[0]+'/..')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When you load a model in PyBaMM it builds by default. Building the model sets all of the model variables and sets up any variables which are coupled between different submodels: this is the process which couples the submodels together and allows one submodel to access variables from another. If you would like to swap out a submodel in an exisitng battery model you need to load it without building it by passing the keyword `build=False`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "model = pybamm.lithium_ion.DFN(\n",
+    "    options = {\n",
+    "        \"particle\": \"Fickian diffusion\", \n",
+    "        \"cell geometry\": \"arbitrary\", \n",
+    "        \"thermal\": \"lumped\", \n",
+    "        \"particle cracking\": \"no cracking\",\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can get the parameter set `Ai2020` for the model, which includes the mechanical properties required by the mechanical model."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.5 C\n",
+      "1 C\n",
+      "2 C\n"
+     ]
+    }
+   ],
+   "source": [
+    "chemistry = pybamm.parameter_sets.Ai2020\n",
+    "param = pybamm.ParameterValues(chemistry=chemistry)\n",
+    "capacity = param[\"Cell capacity [A.h]\"]\n",
+    "param.update({\n",
+    "    \"Current function [A]\": capacity * pybamm.InputParameter(\"C-rate\")\n",
+    "})\n",
+    "# experiment05C = pybamm.Experiment([\"Discharge at 0.5C until 3 V\"])\n",
+    "# experiment1C = pybamm.Experiment([\"Discharge at 1C until 3 V\"])\n",
+    "# experiment2C = pybamm.Experiment([\"Discharge at 2C until 3 V\"])\n",
+    "var = pybamm.standard_spatial_vars\n",
+    "var_pts = {\n",
+    "  var.x_n: 50,\n",
+    "  var.x_s: 50,\n",
+    "  var.x_p: 50,\n",
+    "  var.r_n: 20,\n",
+    "  var.r_p: 20,\n",
+    "}\n",
+    "\n",
+    "sim = pybamm.Simulation(\n",
+    "        model,\n",
+    "        var_pts=var_pts,\n",
+    "        parameter_values=param,\n",
+    "        solver=pybamm.CasadiSolver(dt_max=600)\n",
+    "    )\n",
+    "Crates = [0.5, 1, 2]\n",
+    "solutions = []\n",
+    "\n",
+    "for Crate in Crates:\n",
+    "    print(f\"{Crate} C\")\n",
+    "    sol = sim.solve(t_eval=[0, 3600/Crate*1.05], inputs={\"C-rate\": Crate})\n",
+    "    solutions.append(sol)\n",
+    "\n",
+    "\n",
+    "solution05C, solution1C, solution2C = solutions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Load experimental results of the Enertech cells, Ref. Ai et al. JES 2020\n",
+    "https://iopscience.iop.org/article/10.1149/2.0122001JES"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# load experimental results\n",
+    "import pandas as pd\n",
+    "path = \"pybamm/input/discharge_data/Enertech_cells/\"\n",
+    "data_Disp_01C=pd.read_csv (path + \"0.1C_discharge_displacement.txt\", delimiter= '\\s+',header=None)\n",
+    "data_Disp_05C=pd.read_csv (path + \"0.5C_discharge_displacement.txt\", delimiter= '\\s+',header=None)\n",
+    "data_Disp_1C=pd.read_csv (path + \"1C_discharge_displacement.txt\", delimiter= '\\s+',header=None)\n",
+    "data_Disp_2C=pd.read_csv (path + \"2C_discharge_displacement.txt\", delimiter= '\\s+',header=None)\n",
+    "data_V_01C=pd.read_csv (path + \"0.1C_discharge_U.txt\", delimiter= '\\s+',header=None)\n",
+    "data_V_05C=pd.read_csv (path + \"0.5C_discharge_U.txt\", delimiter= '\\s+',header=None)\n",
+    "data_V_1C=pd.read_csv (path + \"1C_discharge_U.txt\", delimiter= '\\s+',header=None)\n",
+    "data_V_2C=pd.read_csv (path + \"2C_discharge_U.txt\", delimiter= '\\s+',header=None)\n",
+    "data_T_05C=pd.read_csv (path + \"0.5C_discharge_T.txt\", delimiter= '\\s+',header=None)\n",
+    "data_T_1C=pd.read_csv (path + \"1C_discharge_T.txt\", delimiter= '\\s+',header=None)\n",
+    "data_T_2C=pd.read_csv (path + \"2C_discharge_T.txt\", delimiter= '\\s+',header=None)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Plot the results."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1008x288 with 3 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "t_all2C = solution2C[\"Time [h]\"].entries\n",
+    "V_n2C = solution2C[\"Terminal voltage [V]\"].entries\n",
+    "T_n2C = solution2C[\"Volume-averaged cell temperature [K]\"].entries - param[\"Initial temperature [K]\"]\n",
+    "L_x2C = solution2C[\"Cell thickness change [m]\"].entries\n",
+    "\n",
+    "t_all1C = solution1C[\"Time [h]\"].entries\n",
+    "V_n1C = solution1C[\"Terminal voltage [V]\"].entries\n",
+    "T_n1C = solution1C[\"Volume-averaged cell temperature [K]\"].entries - param[\"Initial temperature [K]\"]\n",
+    "L_x1C = solution1C[\"Cell thickness change [m]\"].entries\n",
+    "\n",
+    "t_all05C = solution05C[\"Time [h]\"].entries\n",
+    "V_n05C = solution05C[\"Terminal voltage [V]\"].entries\n",
+    "T_n05C = solution05C[\"Volume-averaged cell temperature [K]\"].entries - param[\"Initial temperature [K]\"]\n",
+    "L_x05C = solution05C[\"Cell thickness change [m]\"].entries\n",
+    "f, (ax1, ax2,ax3) = plt.subplots(1, 3 ,figsize=(14,4))\n",
+    "ax1.plot(t_all2C, V_n2C,'r-',label=\"Simulation\")\n",
+    "ax1.plot(data_V_2C.values[::30,0]/3600, data_V_2C.values[::30,1],'ro',markerfacecolor='none',label=\"Experiment\")\n",
+    "ax1.plot(t_all05C, V_n05C,'g-')\n",
+    "ax1.plot(data_V_05C.values[::100,0]/3600, data_V_05C.values[::100,1],'go',markerfacecolor='none')\n",
+    "ax1.plot(t_all1C, V_n1C,'b-')\n",
+    "ax1.plot(data_V_1C.values[::50,0]/3600, data_V_1C.values[::50,1],'bo',markerfacecolor='none')\n",
+    "ax1.legend()\n",
+    "#plt.xlim(0, 3600);\n",
+    "ax1.set_xlabel(\"Time [h]\")\n",
+    "ax1.set_ylabel(\"Terminal voltage [V]\")\n",
+    "ax1.text(0.1, 3.2, r'2 C', {'color': 'r', 'fontsize': 14})\n",
+    "ax1.text(1.1, 3.2, r'1 C', {'color': 'b', 'fontsize': 14})\n",
+    "ax1.text(1.6, 3.2, r'0.5 C', {'color': 'g', 'fontsize': 14})\n",
+    "\n",
+    "ax2.plot(t_all2C, T_n2C,'r-',label=\"Simulation\")\n",
+    "ax2.plot(data_T_2C.values[0:1754:50,0]/3600, data_T_2C.values[0:1754:50,1],'ro',markerfacecolor='none',label=\"Experiment\")\n",
+    "ax2.plot(t_all05C, T_n05C,'g-')\n",
+    "ax2.plot(data_T_05C.values[0:7301:200,0]/3600, data_T_05C.values[0:7301:200,1],'go',markerfacecolor='none')\n",
+    "ax2.plot(t_all1C, T_n1C,'b-')\n",
+    "ax2.plot(data_T_1C.values[0:3598:100,0]/3600, data_T_1C.values[0:3598:100,1],'bo',markerfacecolor='none')\n",
+    "ax2.legend()\n",
+    "ax2.set_xlabel(\"Time [h]\")\n",
+    "ax2.set_ylabel(\"Temperature rise [K]\")\n",
+    "#plt.xlim(0, 3600);\n",
+    "ax2.text(0.5, 8, r'2 C', {'color': 'r', 'fontsize': 14})\n",
+    "ax2.text(0.8, 4.4, r'1 C', {'color': 'b', 'fontsize': 14})\n",
+    "ax2.text(1.5, 2, r'0.5 C', {'color': 'g', 'fontsize': 14})\n",
+    "\n",
+    "ax3.plot(t_all2C, L_x2C,'r-',label=\"Simulation\")\n",
+    "ax3.plot(data_Disp_2C.values[0:1754:5,0]/3600, data_Disp_2C.values[0:1754:5,1]-data_Disp_2C.values[0,1],'ro',markerfacecolor='none',label=\"Experiment\")\n",
+    "ax3.plot(t_all05C, L_x05C,'g-')\n",
+    "ax3.plot(data_Disp_05C.values[0:1754:10,0]/3600, data_Disp_05C.values[0:1754:10,1]-data_Disp_05C.values[0,1],'go',markerfacecolor='none')\n",
+    "ax3.plot(t_all1C, L_x1C,'b-')\n",
+    "ax3.plot(data_Disp_1C.values[0:1754:10,0]/3600, data_Disp_1C.values[0:1754:10,1]-data_Disp_1C.values[0,1],'bo',markerfacecolor='none')\n",
+    "ax3.legend()\n",
+    "ax3.set_xlabel(\"Time [h]\")\n",
+    "ax3.set_ylabel(\"Thickness change [m]\")\n",
+    "ax3.text(0.1, -0.0001, r'2 C', {'color': 'r', 'fontsize': 14})\n",
+    "ax3.text(0.9, -0.0001, r'1 C', {'color': 'b', 'fontsize': 14})\n",
+    "ax3.text(1.8, -0.0001, r'0.5 C', {'color': 'g', 'fontsize': 14})\n",
+    "#plt.xlim(0, 3600);\n",
+    "f.tight_layout()\n",
+    "f.show()\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Stress data below are from Fig. 6 in Ai et al. JES 2020 https://iopscience.iop.org/article/10.1149/2.0122001JES"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 720x252 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "cs_n_xav = solution2C[\"X-averaged negative particle concentration [mol.m-3]\"].entries\n",
+    "cs_p_xav = solution2C[\"X-averaged positive particle concentration [mol.m-3]\"].entries\n",
+    "st_surf_n =  solution2C[\"Negative particle surface tangential stress\"].entries\n",
+    "st_surf_p =  solution2C[\"Positive particle surface tangential stress\"].entries\n",
+    "\n",
+    "data_st_n_2C=pd.read_csv (path + \"stn_2C.txt\", delimiter= ',',header=3)\n",
+    "data_st_p_2C=pd.read_csv (path + \"stp_2C.txt\", delimiter= ',',header=3)\n",
+    "\n",
+    "f, (ax1, ax2) = plt.subplots(1, 2 ,figsize=(10,3.5))\n",
+    "ax1.plot(t_all2C, st_surf_n[-1,:],'ro',markerfacecolor='none',label=\"Current\")\n",
+    "ax1.plot(data_st_n_2C.values[:,0]/3600, data_st_n_2C.values[:,1],'r-',label=\"Ai et al. 2020\")\n",
+    "ax1.legend()\n",
+    "#plt.xlim(0, 3600);\n",
+    "ax1.set_xlabel(\"Time [h]\")\n",
+    "ax1.set_ylabel(\"$\\sigma_{t,n}/E_n$\")\n",
+    "\n",
+    "ax2.plot(t_all2C, st_surf_p[0,:],'ro',markerfacecolor='none',label=\"Current\")\n",
+    "ax2.plot(data_st_p_2C.values[0:3601,0]/3600, data_st_p_2C.values[0:3601,1],'r-',label=\"Ai et al. 2020\")\n",
+    "ax2.legend()\n",
+    "ax2.set_xlabel(\"Time [h]\")\n",
+    "ax2.set_ylabel(\"$\\sigma_{t,p}/E_p$\")\n",
+    "#plt.xlim(0, 3600);\n",
+    "f.tight_layout()\n",
+    "#f.set_title(\"particle surface tangential stress close to the separator\")\n",
+    "f.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "\n",
+    "[1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2019). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/examples/notebooks/change-input-current.ipynb b/examples/notebooks/change-input-current.ipynb
index d0cf216944..477cde0eb4 100644
--- a/examples/notebooks/change-input-current.ipynb
+++ b/examples/notebooks/change-input-current.ipynb
@@ -327,7 +327,20 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.8.5"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": true,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": true,
+   "toc_window_display": true
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/change-settings.ipynb b/examples/notebooks/change-settings.ipynb
index ab00333a00..a257989be7 100644
--- a/examples/notebooks/change-settings.ipynb
+++ b/examples/notebooks/change-settings.ipynb
@@ -665,7 +665,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/compare-ecker-data.ipynb b/examples/notebooks/compare-ecker-data.ipynb
index 1bcd6bd985..9a766d0558 100644
--- a/examples/notebooks/compare-ecker-data.ipynb
+++ b/examples/notebooks/compare-ecker-data.ipynb
@@ -103,8 +103,8 @@
     "    var.x_n: int(parameter_values.evaluate(model.param.L_n / 1e-6)),\n",
     "    var.x_s: int(parameter_values.evaluate(model.param.L_s / 1e-6)),\n",
     "    var.x_p: int(parameter_values.evaluate(model.param.L_p / 1e-6)),\n",
-    "    var.r_n: int(parameter_values.evaluate(model.param.R_n / 1e-7)),\n",
-    "    var.r_p: int(parameter_values.evaluate(model.param.R_p / 1e-7)),\n",
+    "    var.r_n: int(parameter_values.evaluate(model.param.R_n_typ / 1e-7)),\n",
+    "    var.r_p: int(parameter_values.evaluate(model.param.R_p_typ / 1e-7)),\n",
     "}"
    ]
   },
@@ -168,7 +168,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 936x288 with 2 Axes>"
       ]
@@ -221,13 +221,6 @@
     "\n",
     "[2] Richardson, Giles, et. al. \"Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation.\" Electrochemica Acta 339 (2020): 135862"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
@@ -246,7 +239,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/models/DFN.ipynb b/examples/notebooks/models/DFN.ipynb
index 7dcf280071..dadd18ffd7 100644
--- a/examples/notebooks/models/DFN.ipynb
+++ b/examples/notebooks/models/DFN.ipynb
@@ -71,7 +71,7 @@
     "\n",
     "####  Concentration in the electrode active material:\n",
     "\\begin{gather}\n",
-    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{\\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = j_{\\text{k}}, \\quad \\text{k} \\in \\text{n, p}.\n",
+    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{R, \\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = j_{\\text{k}}, \\quad \\text{k} \\in \\text{n, p}.\n",
     "\\end{gather}\n",
     "\n",
     "#### Reference potential:\n",
@@ -203,7 +203,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "b72126bb294743c38f4aa5069787b9b6",
+       "model_id": "eceebcfd564d4b53bf56bda5abf066ff",
        "version_major": 2,
        "version_minor": 0
       },
@@ -240,7 +240,7 @@
     "|$\\mathcal{C}_{\\text{k}}$   | $\\tau_{\\text{k}}^*/\\tau_{\\text{d}}^*$   | Ratio of solid diffusion and discharge timescales |\n",
     "|$\\mathcal{C}_{\\text{e}}$   |$\\tau_{\\text{e}}^*/\\tau_{\\text{d}}^*$    |Ratio of electrolyte transport and discharge timescales|\n",
     "|$\\mathcal{C}_{\\text{r,k}}$ |$\\tau_{\\text{r,k}}^*/\\tau_{\\text{d}}^*$  |Ratio of reaction and discharge timescales|\n",
-    "|$a_{\\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
+    "|$a_{R, \\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
     "|$\\gamma_{\\text{k}}$        |$c_{\\text{k,max}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentrations in solid|\n",
     "|$\\gamma_{\\text{e}}$        |$c_{\\text{e,typ}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentration in the negative electrode solid and typical electrolyte concentration|\n",
     "\n",
@@ -272,7 +272,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/models/SPM.ipynb b/examples/notebooks/models/SPM.ipynb
index 3ac578ad45..90cee2c20e 100644
--- a/examples/notebooks/models/SPM.ipynb
+++ b/examples/notebooks/models/SPM.ipynb
@@ -23,7 +23,7 @@
     "\\mathcal{C}_{\\text{k}} \\frac{\\partial c_{\\text{s,k}}}{\\partial t} &= -\\frac{1}{r_{\\text{k}}^2} \\frac{\\partial}{\\partial r_{\\text{k}}} \\left(r_{\\text{k}}^2 N_{\\text{s,k}}\\right), \\\\\n",
     "N_{\\text{s,k}} &= -D_{\\text{s,k}}(c_{\\text{s,k}}) \\frac{\\partial c_{\\text{s,k}}}{\\partial r_{\\text{k}}}, \\quad \\text{k} \\in \\text{n, p}, \\end{align}\n",
     "$$\n",
-    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{\\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
+    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{R, \\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
     "\\begin{cases}\n",
     "\t\t  \\frac{I}{L_{\\text{n}}}, \\quad &\\text{k}=\\text{n}, \\\\ \n",
     "\t\t  -\\frac{I}{L_{\\text{p}}}, \\quad &\\text{k}=\\text{p}, \n",
@@ -57,7 +57,15 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
    "source": [
     "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
     "import pybamm\n",
@@ -152,11 +160,11 @@
      "text": [
       "SPM domains:\n",
       "1. negative electrode with variables:\n",
-      "  -( 0 ) <= x_n <= ( Negative electrode thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] )\n",
+      "  -( 0 ) <= x_n <= ( Negative electrode thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) )\n",
       "2. separator with variables:\n",
-      "  -( Negative electrode thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] ) <= x_s <= ( Negative electrode thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] + Separator thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] )\n",
+      "  -( Negative electrode thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) ) <= x_s <= ( Negative electrode thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) + Separator thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) )\n",
       "3. positive electrode with variables:\n",
-      "  -( Negative electrode thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] + Separator thickness [m] / Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m] ) <= x_p <= ( 1 )\n",
+      "  -( Negative electrode thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) + Separator thickness [m] / (Negative electrode thickness [m] + Separator thickness [m] + Positive electrode thickness [m]) ) <= x_p <= ( 1 )\n",
       "4. negative particle with variables:\n",
       "  -( 0 ) <= r_n <= ( 1 )\n",
       "5. positive particle with variables:\n",
@@ -239,8 +247,8 @@
       "x_n has 20 mesh points\n",
       "x_s has 20 mesh points\n",
       "x_p has 20 mesh points\n",
-      "r_n has 10 mesh points\n",
-      "r_p has 10 mesh points\n",
+      "r_n has 30 mesh points\n",
+      "r_p has 30 mesh points\n",
       "y has 10 mesh points\n",
       "z has 10 mesh points\n"
      ]
@@ -499,6 +507,10 @@
       "\t- Negative particle concentration [mol.m-3]\n",
       "\t- X-averaged negative particle concentration\n",
       "\t- X-averaged negative particle concentration [mol.m-3]\n",
+      "\t- R-averaged negative particle concentration\n",
+      "\t- R-averaged negative particle concentration [mol.m-3]\n",
+      "\t- Average negative particle concentration\n",
+      "\t- Average negative particle concentration [mol.m-3]\n",
       "\t- Negative particle surface concentration\n",
       "\t- Negative particle surface concentration [mol.m-3]\n",
       "\t- X-averaged negative particle surface concentration\n",
@@ -506,11 +518,29 @@
       "\t- Negative electrode active volume fraction\n",
       "\t- Negative electrode volume-averaged concentration\n",
       "\t- Negative electrode volume-averaged concentration [mol.m-3]\n",
-      "\t- Negative electrode average extent of lithiation\n",
+      "\t- Negative electrode extent of lithiation\n",
+      "\t- X-averaged negative electrode extent of lithiation\n",
+      "\t- Total lithium in negative electrode [mol]\n",
+      "\t- Minimum negative particle concentration\n",
+      "\t- Maximum negative particle concentration\n",
+      "\t- Minimum negative particle concentration [mol.m-3]\n",
+      "\t- Maximum negative particle concentration [mol.m-3]\n",
+      "\t- Minimum negative particle surface concentration\n",
+      "\t- Maximum negative particle surface concentration\n",
+      "\t- Minimum negative particle surface concentration [mol.m-3]\n",
+      "\t- Maximum negative particle surface concentration [mol.m-3]\n",
+      "\t- Negative particle radius\n",
+      "\t- Negative particle radius [m]\n",
+      "\t- Negative surface area per unit volume\n",
+      "\t- Negative surface area per unit volume [m-1]\n",
       "\t- Positive particle concentration\n",
       "\t- Positive particle concentration [mol.m-3]\n",
       "\t- X-averaged positive particle concentration\n",
       "\t- X-averaged positive particle concentration [mol.m-3]\n",
+      "\t- R-averaged positive particle concentration\n",
+      "\t- R-averaged positive particle concentration [mol.m-3]\n",
+      "\t- Average positive particle concentration\n",
+      "\t- Average positive particle concentration [mol.m-3]\n",
       "\t- Positive particle surface concentration\n",
       "\t- Positive particle surface concentration [mol.m-3]\n",
       "\t- X-averaged positive particle surface concentration\n",
@@ -518,7 +548,21 @@
       "\t- Positive electrode active volume fraction\n",
       "\t- Positive electrode volume-averaged concentration\n",
       "\t- Positive electrode volume-averaged concentration [mol.m-3]\n",
-      "\t- Positive electrode average extent of lithiation\n",
+      "\t- Positive electrode extent of lithiation\n",
+      "\t- X-averaged positive electrode extent of lithiation\n",
+      "\t- Total lithium in positive electrode [mol]\n",
+      "\t- Minimum positive particle concentration\n",
+      "\t- Maximum positive particle concentration\n",
+      "\t- Minimum positive particle concentration [mol.m-3]\n",
+      "\t- Maximum positive particle concentration [mol.m-3]\n",
+      "\t- Minimum positive particle surface concentration\n",
+      "\t- Maximum positive particle surface concentration\n",
+      "\t- Minimum positive particle surface concentration [mol.m-3]\n",
+      "\t- Maximum positive particle surface concentration [mol.m-3]\n",
+      "\t- Positive particle radius\n",
+      "\t- Positive particle radius [m]\n",
+      "\t- Positive surface area per unit volume\n",
+      "\t- Positive surface area per unit volume [m-1]\n",
       "\t- Electrolyte concentration\n",
       "\t- Electrolyte concentration [mol.m-3]\n",
       "\t- Electrolyte concentration [Molar]\n",
@@ -578,6 +622,7 @@
       "\t- Total negative electrode sei thickness [m]\n",
       "\t- X-averaged total negative electrode sei thickness\n",
       "\t- X-averaged total negative electrode sei thickness [m]\n",
+      "\t- X-averaged negative electrode resistance [Ohm.m2]\n",
       "\t- Inner negative electrode sei concentration [mol.m-3]\n",
       "\t- X-averaged inner negative electrode sei concentration [mol.m-3]\n",
       "\t- Outer negative electrode sei concentration [mol.m-3]\n",
@@ -585,6 +630,11 @@
       "\t- Negative sei concentration [mol.m-3]\n",
       "\t- X-averaged negative electrode sei concentration [mol.m-3]\n",
       "\t- Loss of lithium to negative electrode sei [mol]\n",
+      "\t- Total negative electrode sei thickness\n",
+      "\t- Total negative electrode sei thickness [m]\n",
+      "\t- X-averaged total negative electrode sei thickness\n",
+      "\t- X-averaged total negative electrode sei thickness [m]\n",
+      "\t- X-averaged negative electrode resistance [Ohm.m2]\n",
       "\t- Inner negative electrode sei interfacial current density\n",
       "\t- Inner negative electrode sei interfacial current density [A.m-2]\n",
       "\t- X-averaged inner negative electrode sei interfacial current density\n",
@@ -599,7 +649,13 @@
       "\t- X-averaged negative electrode sei interfacial current density [A.m-2]\n",
       "\t- Inner positive electrode sei thickness\n",
       "\t- Inner positive electrode sei thickness [m]\n",
-      "\t- X-averaged inner positive electrode sei thickness\n",
+      "\t- X-averaged inner positive electrode sei thickness\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "\t- X-averaged inner positive electrode sei thickness [m]\n",
       "\t- Outer positive electrode sei thickness\n",
       "\t- Outer positive electrode sei thickness [m]\n",
@@ -609,6 +665,7 @@
       "\t- Total positive electrode sei thickness [m]\n",
       "\t- X-averaged total positive electrode sei thickness\n",
       "\t- X-averaged total positive electrode sei thickness [m]\n",
+      "\t- X-averaged positive electrode resistance [Ohm.m2]\n",
       "\t- Inner positive electrode sei concentration [mol.m-3]\n",
       "\t- X-averaged inner positive electrode sei concentration [mol.m-3]\n",
       "\t- Outer positive electrode sei concentration [mol.m-3]\n",
@@ -616,6 +673,11 @@
       "\t- Positive sei concentration [mol.m-3]\n",
       "\t- X-averaged positive electrode sei concentration [mol.m-3]\n",
       "\t- Loss of lithium to positive electrode sei [mol]\n",
+      "\t- Total positive electrode sei thickness\n",
+      "\t- Total positive electrode sei thickness [m]\n",
+      "\t- X-averaged total positive electrode sei thickness\n",
+      "\t- X-averaged total positive electrode sei thickness [m]\n",
+      "\t- X-averaged positive electrode resistance [Ohm.m2]\n",
       "\t- Inner positive electrode sei interfacial current density\n",
       "\t- Inner positive electrode sei interfacial current density [A.m-2]\n",
       "\t- X-averaged inner positive electrode sei interfacial current density\n",
@@ -631,7 +693,13 @@
       "\t- Electrolyte tortuosity\n",
       "\t- Negative electrolyte tortuosity\n",
       "\t- Positive electrolyte tortuosity\n",
-      "\t- X-averaged negative electrolyte tortuosity\n",
+      "\t- X-averaged negative electrolyte tortuosity\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "\t- X-averaged positive electrolyte tortuosity\n",
       "\t- Separator tortuosity\n",
       "\t- X-averaged separator tortuosity\n",
@@ -657,12 +725,25 @@
       "\t- X-averaged negative particle flux\n",
       "\t- Positive particle flux\n",
       "\t- X-averaged positive particle flux\n",
+      "\t- Total concentration in electrolyte [mol]\n",
       "\t- Ohmic heating\n",
       "\t- Ohmic heating [W.m-3]\n",
+      "\t- X-averaged Ohmic heating\n",
+      "\t- X-averaged Ohmic heating [W.m-3]\n",
+      "\t- Volume-averaged Ohmic heating\n",
+      "\t- Volume-averaged Ohmic heating [W.m-3]\n",
       "\t- Irreversible electrochemical heating\n",
       "\t- Irreversible electrochemical heating [W.m-3]\n",
+      "\t- X-averaged irreversible electrochemical heating\n",
+      "\t- X-averaged irreversible electrochemical heating [W.m-3]\n",
+      "\t- Volume-averaged irreversible electrochemical heating\n",
+      "\t- Volume-averaged irreversible electrochemical heating[W.m-3]\n",
       "\t- Reversible heating\n",
       "\t- Reversible heating [W.m-3]\n",
+      "\t- X-averaged reversible heating\n",
+      "\t- X-averaged reversible heating [W.m-3]\n",
+      "\t- Volume-averaged reversible heating\n",
+      "\t- Volume-averaged reversible heating [W.m-3]\n",
       "\t- Total heating\n",
       "\t- Total heating [W.m-3]\n",
       "\t- X-averaged total heating\n",
@@ -873,6 +954,10 @@
       "\t- X-averaged battery electrolyte ohmic losses [V]\n",
       "\t- X-averaged battery concentration overpotential [V]\n",
       "\t- Battery voltage [V]\n",
+      "\t- Change in measured open circuit voltage\n",
+      "\t- Change in measured open circuit voltage [V]\n",
+      "\t- Local ECM resistance\n",
+      "\t- Local ECM resistance [Ohm]\n",
       "\t- Terminal power [W]\n"
      ]
     }
@@ -915,7 +1000,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
        "<Figure size 936x288 with 3 Axes>"
       ]
@@ -974,7 +1059,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "5b1ede34a7c9439db8d9707083ae0c54",
+       "model_id": "78331f956c1345dbb8cb24df52745532",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1023,7 +1108,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "55ac9b31b73049408ab8a87c8863c244",
+       "model_id": "68caf5d90efa4d93b943ede761585424",
        "version_major": 2,
        "version_minor": 0
       },
@@ -1058,7 +1143,7 @@
     "| $L_{\\text{k}}$            | $L_{\\text{k}}^*/L^*$                    | Ratio of region thickness to cell thickness|\n",
     "|$\\mathcal{C}_{\\text{k}}$   | $\\tau_{\\text{k}}^*/\\tau_{\\text{d}}^*$   | Ratio of solid diffusion and discharge timescales |\n",
     "|$\\mathcal{C}_{\\text{r,k}}$ |$\\tau_{\\text{r,k}}^*/\\tau_{\\text{d}}^*$  |Ratio of reaction and discharge timescales|\n",
-    "|$a_{\\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
+    "|$a_{R, \\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
     "|$\\gamma_{\\text{k}}$        |$c_{\\text{k,max}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentrations in solid|"
    ]
   },
@@ -1093,7 +1178,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/models/SPMe.ipynb b/examples/notebooks/models/SPMe.ipynb
index b9059f081b..7b8fb0811b 100644
--- a/examples/notebooks/models/SPMe.ipynb
+++ b/examples/notebooks/models/SPMe.ipynb
@@ -33,7 +33,7 @@
     "\\mathcal{C}_{\\text{k}} \\frac{\\partial c_{\\text{s,k}}}{\\partial t} &= -\\frac{1}{r_{\\text{k}}^2} \\frac{\\partial}{\\partial r_{\\text{k}}} \\left(r_{\\text{k}}^2 N_{\\text{s,k}}\\right), \\\\\n",
     "N_{\\text{s,k}} &= -D_{\\text{s,k}}(c_{\\text{s,k}}) \\frac{\\partial c_{\\text{s,k}}}{\\partial r_{\\text{k}}}, \\quad \\text{k} \\in \\text{n, p}, \\end{align}\n",
     "$$\n",
-    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{\\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
+    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{R, \\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
     "\\begin{cases}\n",
     "\t\t  \\frac{I}{L_{\\text{n}}}, \\quad &\\text{k}=\\text{n}, \\\\ \n",
     "\t\t  -\\frac{I}{L_{\\text{p}}}, \\quad &\\text{k}=\\text{p}, \n",
@@ -155,7 +155,7 @@
     {
      "data": {
       "text/plain": [
-       "<pybamm.solvers.solution.Solution at 0x7f69f08dd2e8>"
+       "<pybamm.solvers.solution.Solution at 0x7f5cd829b4a8>"
       ]
      },
      "execution_count": 3,
@@ -183,7 +183,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "47ee8d1901bd4bdd87fba1d347da16ec",
+       "model_id": "5f19fdea006d4f22ae77a584c87d5eb3",
        "version_major": 2,
        "version_minor": 0
       },
@@ -218,7 +218,7 @@
     "|$\\mathcal{C}_{\\text{k}}$   | $\\tau_{\\text{k}}^*/\\tau_{\\text{d}}^*$   | Ratio of solid diffusion and discharge timescales |\n",
     "|$\\mathcal{C}_{\\text{e}}$   |$\\tau_{\\text{e}}^*/\\tau_{\\text{d}}^*$    |Ratio of electrolyte transport and discharge timescales|\n",
     "|$\\mathcal{C}_{\\text{r,k}}$ |$\\tau_{\\text{r,k}}^*/\\tau_{\\text{d}}^*$  |Ratio of reaction and discharge timescales|\n",
-    "|$a_{\\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
+    "|$a_{R, \\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
     "|$\\gamma_{\\text{k}}$        |$c_{\\text{k,max}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentrations in solid|\n",
     "|$\\gamma_{\\text{e}}$        |$c_{\\text{e,typ}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentration in the negative electrode solid and typical electrolyte concentration|\n",
     "\n",
@@ -256,7 +256,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/models/compare-lithium-ion.ipynb b/examples/notebooks/models/compare-lithium-ion.ipynb
index 3d3ee5dc80..5d904ace04 100644
--- a/examples/notebooks/models/compare-lithium-ion.ipynb
+++ b/examples/notebooks/models/compare-lithium-ion.ipynb
@@ -36,7 +36,15 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
    "source": [
     "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
     "import pybamm\n",
@@ -103,7 +111,7 @@
     {
      "data": {
       "text/plain": [
-       "<pybamm.models.full_battery_models.lithium_ion.dfn.DFN at 0x13ac79590>"
+       "<pybamm.models.full_battery_models.lithium_ion.dfn.DFN at 0x7f505040a198>"
       ]
      },
      "execution_count": 4,
@@ -248,9 +256,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Solved the Doyle-Fuller-Newman model in 0.420 seconds\n",
-      "Solved the Single Particle Model in 0.071 seconds\n",
-      "Solved the Single Particle Model with electrolyte in 0.190 seconds\n"
+      "Solved the Doyle-Fuller-Newman model in 0.604 seconds\n",
+      "Solved the Single Particle Model in 0.055 seconds\n",
+      "Solved the Single Particle Model with electrolyte in 0.081 seconds\n"
      ]
     }
    ],
@@ -288,7 +296,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -341,7 +349,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "94384243ffee420db59217c59b2dcf6e",
+       "model_id": "ab6a3a9354d14b7cbdff69d2cb0fc8b6",
        "version_major": 2,
        "version_minor": 0
       },
@@ -380,7 +388,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "380e2f7a84974c6fa04c382c17e7dba8",
+       "model_id": "021df018d33c43b488aa2e16597563b0",
        "version_major": 2,
        "version_minor": 0
       },
@@ -443,7 +451,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.6.9"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/models/pouch-cell-model.ipynb b/examples/notebooks/models/pouch-cell-model.ipynb
index fd3d054500..bd86489183 100644
--- a/examples/notebooks/models/pouch-cell-model.ipynb
+++ b/examples/notebooks/models/pouch-cell-model.ipynb
@@ -91,7 +91,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:361: UserWarning: 1+1D Thermal models are only valid if both tabs are placed at the top of the cell.\n",
+      "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:375: UserWarning: 1+1D Thermal models are only valid if both tabs are placed at the top of the cell.\n",
       "  \"1+1D Thermal models are only valid if both tabs are \"\n"
      ]
     }
@@ -339,7 +339,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We then add the solution object from the 1+1D model. This is just so that PyBaMM uses the same times behind the scenes when dealing with COMSOL model and the reduced-order models: the variables in `comsol_model.variables` are functions of time only that return the (interpolated in space) COMSOL solution."
+    "We then add the solution object from the 1+1D model. This is just so that PyBaMM uses the same (dimensionless) times behind the scenes when dealing with COMSOL model and the reduced-order models: the variables in `comsol_model.variables` are functions of time only that return the (interpolated in space) COMSOL solution. We also need to update the time and length scales for the COMSOL model so that any dimensionless variables are scaled correctly. "
    ]
   },
   {
diff --git a/examples/notebooks/models/thermal-models.ipynb b/examples/notebooks/models/thermal-models.ipynb
index 6d6b72c4ac..dcbf58100d 100644
--- a/examples/notebooks/models/thermal-models.ipynb
+++ b/examples/notebooks/models/thermal-models.ipynb
@@ -159,7 +159,7 @@
     "\n",
     "The 1D model solves for $T(x,t)$, capturing variations through the thickness of the cell, but ignoring variations in the other dimensions. The temperature is found as the solution of a partial differential equation, given here in dimensional terms\n",
     "\n",
-    "$$\\rho_k c_{p,k} \\frac{\\partial T}{\\partial t} = \\lambda \\nabla^2 T + Q(x,t)$$\n",
+    "$$\\rho_k c_{p,k} \\frac{\\partial T}{\\partial t} = \\lambda_k \\nabla^2 T + Q(x,t)$$\n",
     "\n",
     "with boundary conditions \n",
     "\n",
@@ -167,7 +167,7 @@
     "\n",
     "and initial condition\n",
     "\n",
-    "$$ \\frac{\\partial T}{\\partial t}\\bigg|_{t=0} = T_0.$$\n",
+    "$$ T\\big|_{t=0} = T_0.$$\n",
     "\n",
     "Here $\\lambda_k$ is the thermal conductivity of component $k$, and the heat transfer coefficients $h_{cn}$ and $h_{cp}$ correspond to heat transfer at the large surface of the pouch on the side of the negative current collector, heat transfer at the large surface of the pouch on the side of the positive current collector, respectively. The heat source term $Q$ is as described in the section on lumped models. Note: the 1D model neglects any cooling from the tabs or edges of the cell -- it assumes a pouch cell geometry and _only_ accounts for cooling from the two large surfaces of the pouch. \n",
     "\n",
@@ -196,16 +196,16 @@
     "\n",
     "along with boundary conditions\n",
     "\n",
-    "$$ -\\lambda_{eff} \\nabla_\\perp T \\cdot \\boldsymbol{n} = h_{cn}(T-T_\\infty),$$\n",
+    "$$ -\\lambda_{eff} \\nabla_\\perp T \\cdot \\boldsymbol{n} = \\frac{L_{cn}h_{cn} + (L_n+L_s+L_p+L_{cp})h_{edge}}{L_{cn}+L_n+L_s+L_p+L_{cp}}(T-T_\\infty),$$\n",
     "at the negative tab,\n",
-    "$$ -\\lambda_{eff} \\nabla_\\perp T \\cdot \\boldsymbol{n} = h_{cp}(T-T_\\infty),$$  \n",
+    "$$ -\\lambda_{eff} \\nabla_\\perp T \\cdot \\boldsymbol{n} = \\frac{(L_{cn}+L_n+L_s+L_p)h_{edge}+L_{cp}h_{cp}}{L_{cn}+L_n+L_s+L_p+L_{cp}}(T-T_\\infty),$$  \n",
     "at the positive tab, and\n",
     "$$ -\\lambda_{eff} \\nabla_\\perp T \\cdot \\boldsymbol{n} = h_{edge}(T-T_\\infty),$$  \n",
-    "elsewhere.\n",
+    "elsewhere. Again, an initial temperature $T_0$ must be prescribed.\n",
     "\n",
     "Here the heat source term is averaged in the x direction so that $\\bar{Q}=\\bar{Q}(y,z)$. The parameter $\\lambda_{eff}$ is the effective thermal conductivity, computed as \n",
     "\n",
-    "$$ \\rho_{eff} = \\frac{\\sum_k \\rho_k c_{p,k} L_k}{\\sum_k L_k}.$$\n",
+    "$$ \\lambda_{eff} = \\frac{\\sum_k \\lambda_k L_k}{\\sum_k L_k}.$$\n",
     "\n",
     "The heat transfer coefficients $h_{cn}$, $h_{cp}$ and $h_{egde}$ correspond to heat transfer at the large surface of the pouch on the side of the negative current collector, heat transfer at the large surface of the pouch on the side of the positive current collector, and  heat transfer at the remaining, respectively.\n",
     "\n",
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -383,13 +383,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "5029a982f07843c6ac1d0a884f114e80",
+       "model_id": "f452cfe20acd4e5b8950c303ce562255",
        "version_major": 2,
        "version_minor": 0
       },
@@ -403,10 +403,10 @@
     {
      "data": {
       "text/plain": [
-       "<pybamm.plotting.quick_plot.QuickPlot at 0x7f5b90231358>"
+       "<pybamm.plotting.quick_plot.QuickPlot at 0x7feb1a363a58>"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/examples/notebooks/parameter-values.ipynb b/examples/notebooks/parameter-values.ipynb
index cb78669cd6..d89916f930 100644
--- a/examples/notebooks/parameter-values.ipynb
+++ b/examples/notebooks/parameter-values.ipynb
@@ -493,7 +493,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.7.8"
   }
  },
  "nbformat": 4,
diff --git a/examples/notebooks/solution-data-and-processed-variables.ipynb b/examples/notebooks/solution-data-and-processed-variables.ipynb
index 58d236563f..a97ca8a187 100644
--- a/examples/notebooks/solution-data-and-processed-variables.ipynb
+++ b/examples/notebooks/solution-data-and-processed-variables.ipynb
@@ -16,29 +16,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
+     "name": "stdout",
      "text": [
+      "\u001b[33mWARNING: You are using pip version 20.2.1; however, version 20.2.4 is available.\n",
+      "You should consider upgrading via the '/Users/vsulzer/Documents/Energy_storage/PyBaMM/.tox/dev/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
       "Note: you may need to restart the kernel to use updated packages.\n"
      ]
     },
     {
+     "output_type": "display_data",
      "data": {
+      "text/plain": "interactive(children=(FloatSlider(value=0.0, description='t', max=3510.0, step=35.1), Output()), _dom_classes=…",
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "8a37cdae11054d50829ec2d08eadca66",
        "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=3510.0, step=35.1), Output()), _dom_classes=…"
-      ]
+       "version_minor": 0,
+       "model_id": "3a7fc02a725a413e88f064e001ecc237"
+      }
      },
-     "metadata": {},
-     "output_type": "display_data"
+     "metadata": {}
     }
    ],
    "source": [
@@ -71,18 +71,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "dict_keys(['Negative particle surface concentration [mol.m-3]', 'Electrolyte concentration [mol.m-3]', 'Positive particle surface concentration [mol.m-3]', 'Current [A]', 'Negative electrode potential [V]', 'Electrolyte potential [V]', 'Positive electrode potential [V]', 'Terminal voltage [V]'])"
       ]
      },
-     "execution_count": 2,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 16
     }
    ],
    "source": [
@@ -91,18 +91,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "(20, 40)"
       ]
      },
-     "execution_count": 3,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 17
     }
    ],
    "source": [
@@ -111,18 +111,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "(40,)"
       ]
      },
-     "execution_count": 4,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 18
     }
    ],
    "source": [
@@ -138,14 +138,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
+   "execution_count": 19,
+   "metadata": {
+    "tags": [
+     "outputPrepend"
+    ]
+   },
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
+     "name": "stdout",
      "text": [
-      "['Active material volume fraction', 'Ambient temperature', 'Ambient temperature [K]', 'Battery voltage [V]', 'C-rate', 'Cell temperature', 'Cell temperature [K]', 'Current [A]', 'Current collector current density', 'Current collector current density [A.m-2]', 'Discharge capacity [A.h]', 'Electrode current density', 'Electrode tortuosity', 'Electrolyte concentration', 'Electrolyte concentration [Molar]', 'Electrolyte concentration [mol.m-3]', 'Electrolyte current density', 'Electrolyte current density [A.m-2]', 'Electrolyte flux', 'Electrolyte flux [mol.m-2.s-1]', 'Electrolyte potential', 'Electrolyte potential [V]', 'Electrolyte tortuosity', 'Exchange current density', 'Exchange current density [A.m-2]', 'Exchange current density per volume [A.m-3]', 'Gradient of electrolyte potential', 'Gradient of negative electrode potential', 'Gradient of negative electrolyte potential', 'Gradient of positive electrode potential', 'Gradient of positive electrolyte potential', 'Gradient of separator electrolyte potential', 'Inner negative electrode sei concentration [mol.m-3]', 'Inner negative electrode sei interfacial current density', 'Inner negative electrode sei interfacial current density [A.m-2]', 'Inner negative electrode sei thickness', 'Inner negative electrode sei thickness [m]', 'Inner positive electrode sei concentration [mol.m-3]', 'Inner positive electrode sei interfacial current density', 'Inner positive electrode sei interfacial current density [A.m-2]', 'Inner positive electrode sei thickness', 'Inner positive electrode sei thickness [m]', 'Interfacial current density', 'Interfacial current density [A.m-2]', 'Interfacial current density per volume [A.m-3]', 'Irreversible electrochemical heating', 'Irreversible electrochemical heating [W.m-3]', 'Leading-order active material volume fraction', 'Leading-order current collector current density', 'Leading-order electrode tortuosity', 'Leading-order electrolyte tortuosity', 'Leading-order negative electrode active material volume fraction', 'Leading-order negative electrode porosity', 'Leading-order negative electrode tortuosity', 'Leading-order negative electrolyte tortuosity', 'Leading-order porosity', 'Leading-order positive electrode active material volume fraction', 'Leading-order positive electrode porosity', 'Leading-order positive electrode tortuosity', 'Leading-order positive electrolyte tortuosity', 'Leading-order separator active material volume fraction', 'Leading-order separator porosity', 'Leading-order separator tortuosity', 'Leading-order x-averaged negative electrode active material volume fraction', 'Leading-order x-averaged negative electrode porosity', 'Leading-order x-averaged negative electrode porosity change', 'Leading-order x-averaged negative electrode tortuosity', 'Leading-order x-averaged negative electrolyte tortuosity', 'Leading-order x-averaged positive electrode active material volume fraction', 'Leading-order x-averaged positive electrode porosity', 'Leading-order x-averaged positive electrode porosity change', 'Leading-order x-averaged positive electrode tortuosity', 'Leading-order x-averaged positive electrolyte tortuosity', 'Leading-order x-averaged separator active material volume fraction', 'Leading-order x-averaged separator porosity', 'Leading-order x-averaged separator porosity change', 'Leading-order x-averaged separator tortuosity', 'Local voltage', 'Local voltage [V]', 'Loss of lithium to negative electrode sei [mol]', 'Loss of lithium to positive electrode sei [mol]', 'Measured battery open circuit voltage [V]', 'Measured open circuit voltage', 'Measured open circuit voltage [V]', 'Negative current collector potential', 'Negative current collector potential [V]', 'Negative current collector temperature', 'Negative current collector temperature [K]', 'Negative electrode active material volume fraction', 'Negative electrode active volume fraction', 'Negative electrode average extent of lithiation', 'Negative electrode current density', 'Negative electrode current density [A.m-2]', 'Negative electrode entropic change', 'Negative electrode exchange current density', 'Negative electrode exchange current density [A.m-2]', 'Negative electrode exchange current density per volume [A.m-3]', 'Negative electrode interfacial current density', 'Negative electrode interfacial current density [A.m-2]', 'Negative electrode interfacial current density per volume [A.m-3]', 'Negative electrode ohmic losses', 'Negative electrode ohmic losses [V]', 'Negative electrode open circuit potential', 'Negative electrode open circuit potential [V]', 'Negative electrode oxygen exchange current density', 'Negative electrode oxygen exchange current density [A.m-2]', 'Negative electrode oxygen exchange current density per volume [A.m-3]', 'Negative electrode oxygen interfacial current density', 'Negative electrode oxygen interfacial current density [A.m-2]', 'Negative electrode oxygen interfacial current density per volume [A.m-3]', 'Negative electrode oxygen open circuit potential', 'Negative electrode oxygen open circuit potential [V]', 'Negative electrode oxygen reaction overpotential', 'Negative electrode oxygen reaction overpotential [V]', 'Negative electrode porosity', 'Negative electrode porosity change', 'Negative electrode potential', 'Negative electrode potential [V]', 'Negative electrode pressure', 'Negative electrode reaction overpotential', 'Negative electrode reaction overpotential [V]', 'Negative electrode sei film overpotential', 'Negative electrode sei film overpotential [V]', 'Negative electrode sei interfacial current density', 'Negative electrode sei interfacial current density [A.m-2]', 'Negative electrode surface potential difference', 'Negative electrode surface potential difference [V]', 'Negative electrode temperature', 'Negative electrode temperature [K]', 'Negative electrode tortuosity', 'Negative electrode transverse volume-averaged acceleration', 'Negative electrode transverse volume-averaged acceleration [m.s-2]', 'Negative electrode transverse volume-averaged velocity', 'Negative electrode transverse volume-averaged velocity [m.s-2]', 'Negative electrode volume-averaged acceleration', 'Negative electrode volume-averaged acceleration [m.s-1]', 'Negative electrode volume-averaged concentration', 'Negative electrode volume-averaged concentration [mol.m-3]', 'Negative electrode volume-averaged velocity', 'Negative electrode volume-averaged velocity [m.s-1]', 'Negative electrolyte concentration', 'Negative electrolyte concentration [Molar]', 'Negative electrolyte concentration [mol.m-3]', 'Negative electrolyte current density', 'Negative electrolyte current density [A.m-2]', 'Negative electrolyte potential', 'Negative electrolyte potential [V]', 'Negative electrolyte tortuosity', 'Negative particle concentration', 'Negative particle concentration [mol.m-3]', 'Negative particle flux', 'Negative particle surface concentration', 'Negative particle surface concentration [mol.m-3]', 'Negative sei concentration [mol.m-3]', 'Negative surface area per unit volume distribution in x', 'Ohmic heating', 'Ohmic heating [W.m-3]', 'Outer negative electrode sei concentration [mol.m-3]', 'Outer negative electrode sei interfacial current density', 'Outer negative electrode sei interfacial current density [A.m-2]', 'Outer negative electrode sei thickness', 'Outer negative electrode sei thickness [m]', 'Outer positive electrode sei concentration [mol.m-3]', 'Outer positive electrode sei interfacial current density', 'Outer positive electrode sei interfacial current density [A.m-2]', 'Outer positive electrode sei thickness', 'Outer positive electrode sei thickness [m]', 'Oxygen exchange current density', 'Oxygen exchange current density [A.m-2]', 'Oxygen exchange current density per volume [A.m-3]', 'Oxygen interfacial current density', 'Oxygen interfacial current density [A.m-2]', 'Oxygen interfacial current density per volume [A.m-3]', 'Porosity', 'Porosity change', 'Positive current collector potential', 'Positive current collector potential [V]', 'Positive current collector temperature', 'Positive current collector temperature [K]', 'Positive electrode active material volume fraction', 'Positive electrode active volume fraction', 'Positive electrode average extent of lithiation', 'Positive electrode current density', 'Positive electrode current density [A.m-2]', 'Positive electrode entropic change', 'Positive electrode exchange current density', 'Positive electrode exchange current density [A.m-2]', 'Positive electrode exchange current density per volume [A.m-3]', 'Positive electrode interfacial current density', 'Positive electrode interfacial current density [A.m-2]', 'Positive electrode interfacial current density per volume [A.m-3]', 'Positive electrode ohmic losses', 'Positive electrode ohmic losses [V]', 'Positive electrode open circuit potential', 'Positive electrode open circuit potential [V]', 'Positive electrode oxygen exchange current density', 'Positive electrode oxygen exchange current density [A.m-2]', 'Positive electrode oxygen exchange current density per volume [A.m-3]', 'Positive electrode oxygen interfacial current density', 'Positive electrode oxygen interfacial current density [A.m-2]', 'Positive electrode oxygen interfacial current density per volume [A.m-3]', 'Positive electrode oxygen open circuit potential', 'Positive electrode oxygen open circuit potential [V]', 'Positive electrode oxygen reaction overpotential', 'Positive electrode oxygen reaction overpotential [V]', 'Positive electrode porosity', 'Positive electrode porosity change', 'Positive electrode potential', 'Positive electrode potential [V]', 'Positive electrode pressure', 'Positive electrode reaction overpotential', 'Positive electrode reaction overpotential [V]', 'Positive electrode sei film overpotential', 'Positive electrode sei film overpotential [V]', 'Positive electrode sei interfacial current density', 'Positive electrode sei interfacial current density [A.m-2]', 'Positive electrode surface potential difference', 'Positive electrode surface potential difference [V]', 'Positive electrode temperature', 'Positive electrode temperature [K]', 'Positive electrode tortuosity', 'Positive electrode transverse volume-averaged acceleration', 'Positive electrode transverse volume-averaged acceleration [m.s-2]', 'Positive electrode transverse volume-averaged velocity', 'Positive electrode transverse volume-averaged velocity [m.s-2]', 'Positive electrode volume-averaged acceleration', 'Positive electrode volume-averaged acceleration [m.s-1]', 'Positive electrode volume-averaged concentration', 'Positive electrode volume-averaged concentration [mol.m-3]', 'Positive electrode volume-averaged velocity', 'Positive electrode volume-averaged velocity [m.s-1]', 'Positive electrolyte concentration', 'Positive electrolyte concentration [Molar]', 'Positive electrolyte concentration [mol.m-3]', 'Positive electrolyte current density', 'Positive electrolyte current density [A.m-2]', 'Positive electrolyte potential', 'Positive electrolyte potential [V]', 'Positive electrolyte tortuosity', 'Positive particle concentration', 'Positive particle concentration [mol.m-3]', 'Positive particle flux', 'Positive particle surface concentration', 'Positive particle surface concentration [mol.m-3]', 'Positive sei concentration [mol.m-3]', 'Positive surface area per unit volume distribution in x', 'Pressure', 'R-averaged negative particle concentration', 'R-averaged negative particle concentration [mol.m-3]', 'R-averaged positive particle concentration', 'R-averaged positive particle concentration [mol.m-3]', 'Reversible heating', 'Reversible heating [W.m-3]', 'Sei interfacial current density', 'Sei interfacial current density [A.m-2]', 'Sei interfacial current density per volume [A.m-3]', 'Separator active material volume fraction', 'Separator electrolyte concentration', 'Separator electrolyte concentration [Molar]', 'Separator electrolyte concentration [mol.m-3]', 'Separator electrolyte potential', 'Separator electrolyte potential [V]', 'Separator porosity', 'Separator porosity change', 'Separator pressure', 'Separator temperature', 'Separator temperature [K]', 'Separator tortuosity', 'Separator transverse volume-averaged acceleration', 'Separator transverse volume-averaged acceleration [m.s-2]', 'Separator transverse volume-averaged velocity', 'Separator transverse volume-averaged velocity [m.s-2]', 'Separator volume-averaged acceleration', 'Separator volume-averaged acceleration [m.s-1]', 'Separator volume-averaged velocity', 'Separator volume-averaged velocity [m.s-1]', 'Sum of electrolyte reaction source terms', 'Sum of interfacial current densities', 'Sum of negative electrode electrolyte reaction source terms', 'Sum of negative electrode interfacial current densities', 'Sum of positive electrode electrolyte reaction source terms', 'Sum of positive electrode interfacial current densities', 'Sum of x-averaged negative electrode electrolyte reaction source terms', 'Sum of x-averaged negative electrode interfacial current densities', 'Sum of x-averaged positive electrode electrolyte reaction source terms', 'Sum of x-averaged positive electrode interfacial current densities', 'Terminal power [W]', 'Terminal voltage', 'Terminal voltage [V]', 'Time', 'Time [h]', 'Time [min]', 'Time [s]', 'Total current density', 'Total current density [A.m-2]', 'Total heating', 'Total heating [W.m-3]', 'Total negative electrode sei thickness', 'Total negative electrode sei thickness [m]', 'Total positive electrode sei thickness', 'Total positive electrode sei thickness [m]', 'Transverse volume-averaged acceleration', 'Transverse volume-averaged acceleration [m.s-2]', 'Transverse volume-averaged velocity', 'Transverse volume-averaged velocity [m.s-2]', 'Volume-averaged Ohmic heating', 'Volume-averaged Ohmic heating [W.m-3]', 'Volume-averaged acceleration', 'Volume-averaged acceleration [m.s-1]', 'Volume-averaged cell temperature', 'Volume-averaged cell temperature [K]', 'Volume-averaged irreversible electrochemical heating', 'Volume-averaged irreversible electrochemical heating[W.m-3]', 'Volume-averaged reversible heating', 'Volume-averaged reversible heating [W.m-3]', 'Volume-averaged total heating', 'Volume-averaged total heating [W.m-3]', 'Volume-averaged velocity', 'Volume-averaged velocity [m.s-1]', 'X-averaged Ohmic heating', 'X-averaged Ohmic heating [W.m-3]', 'X-averaged battery concentration overpotential [V]', 'X-averaged battery electrolyte ohmic losses [V]', 'X-averaged battery open circuit voltage [V]', 'X-averaged battery reaction overpotential [V]', 'X-averaged battery solid phase ohmic losses [V]', 'X-averaged cell temperature', 'X-averaged cell temperature [K]', 'X-averaged concentration overpotential', 'X-averaged concentration overpotential [V]', 'X-averaged electrolyte concentration', 'X-averaged electrolyte concentration [Molar]', 'X-averaged electrolyte concentration [mol.m-3]', 'X-averaged electrolyte ohmic losses', 'X-averaged electrolyte ohmic losses [V]', 'X-averaged electrolyte overpotential', 'X-averaged electrolyte overpotential [V]', 'X-averaged electrolyte potential', 'X-averaged electrolyte potential [V]', 'X-averaged inner negative electrode sei concentration [mol.m-3]', 'X-averaged inner negative electrode sei interfacial current density', 'X-averaged inner negative electrode sei interfacial current density [A.m-2]', 'X-averaged inner negative electrode sei thickness', 'X-averaged inner negative electrode sei thickness [m]', 'X-averaged inner positive electrode sei concentration [mol.m-3]', 'X-averaged inner positive electrode sei interfacial current density', 'X-averaged inner positive electrode sei interfacial current density [A.m-2]', 'X-averaged inner positive electrode sei thickness', 'X-averaged inner positive electrode sei thickness [m]', 'X-averaged irreversible electrochemical heating', 'X-averaged irreversible electrochemical heating [W.m-3]', 'X-averaged negative electrode active material volume fraction', 'X-averaged negative electrode entropic change', 'X-averaged negative electrode exchange current density', 'X-averaged negative electrode exchange current density [A.m-2]', 'X-averaged negative electrode exchange current density per volume [A.m-3]', 'X-averaged negative electrode interfacial current density', 'X-averaged negative electrode interfacial current density [A.m-2]', 'X-averaged negative electrode interfacial current density per volume [A.m-3]', 'X-averaged negative electrode ohmic losses', 'X-averaged negative electrode ohmic losses [V]', 'X-averaged negative electrode open circuit potential', 'X-averaged negative electrode open circuit potential [V]', 'X-averaged negative electrode oxygen exchange current density', 'X-averaged negative electrode oxygen exchange current density [A.m-2]', 'X-averaged negative electrode oxygen exchange current density per volume [A.m-3]', 'X-averaged negative electrode oxygen interfacial current density', 'X-averaged negative electrode oxygen interfacial current density [A.m-2]', 'X-averaged negative electrode oxygen interfacial current density per volume [A.m-3]', 'X-averaged negative electrode oxygen open circuit potential', 'X-averaged negative electrode oxygen open circuit potential [V]', 'X-averaged negative electrode oxygen reaction overpotential', 'X-averaged negative electrode oxygen reaction overpotential [V]', 'X-averaged negative electrode porosity', 'X-averaged negative electrode porosity change', 'X-averaged negative electrode potential', 'X-averaged negative electrode potential [V]', 'X-averaged negative electrode pressure', 'X-averaged negative electrode reaction overpotential', 'X-averaged negative electrode reaction overpotential [V]', 'X-averaged negative electrode resistance [Ohm.m2]', 'X-averaged negative electrode sei concentration [mol.m-3]', 'X-averaged negative electrode sei film overpotential', 'X-averaged negative electrode sei film overpotential [V]', 'X-averaged negative electrode sei interfacial current density', 'X-averaged negative electrode sei interfacial current density [A.m-2]', 'X-averaged negative electrode surface potential difference', 'X-averaged negative electrode surface potential difference [V]', 'X-averaged negative electrode temperature', 'X-averaged negative electrode temperature [K]', 'X-averaged negative electrode tortuosity', 'X-averaged negative electrode total interfacial current density', 'X-averaged negative electrode total interfacial current density [A.m-2]', 'X-averaged negative electrode total interfacial current density per volume [A.m-3]', 'X-averaged negative electrode transverse volume-averaged acceleration', 'X-averaged negative electrode transverse volume-averaged acceleration [m.s-2]', 'X-averaged negative electrode transverse volume-averaged velocity', 'X-averaged negative electrode transverse volume-averaged velocity [m.s-2]', 'X-averaged negative electrode volume-averaged acceleration', 'X-averaged negative electrode volume-averaged acceleration [m.s-1]', 'X-averaged negative electrolyte concentration', 'X-averaged negative electrolyte concentration [mol.m-3]', 'X-averaged negative electrolyte potential', 'X-averaged negative electrolyte potential [V]', 'X-averaged negative electrolyte tortuosity', 'X-averaged negative particle concentration', 'X-averaged negative particle concentration [mol.m-3]', 'X-averaged negative particle flux', 'X-averaged negative particle surface concentration', 'X-averaged negative particle surface concentration [mol.m-3]', 'X-averaged open circuit voltage', 'X-averaged open circuit voltage [V]', 'X-averaged outer negative electrode sei concentration [mol.m-3]', 'X-averaged outer negative electrode sei interfacial current density', 'X-averaged outer negative electrode sei interfacial current density [A.m-2]', 'X-averaged outer negative electrode sei thickness', 'X-averaged outer negative electrode sei thickness [m]', 'X-averaged outer positive electrode sei concentration [mol.m-3]', 'X-averaged outer positive electrode sei interfacial current density', 'X-averaged outer positive electrode sei interfacial current density [A.m-2]', 'X-averaged outer positive electrode sei thickness', 'X-averaged outer positive electrode sei thickness [m]', 'X-averaged positive electrode active material volume fraction', 'X-averaged positive electrode entropic change', 'X-averaged positive electrode exchange current density', 'X-averaged positive electrode exchange current density [A.m-2]', 'X-averaged positive electrode exchange current density per volume [A.m-3]', 'X-averaged positive electrode interfacial current density', 'X-averaged positive electrode interfacial current density [A.m-2]', 'X-averaged positive electrode interfacial current density per volume [A.m-3]', 'X-averaged positive electrode ohmic losses', 'X-averaged positive electrode ohmic losses [V]', 'X-averaged positive electrode open circuit potential', 'X-averaged positive electrode open circuit potential [V]', 'X-averaged positive electrode oxygen exchange current density', 'X-averaged positive electrode oxygen exchange current density [A.m-2]', 'X-averaged positive electrode oxygen exchange current density per volume [A.m-3]', 'X-averaged positive electrode oxygen interfacial current density', 'X-averaged positive electrode oxygen interfacial current density [A.m-2]', 'X-averaged positive electrode oxygen interfacial current density per volume [A.m-3]', 'X-averaged positive electrode oxygen open circuit potential', 'X-averaged positive electrode oxygen open circuit potential [V]', 'X-averaged positive electrode oxygen reaction overpotential', 'X-averaged positive electrode oxygen reaction overpotential [V]', 'X-averaged positive electrode porosity', 'X-averaged positive electrode porosity change', 'X-averaged positive electrode potential', 'X-averaged positive electrode potential [V]', 'X-averaged positive electrode pressure', 'X-averaged positive electrode reaction overpotential', 'X-averaged positive electrode reaction overpotential [V]', 'X-averaged positive electrode resistance [Ohm.m2]', 'X-averaged positive electrode sei concentration [mol.m-3]', 'X-averaged positive electrode sei film overpotential', 'X-averaged positive electrode sei film overpotential [V]', 'X-averaged positive electrode sei interfacial current density', 'X-averaged positive electrode sei interfacial current density [A.m-2]', 'X-averaged positive electrode surface potential difference', 'X-averaged positive electrode surface potential difference [V]', 'X-averaged positive electrode temperature', 'X-averaged positive electrode temperature [K]', 'X-averaged positive electrode tortuosity', 'X-averaged positive electrode total interfacial current density', 'X-averaged positive electrode total interfacial current density [A.m-2]', 'X-averaged positive electrode total interfacial current density per volume [A.m-3]', 'X-averaged positive electrode transverse volume-averaged acceleration', 'X-averaged positive electrode transverse volume-averaged acceleration [m.s-2]', 'X-averaged positive electrode transverse volume-averaged velocity', 'X-averaged positive electrode transverse volume-averaged velocity [m.s-2]', 'X-averaged positive electrode volume-averaged acceleration', 'X-averaged positive electrode volume-averaged acceleration [m.s-1]', 'X-averaged positive electrolyte concentration', 'X-averaged positive electrolyte concentration [mol.m-3]', 'X-averaged positive electrolyte potential', 'X-averaged positive electrolyte potential [V]', 'X-averaged positive electrolyte tortuosity', 'X-averaged positive particle concentration', 'X-averaged positive particle concentration [mol.m-3]', 'X-averaged positive particle flux', 'X-averaged positive particle surface concentration', 'X-averaged positive particle surface concentration [mol.m-3]', 'X-averaged reaction overpotential', 'X-averaged reaction overpotential [V]', 'X-averaged reversible heating', 'X-averaged reversible heating [W.m-3]', 'X-averaged sei film overpotential', 'X-averaged sei film overpotential [V]', 'X-averaged separator active material volume fraction', 'X-averaged separator electrolyte concentration', 'X-averaged separator electrolyte concentration [mol.m-3]', 'X-averaged separator electrolyte potential', 'X-averaged separator electrolyte potential [V]', 'X-averaged separator porosity', 'X-averaged separator porosity change', 'X-averaged separator pressure', 'X-averaged separator temperature', 'X-averaged separator temperature [K]', 'X-averaged separator tortuosity', 'X-averaged separator transverse volume-averaged acceleration', 'X-averaged separator transverse volume-averaged acceleration [m.s-2]', 'X-averaged separator transverse volume-averaged velocity', 'X-averaged separator transverse volume-averaged velocity [m.s-2]', 'X-averaged separator volume-averaged acceleration', 'X-averaged separator volume-averaged acceleration [m.s-1]', 'X-averaged solid phase ohmic losses', 'X-averaged solid phase ohmic losses [V]', 'X-averaged total heating', 'X-averaged total heating [W.m-3]', 'X-averaged total negative electrode sei thickness', 'X-averaged total negative electrode sei thickness [m]', 'X-averaged total positive electrode sei thickness', 'X-averaged total positive electrode sei thickness [m]', 'X-averaged volume-averaged acceleration', 'X-averaged volume-averaged acceleration [m.s-1]', 'r_n', 'r_n [m]', 'r_p', 'r_p [m]', 'x', 'x [m]', 'x_n', 'x_n [m]', 'x_p', 'x_p [m]', 'x_s', 'x_s [m]']\n"
+      " electrode temperature', 'Negative electrode temperature [K]', 'Negative electrode tortuosity', 'Negative electrode transverse volume-averaged acceleration', 'Negative electrode transverse volume-averaged acceleration [m.s-2]', 'Negative electrode transverse volume-averaged velocity', 'Negative electrode transverse volume-averaged velocity [m.s-2]', 'Negative electrode volume-averaged acceleration', 'Negative electrode volume-averaged acceleration [m.s-1]', 'Negative electrode volume-averaged concentration', 'Negative electrode volume-averaged concentration [mol.m-3]', 'Negative electrode volume-averaged velocity', 'Negative electrode volume-averaged velocity [m.s-1]', 'Negative electrolyte concentration', 'Negative electrolyte concentration [Molar]', 'Negative electrolyte concentration [mol.m-3]', 'Negative electrolyte current density', 'Negative electrolyte current density [A.m-2]', 'Negative electrolyte potential', 'Negative electrolyte potential [V]', 'Negative electrolyte tortuosity', 'Negative particle concentration', 'Negative particle concentration [mol.m-3]', 'Negative particle flux', 'Negative particle surface concentration', 'Negative particle surface concentration [mol.m-3]', 'Negative sei concentration [mol.m-3]', 'Negative surface area per unit volume distribution in x', 'Ohmic heating', 'Ohmic heating [W.m-3]', 'Outer negative electrode sei concentration [mol.m-3]', 'Outer negative electrode sei interfacial current density', 'Outer negative electrode sei interfacial current density [A.m-2]', 'Outer negative electrode sei thickness', 'Outer negative electrode sei thickness [m]', 'Outer positive electrode sei concentration [mol.m-3]', 'Outer positive electrode sei interfacial current density', 'Outer positive electrode sei interfacial current density [A.m-2]', 'Outer positive electrode sei thickness', 'Outer positive electrode sei thickness [m]', 'Oxygen exchange current density', 'Oxygen exchange current density [A.m-2]', 'Oxygen exchange current density per volume [A.m-3]', 'Oxygen interfacial current density', 'Oxygen interfacial current density [A.m-2]', 'Oxygen interfacial current density per volume [A.m-3]', 'Porosity', 'Porosity change', 'Positive current collector potential', 'Positive current collector potential [V]', 'Positive current collector temperature', 'Positive current collector temperature [K]', 'Positive electrode active material volume fraction', 'Positive electrode active volume fraction', 'Positive electrode current density', 'Positive electrode current density [A.m-2]', 'Positive electrode entropic change', 'Positive electrode exchange current density', 'Positive electrode exchange current density [A.m-2]', 'Positive electrode exchange current density per volume [A.m-3]', 'Positive electrode extent of lithiation', 'Positive electrode interfacial current density', 'Positive electrode interfacial current density [A.m-2]', 'Positive electrode interfacial current density per volume [A.m-3]', 'Positive electrode ohmic losses', 'Positive electrode ohmic losses [V]', 'Positive electrode open circuit potential', 'Positive electrode open circuit potential [V]', 'Positive electrode oxygen exchange current density', 'Positive electrode oxygen exchange current density [A.m-2]', 'Positive electrode oxygen exchange current density per volume [A.m-3]', 'Positive electrode oxygen interfacial current density', 'Positive electrode oxygen interfacial current density [A.m-2]', 'Positive electrode oxygen interfacial current density per volume [A.m-3]', 'Positive electrode oxygen open circuit potential', 'Positive electrode oxygen open circuit potential [V]', 'Positive electrode oxygen reaction overpotential', 'Positive electrode oxygen reaction overpotential [V]', 'Positive electrode porosity', 'Positive electrode porosity change', 'Positive electrode potential', 'Positive electrode potential [V]', 'Positive electrode pressure', 'Positive electrode reaction overpotential', 'Positive electrode reaction overpotential [V]', 'Positive electrode sei film overpotential', 'Positive electrode sei film overpotential [V]', 'Positive electrode sei interfacial current density', 'Positive electrode sei interfacial current density [A.m-2]', 'Positive electrode surface potential difference', 'Positive electrode surface potential difference [V]', 'Positive electrode temperature', 'Positive electrode temperature [K]', 'Positive electrode tortuosity', 'Positive electrode transverse volume-averaged acceleration', 'Positive electrode transverse volume-averaged acceleration [m.s-2]', 'Positive electrode transverse volume-averaged velocity', 'Positive electrode transverse volume-averaged velocity [m.s-2]', 'Positive electrode volume-averaged acceleration', 'Positive electrode volume-averaged acceleration [m.s-1]', 'Positive electrode volume-averaged concentration', 'Positive electrode volume-averaged concentration [mol.m-3]', 'Positive electrode volume-averaged velocity', 'Positive electrode volume-averaged velocity [m.s-1]', 'Positive electrolyte concentration', 'Positive electrolyte concentration [Molar]', 'Positive electrolyte concentration [mol.m-3]', 'Positive electrolyte current density', 'Positive electrolyte current density [A.m-2]', 'Positive electrolyte potential', 'Positive electrolyte potential [V]', 'Positive electrolyte tortuosity', 'Positive particle concentration', 'Positive particle concentration [mol.m-3]', 'Positive particle flux', 'Positive particle surface concentration', 'Positive particle surface concentration [mol.m-3]', 'Positive sei concentration [mol.m-3]', 'Positive surface area per unit volume distribution in x', 'Pressure', 'R-averaged negative particle concentration', 'R-averaged negative particle concentration [mol.m-3]', 'R-averaged positive particle concentration', 'R-averaged positive particle concentration [mol.m-3]', 'Reversible heating', 'Reversible heating [W.m-3]', 'Sei interfacial current density', 'Sei interfacial current density [A.m-2]', 'Sei interfacial current density per volume [A.m-3]', 'Separator active material volume fraction', 'Separator electrolyte concentration', 'Separator electrolyte concentration [Molar]', 'Separator electrolyte concentration [mol.m-3]', 'Separator electrolyte potential', 'Separator electrolyte potential [V]', 'Separator porosity', 'Separator porosity change', 'Separator pressure', 'Separator temperature', 'Separator temperature [K]', 'Separator tortuosity', 'Separator transverse volume-averaged acceleration', 'Separator transverse volume-averaged acceleration [m.s-2]', 'Separator transverse volume-averaged velocity', 'Separator transverse volume-averaged velocity [m.s-2]', 'Separator volume-averaged acceleration', 'Separator volume-averaged acceleration [m.s-1]', 'Separator volume-averaged velocity', 'Separator volume-averaged velocity [m.s-1]', 'Sum of electrolyte reaction source terms', 'Sum of interfacial current densities', 'Sum of negative electrode electrolyte reaction source terms', 'Sum of negative electrode interfacial current densities', 'Sum of positive electrode electrolyte reaction source terms', 'Sum of positive electrode interfacial current densities', 'Sum of x-averaged negative electrode electrolyte reaction source terms', 'Sum of x-averaged negative electrode interfacial current densities', 'Sum of x-averaged positive electrode electrolyte reaction source terms', 'Sum of x-averaged positive electrode interfacial current densities', 'Terminal power [W]', 'Terminal voltage', 'Terminal voltage [V]', 'Time', 'Time [h]', 'Time [min]', 'Time [s]', 'Total concentration in electrolyte [mol]', 'Total current density', 'Total current density [A.m-2]', 'Total heating', 'Total heating [W.m-3]', 'Total lithium in negative electrode [mol]', 'Total lithium in positive electrode [mol]', 'Total negative electrode sei thickness', 'Total negative electrode sei thickness [m]', 'Total positive electrode sei thickness', 'Total positive electrode sei thickness [m]', 'Transverse volume-averaged acceleration', 'Transverse volume-averaged acceleration [m.s-2]', 'Transverse volume-averaged velocity', 'Transverse volume-averaged velocity [m.s-2]', 'Volume-averaged Ohmic heating', 'Volume-averaged Ohmic heating [W.m-3]', 'Volume-averaged acceleration', 'Volume-averaged acceleration [m.s-1]', 'Volume-averaged cell temperature', 'Volume-averaged cell temperature [K]', 'Volume-averaged irreversible electrochemical heating', 'Volume-averaged irreversible electrochemical heating[W.m-3]', 'Volume-averaged reversible heating', 'Volume-averaged reversible heating [W.m-3]', 'Volume-averaged total heating', 'Volume-averaged total heating [W.m-3]', 'Volume-averaged velocity', 'Volume-averaged velocity [m.s-1]', 'X-averaged Ohmic heating', 'X-averaged Ohmic heating [W.m-3]', 'X-averaged battery concentration overpotential [V]', 'X-averaged battery electrolyte ohmic losses [V]', 'X-averaged battery open circuit voltage [V]', 'X-averaged battery reaction overpotential [V]', 'X-averaged battery solid phase ohmic losses [V]', 'X-averaged cell temperature', 'X-averaged cell temperature [K]', 'X-averaged concentration overpotential', 'X-averaged concentration overpotential [V]', 'X-averaged electrolyte concentration', 'X-averaged electrolyte concentration [Molar]', 'X-averaged electrolyte concentration [mol.m-3]', 'X-averaged electrolyte ohmic losses', 'X-averaged electrolyte ohmic losses [V]', 'X-averaged electrolyte overpotential', 'X-averaged electrolyte overpotential [V]', 'X-averaged electrolyte potential', 'X-averaged electrolyte potential [V]', 'X-averaged inner negative electrode sei concentration [mol.m-3]', 'X-averaged inner negative electrode sei interfacial current density', 'X-averaged inner negative electrode sei interfacial current density [A.m-2]', 'X-averaged inner negative electrode sei thickness', 'X-averaged inner negative electrode sei thickness [m]', 'X-averaged inner positive electrode sei concentration [mol.m-3]', 'X-averaged inner positive electrode sei interfacial current density', 'X-averaged inner positive electrode sei interfacial current density [A.m-2]', 'X-averaged inner positive electrode sei thickness', 'X-averaged inner positive electrode sei thickness [m]', 'X-averaged irreversible electrochemical heating', 'X-averaged irreversible electrochemical heating [W.m-3]', 'X-averaged negative electrode active material volume fraction', 'X-averaged negative electrode entropic change', 'X-averaged negative electrode exchange current density', 'X-averaged negative electrode exchange current density [A.m-2]', 'X-averaged negative electrode exchange current density per volume [A.m-3]', 'X-averaged negative electrode extent of lithiation', 'X-averaged negative electrode interfacial current density', 'X-averaged negative electrode interfacial current density [A.m-2]', 'X-averaged negative electrode interfacial current density per volume [A.m-3]', 'X-averaged negative electrode ohmic losses', 'X-averaged negative electrode ohmic losses [V]', 'X-averaged negative electrode open circuit potential', 'X-averaged negative electrode open circuit potential [V]', 'X-averaged negative electrode oxygen exchange current density', 'X-averaged negative electrode oxygen exchange current density [A.m-2]', 'X-averaged negative electrode oxygen exchange current density per volume [A.m-3]', 'X-averaged negative electrode oxygen interfacial current density', 'X-averaged negative electrode oxygen interfacial current density [A.m-2]', 'X-averaged negative electrode oxygen interfacial current density per volume [A.m-3]', 'X-averaged negative electrode oxygen open circuit potential', 'X-averaged negative electrode oxygen open circuit potential [V]', 'X-averaged negative electrode oxygen reaction overpotential', 'X-averaged negative electrode oxygen reaction overpotential [V]', 'X-averaged negative electrode porosity', 'X-averaged negative electrode porosity change', 'X-averaged negative electrode potential', 'X-averaged negative electrode potential [V]', 'X-averaged negative electrode pressure', 'X-averaged negative electrode reaction overpotential', 'X-averaged negative electrode reaction overpotential [V]', 'X-averaged negative electrode resistance [Ohm.m2]', 'X-averaged negative electrode sei concentration [mol.m-3]', 'X-averaged negative electrode sei film overpotential', 'X-averaged negative electrode sei film overpotential [V]', 'X-averaged negative electrode sei interfacial current density', 'X-averaged negative electrode sei interfacial current density [A.m-2]', 'X-averaged negative electrode surface potential difference', 'X-averaged negative electrode surface potential difference [V]', 'X-averaged negative electrode temperature', 'X-averaged negative electrode temperature [K]', 'X-averaged negative electrode tortuosity', 'X-averaged negative electrode total interfacial current density', 'X-averaged negative electrode total interfacial current density [A.m-2]', 'X-averaged negative electrode total interfacial current density per volume [A.m-3]', 'X-averaged negative electrode transverse volume-averaged acceleration', 'X-averaged negative electrode transverse volume-averaged acceleration [m.s-2]', 'X-averaged negative electrode transverse volume-averaged velocity', 'X-averaged negative electrode transverse volume-averaged velocity [m.s-2]', 'X-averaged negative electrode volume-averaged acceleration', 'X-averaged negative electrode volume-averaged acceleration [m.s-1]', 'X-averaged negative electrolyte concentration', 'X-averaged negative electrolyte concentration [mol.m-3]', 'X-averaged negative electrolyte potential', 'X-averaged negative electrolyte potential [V]', 'X-averaged negative electrolyte tortuosity', 'X-averaged negative particle concentration', 'X-averaged negative particle concentration [mol.m-3]', 'X-averaged negative particle flux', 'X-averaged negative particle surface concentration', 'X-averaged negative particle surface concentration [mol.m-3]', 'X-averaged open circuit voltage', 'X-averaged open circuit voltage [V]', 'X-averaged outer negative electrode sei concentration [mol.m-3]', 'X-averaged outer negative electrode sei interfacial current density', 'X-averaged outer negative electrode sei interfacial current density [A.m-2]', 'X-averaged outer negative electrode sei thickness', 'X-averaged outer negative electrode sei thickness [m]', 'X-averaged outer positive electrode sei concentration [mol.m-3]', 'X-averaged outer positive electrode sei interfacial current density', 'X-averaged outer positive electrode sei interfacial current density [A.m-2]', 'X-averaged outer positive electrode sei thickness', 'X-averaged outer positive electrode sei thickness [m]', 'X-averaged positive electrode active material volume fraction', 'X-averaged positive electrode entropic change', 'X-averaged positive electrode exchange current density', 'X-averaged positive electrode exchange current density [A.m-2]', 'X-averaged positive electrode exchange current density per volume [A.m-3]', 'X-averaged positive electrode extent of lithiation', 'X-averaged positive electrode interfacial current density', 'X-averaged positive electrode interfacial current density [A.m-2]', 'X-averaged positive electrode interfacial current density per volume [A.m-3]', 'X-averaged positive electrode ohmic losses', 'X-averaged positive electrode ohmic losses [V]', 'X-averaged positive electrode open circuit potential', 'X-averaged positive electrode open circuit potential [V]', 'X-averaged positive electrode oxygen exchange current density', 'X-averaged positive electrode oxygen exchange current density [A.m-2]', 'X-averaged positive electrode oxygen exchange current density per volume [A.m-3]', 'X-averaged positive electrode oxygen interfacial current density', 'X-averaged positive electrode oxygen interfacial current density [A.m-2]', 'X-averaged positive electrode oxygen interfacial current density per volume [A.m-3]', 'X-averaged positive electrode oxygen open circuit potential', 'X-averaged positive electrode oxygen open circuit potential [V]', 'X-averaged positive electrode oxygen reaction overpotential', 'X-averaged positive electrode oxygen reaction overpotential [V]', 'X-averaged positive electrode porosity', 'X-averaged positive electrode porosity change', 'X-averaged positive electrode potential', 'X-averaged positive electrode potential [V]', 'X-averaged positive electrode pressure', 'X-averaged positive electrode reaction overpotential', 'X-averaged positive electrode reaction overpotential [V]', 'X-averaged positive electrode resistance [Ohm.m2]', 'X-averaged positive electrode sei concentration [mol.m-3]', 'X-averaged positive electrode sei film overpotential', 'X-averaged positive electrode sei film overpotential [V]', 'X-averaged positive electrode sei interfacial current density', 'X-averaged positive electrode sei interfacial current density [A.m-2]', 'X-averaged positive electrode surface potential difference', 'X-averaged positive electrode surface potential difference [V]', 'X-averaged positive electrode temperature', 'X-averaged positive electrode temperature [K]', 'X-averaged positive electrode tortuosity', 'X-averaged positive electrode total interfacial current density', 'X-averaged positive electrode total interfacial current density [A.m-2]', 'X-averaged positive electrode total interfacial current density per volume [A.m-3]', 'X-averaged positive electrode transverse volume-averaged acceleration', 'X-averaged positive electrode transverse volume-averaged acceleration [m.s-2]', 'X-averaged positive electrode transverse volume-averaged velocity', 'X-averaged positive electrode transverse volume-averaged velocity [m.s-2]', 'X-averaged positive electrode volume-averaged acceleration', 'X-averaged positive electrode volume-averaged acceleration [m.s-1]', 'X-averaged positive electrolyte concentration', 'X-averaged positive electrolyte concentration [mol.m-3]', 'X-averaged positive electrolyte potential', 'X-averaged positive electrolyte potential [V]', 'X-averaged positive electrolyte tortuosity', 'X-averaged positive particle concentration', 'X-averaged positive particle concentration [mol.m-3]', 'X-averaged positive particle flux', 'X-averaged positive particle surface concentration', 'X-averaged positive particle surface concentration [mol.m-3]', 'X-averaged reaction overpotential', 'X-averaged reaction overpotential [V]', 'X-averaged reversible heating', 'X-averaged reversible heating [W.m-3]', 'X-averaged sei film overpotential', 'X-averaged sei film overpotential [V]', 'X-averaged separator active material volume fraction', 'X-averaged separator electrolyte concentration', 'X-averaged separator electrolyte concentration [mol.m-3]', 'X-averaged separator electrolyte potential', 'X-averaged separator electrolyte potential [V]', 'X-averaged separator porosity', 'X-averaged separator porosity change', 'X-averaged separator pressure', 'X-averaged separator temperature', 'X-averaged separator temperature [K]', 'X-averaged separator tortuosity', 'X-averaged separator transverse volume-averaged acceleration', 'X-averaged separator transverse volume-averaged acceleration [m.s-2]', 'X-averaged separator transverse volume-averaged velocity', 'X-averaged separator transverse volume-averaged velocity [m.s-2]', 'X-averaged separator volume-averaged acceleration', 'X-averaged separator volume-averaged acceleration [m.s-1]', 'X-averaged solid phase ohmic losses', 'X-averaged solid phase ohmic losses [V]', 'X-averaged total heating', 'X-averaged total heating [W.m-3]', 'X-averaged total negative electrode sei thickness', 'X-averaged total negative electrode sei thickness [m]', 'X-averaged total positive electrode sei thickness', 'X-averaged total positive electrode sei thickness [m]', 'X-averaged volume-averaged acceleration', 'X-averaged volume-averaged acceleration [m.s-1]', 'r_n', 'r_n [m]', 'r_p', 'r_p [m]', 'x', 'x [m]', 'x_n', 'x_n [m]', 'x_p', 'x_p [m]', 'x_s', 'x_s [m]']\n"
      ]
     }
    ],
@@ -164,17 +168,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
+     "name": "stdout",
      "text": [
-      "Time\n",
-      "Time [h]\n",
-      "Time [min]\n",
-      "Time [s]\n"
+      "Time\nTime [h]\nTime [min]\nTime [s]\n"
      ]
     }
    ],
@@ -191,18 +192,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<pybamm.solvers.processed_variable.ProcessedVariable at 0x7fc8687367b8>"
+       "<pybamm.solvers.processed_variable.ProcessedVariable at 0x14538fbe0>"
       ]
      },
-     "execution_count": 7,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 21
     }
    ],
    "source": [
@@ -218,18 +219,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "dict_keys(['Negative particle surface concentration [mol.m-3]', 'Electrolyte concentration [mol.m-3]', 'Positive particle surface concentration [mol.m-3]', 'Current [A]', 'Negative electrode potential [V]', 'Electrolyte potential [V]', 'Positive electrode potential [V]', 'Terminal voltage [V]', 'Time [h]'])"
       ]
      },
-     "execution_count": 8,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 22
     }
    ],
    "source": [
@@ -245,10 +246,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([0.   , 0.025, 0.05 , 0.075, 0.1  , 0.125, 0.15 , 0.175, 0.2  ,\n",
@@ -258,9 +260,8 @@
        "       0.9  , 0.925, 0.95 , 0.975])"
       ]
      },
-     "execution_count": 9,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 23
     }
    ],
    "source": [
@@ -276,7 +277,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -285,18 +286,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([0.        , 0.16666667, 0.25      , 0.47222222, 0.83333333])"
       ]
      },
-     "execution_count": 11,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 25
     }
    ],
    "source": [
@@ -312,18 +313,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
        "array([298.15, 298.15, 298.15, 298.15, 298.15])"
       ]
      },
-     "execution_count": 12,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 26
     }
    ],
    "source": [
@@ -349,7 +350,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -358,10 +359,14 @@
     "    \"outputs.pickle\", [\"Time [h]\", \"Current [A]\", \"Terminal voltage [V]\", \"Electrolyte concentration [mol.m-3]\"]\n",
     ")\n",
     "# to a matlab file\n",
+    "# need to give variable names without space\n",
     "solution.save_data(\n",
     "    \"outputs.mat\", \n",
     "    [\"Time [h]\", \"Current [A]\", \"Terminal voltage [V]\", \"Electrolyte concentration [mol.m-3]\"], \n",
-    "    to_format=\"matlab\"\n",
+    "    to_format=\"matlab\",\n",
+    "    short_names={\n",
+    "        \"Time [h]\": \"t\", \"Current [A]\": \"I\", \"Terminal voltage [V]\": \"V\", \"Electrolyte concentration [mol.m-3]\": \"c_e\",\n",
+    "    }\n",
     ")\n",
     "# to a csv file (time-dependent outputs only, no spatial dependence allowed)\n",
     "solution.save_data(\n",
@@ -380,12 +385,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
      "output_type": "stream",
+     "name": "stdout",
      "text": [
       "Time 0\n",
       "[3.77047806 3.71250683]\n",
@@ -436,30 +441,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
+     "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x7fc81b225da0>"
+       "<matplotlib.legend.Legend at 0x1415edc40>"
       ]
      },
-     "execution_count": 15,
      "metadata": {},
-     "output_type": "execute_result"
+     "execution_count": 29
     },
     {
+     "output_type": "display_data",
      "data": {
-      "image/png": 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\n"
      },
      "metadata": {
       "needs_background": "light"
-     },
-     "output_type": "display_data"
+     }
     }
    ],
    "source": [
@@ -497,9 +501,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.9"
+   "version": "3.8.5-final"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}
\ No newline at end of file
diff --git a/examples/notebooks/speed-up-solver.ipynb b/examples/notebooks/speed-up-solver.ipynb
new file mode 100644
index 0000000000..0c25b94dfc
--- /dev/null
+++ b/examples/notebooks/speed-up-solver.ipynb
@@ -0,0 +1,1078 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Speeding up the solvers"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook contains a collection of tips on how to speed up the solvers"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\u001b[33mWARNING: You are using pip version 20.2.1; however, version 20.2.4 is available.\n",
+      "You should consider upgrading via the '/Users/vsulzer/Documents/Energy_storage/PyBaMM/.tox/dev/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
+    "import pybamm\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Choosing a solver"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Since it is very easy to switch which solver is used for the model, we recommend you try different solvers for your particular use case. In general, the `CasadiSolver` is the fastest.\n",
+    "\n",
+    "Once you have found a good solver, you can further improve performance by trying out different values for the `method`, `rtol`, and `atol` arguments. Further options are sometimes available, but are solver specific. See [solver API docs](https://pybamm.readthedocs.io/en/latest/source/solvers/index.html) for details."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Choosing and optimizing CasadiSolver settings"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Fast mode vs safe mode"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The `CasadiSolver` comes with a `mode` argument which can be set to \"fast\" or \"safe\" (the third option, \"safe without grid\", is experimental and should not be used for now).\n",
+    "The \"fast\" mode is faster but ignores any \"events\" (such as a voltage cut-off point), while the \"safe\" mode is slower but does stop at events (with manually implemented \"step-and-check\" under the hood). Therefore, \"fast\" mode should be used whenever events are not expected to be hit (for example, when simulating a drive cycle or a constant-current discharge where the time interval is such that the simulation will finish before reaching the voltage cut-off). Conversely, \"safe\" mode should be used whenever events are important: in particular, when using the `Experiment` class."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To demonstrate the difference between safe mode and fast mode, consider the following example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Set up model\n",
+    "model = pybamm.lithium_ion.DFN()\n",
+    "param = model.default_parameter_values\n",
+    "cap = param[\"Cell capacity [A.h]\"]\n",
+    "param[\"Current function [A]\"] = cap * pybamm.InputParameter(\"Crate\")\n",
+    "sim = pybamm.Simulation(model, parameter_values=param)\n",
+    "\n",
+    "# Set up solvers. Reduce max_num_steps for the fast solver, for faster errors\n",
+    "fast_solver = pybamm.CasadiSolver(mode=\"fast\", extra_options_setup={\"max_num_steps\": 1000})\n",
+    "safe_solver = pybamm.CasadiSolver(mode=\"safe\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Both solvers can solve the model up to 3700 s, but the fast solver ignores the voltage cut-off around 3.1 V"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Safe: 478.735 ms\n",
+      "Fast: 126.935 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "safe_sol = sim.solve([0,3700], solver=safe_solver, inputs={\"Crate\": 1})\n",
+    "fast_sol = sim.solve([0,3700], solver=fast_solver, inputs={\"Crate\": 1})\n",
+    "\n",
+    "timer = pybamm.Timer()\n",
+    "print(\"Safe:\", timer.format(safe_sol.solve_time))\n",
+    "print(\"Fast:\", timer.format(fast_sol.solve_time))\n",
+    "\n",
+    "cutoff = param[\"Lower voltage cut-off [V]\"]\n",
+    "plt.plot(fast_sol[\"Time [h]\"].data, fast_sol[\"Terminal voltage [V]\"].data, \"b-\", label=\"Fast\")\n",
+    "plt.plot(safe_sol[\"Time [h]\"].data, safe_sol[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
+    "plt.plot(fast_sol[\"Time [h]\"].data, cutoff * np.ones_like(fast_sol[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
+    "plt.legend();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If we increase the integration interval, the safe solver still stops at the same point, but the fast solver fails"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Safe: 514.168 ms\n",
+      "Solving fast mode, error occured: .../casadi/interfaces/sundials/idas_interface.cpp:591: IDASolve returned \"IDA_TOO_MUCH_WORK\". Consult IDAS documentation.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "At t = 0.179234, , mxstep steps taken before reaching tout.\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "safe_sol = sim.solve([0,4500], solver=safe_solver, inputs={\"Crate\": 1})\n",
+    "\n",
+    "print(\"Safe:\", timer.format(safe_sol.solve_time))\n",
+    "\n",
+    "plt.plot(safe_sol[\"Time [h]\"].data, safe_sol[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
+    "plt.plot(safe_sol[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
+    "plt.legend();\n",
+    "\n",
+    "try:\n",
+    "    sim.solve([0,4500], solver=fast_solver, inputs={\"Crate\": 1})\n",
+    "except pybamm.SolverError as e:\n",
+    "    print(\"Solving fast mode, error occured:\", e.args[0])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It should be noted here that the time in the warning \"At t = 0.179234, , mxstep steps taken before reaching tout\" is dimensionless time, since this is the time that the casadi solver sees. This can be converted to dimensional time as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Errored at 4050.4391486585105 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"Errored at {0.179234 * param.evaluate(model.timescale)} seconds\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can solve with fast mode up to this time to understand why the model is failing"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "178f5a54760d4e1b877c8de57998f4c5",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=4050.0, step=40.5), Output()), _dom_classes=…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fast_sol = sim.solve([0,4050], solver=fast_solver, inputs={\"Crate\": 1})\n",
+    "fast_sol.plot([\n",
+    "    \"Minimum negative particle surface concentration\",\n",
+    "    \"Electrolyte concentration [mol.m-3]\",\n",
+    "    \"Maximum positive particle surface concentration\",\n",
+    "    \"Terminal voltage [V]\",\n",
+    "], time_unit=\"seconds\", figsize=(9,9));"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this case, we can see that the reason the solver is failing is that the concentration at the surface of the particles in the positive electrode hit their maximum (dimensionless) value of 1. Since the exchange current density has a term `sqrt(1-c_s_surf)`, the square root of a negative number is complex, `c_s_surf` going above 1 will cause the solver to fail."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As a final note, there are some cases where the \"safe\" mode prints some warnings. This is linked to how the solver looks for events (sometimes stepping too far), and can be safely ignored if the solution looks sensible."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "At t = 0.00674362 and h = 6.42387e-13, the corrector convergence failed repeatedly or with |h| = hmin.\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "At t = 0.00674306 and h = 4.37843e-13, the corrector convergence failed repeatedly or with |h| = hmin.\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "psetup failed: .../casadi/interfaces/sundials/idas_interface.cpp:849: Calculating Jacobian failed\n",
+      "At t = 0.00674306 and h = 4.37843e-13, the corrector convergence failed repeatedly or with |h| = hmin.\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "safe_sol_160 = sim.solve([0,160], solver=safe_solver, inputs={\"Crate\": 10})\n",
+    "plt.plot(safe_sol_160[\"Time [h]\"].data, safe_sol_160[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe\")\n",
+    "plt.plot(safe_sol_160[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol_160[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
+    "plt.legend();"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Reducing the time interval to [0, 150], we see that the solution is exactly the same, without the warnings"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "safe_sol_150 = sim.solve([0,150], solver=safe_solver, inputs={\"Crate\": 10})\n",
+    "plt.plot(safe_sol_150[\"Time [h]\"].data, safe_sol_150[\"Terminal voltage [V]\"].data, \"r-\", label=\"Safe [0,150]\")\n",
+    "plt.plot(safe_sol_160[\"Time [h]\"].data, safe_sol_160[\"Terminal voltage [V]\"].data, \"b.\", label=\"Safe [0,160]\")\n",
+    "plt.plot(safe_sol_150[\"Time [h]\"].data, cutoff * np.ones_like(safe_sol_150[\"Time [h]\"].data), \"k--\", label=\"Voltage cut-off\")\n",
+    "plt.legend();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "safe_solver_2 = pybamm.CasadiSolver(mode=\"safe\", dt_max=30)\n",
+    "safe_sol_2 = sim.solve([0,160], solver=safe_solver_2, inputs={\"Crate\": 10})"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Choosing dt_max to speed up the safe mode"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The parameter `dt_max` controls how large the steps taken by the `CasadiSolver` with \"safe\" mode are when looking for events."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "With dt_max=10, took 2.014 s (integration time: 1.070 s)\n",
+      "With dt_max=20, took 1.968 s (integration time: 1.046 s)\n",
+      "With dt_max=100, took 1.068 s (integration time: 575.149 ms)\n",
+      "With dt_max=1000, took 210.147 ms (integration time: 130.744 ms)\n",
+      "With dt_max=3700, took 138.511 ms (integration time: 82.309 ms)\n",
+      "With 'fast' mode, took 106.222 ms (integration time: 84.668 ms)\n"
+     ]
+    }
+   ],
+   "source": [
+    "for dt_max in [10,20,100,1000,3700]:\n",
+    "    safe_sol = sim.solve(\n",
+    "        [0,3600], \n",
+    "        solver=pybamm.CasadiSolver(mode=\"safe\", dt_max=dt_max),\n",
+    "        inputs={\"Crate\": 1}\n",
+    "    )\n",
+    "    print(f\"With dt_max={dt_max}, took {timer.format(safe_sol.solve_time)} \"+\n",
+    "          f\"(integration time: {timer.format(safe_sol.integration_time)})\")\n",
+    "\n",
+    "fast_sol = sim.solve([0,3600], solver=fast_solver, inputs={\"Crate\": 1})\n",
+    "print(f\"With 'fast' mode, took {timer.format(fast_sol.solve_time)} \"+\n",
+    "      f\"(integration time: {timer.format(fast_sol.integration_time)})\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In general, a larger value of `dt_max` gives a faster solution, since fewer integrator creations and calls are required.\n",
+    "\n",
+    "Below the solution time interval of 36s, the value of `dt_max` does not affect the solve time, since steps must be at least 36s large.\n",
+    "The discrepancy between the solve time and integration time is due to the extra operations recorded by \"solve time\", such as creating the integrator. The \"fast\" solver does not need to do this (it reuses the first one it had already created), so the solve time is much closer to the integration time."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The example above was a case where no events are triggered, so the largest `dt_max` works well. If we step over events, then it is possible to makes `dt_max` too large, so that the solver will attempt (and fail) to take large steps past the event, iteratively reducing the step size until it works. For example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "With dt_max=10, took 1.706 s (integration time: 924.682 ms)\n",
+      "With dt_max=20, took 1.636 s (integration time: 878.195 ms)\n",
+      "With dt_max=100, took 908.828 ms (integration time: 486.413 ms)\n",
+      "With dt_max=1000, took 227.665 ms (integration time: 116.490 ms)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "At t = 0.179234, , mxstep steps taken before reaching tout.\n",
+      "At t = 0.179234, , mxstep steps taken before reaching tout.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "With dt_max=3600, took 4.185 s (integration time: 104.263 ms)\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "At t = 0.179234, , mxstep steps taken before reaching tout.\n"
+     ]
+    }
+   ],
+   "source": [
+    "for dt_max in [10,20,100,1000,3600]:\n",
+    "    # Reduce max_num_steps to fail faster\n",
+    "    safe_sol = sim.solve(\n",
+    "        [0,4500], \n",
+    "        solver=pybamm.CasadiSolver(mode=\"safe\", dt_max=dt_max, extra_options_setup={\"max_num_steps\": 1000}),\n",
+    "        inputs={\"Crate\": 1}\n",
+    "    )\n",
+    "    print(f\"With dt_max={dt_max}, took {timer.format(safe_sol.solve_time)} \"+\n",
+    "          f\"(integration time: {timer.format(safe_sol.integration_time)})\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The integration time with `dt_max=3600` remains the fastest, but the solve time is the slowest due to all the failed steps."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Choosing the period for faster experiments"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The \"period\" argument of the experiments also affects how long the simulations take, for a similar reason to `dt_max`. Therefore, this argument can be manually tuned to speed up how long an experiment takes to solve."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We start with one cycle of CCCV"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Took  5.662 s\n"
+     ]
+    }
+   ],
+   "source": [
+    "experiment = pybamm.Experiment(\n",
+    "    [\n",
+    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "        \"Charge at 1 A until 4.1 V\",\n",
+    "        \"Hold at 4.1 V until 50 mA\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "    ]\n",
+    ")\n",
+    "solver = pybamm.CasadiSolver(mode=\"safe\", extra_options_setup={\"max_num_steps\": 1000})\n",
+    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
+    "sol = sim.solve()\n",
+    "print(\"Took \", timer.format(sol.solve_time))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This gives a nice, smooth voltage curve"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can speed up the experiment by increasing the period, but tradeoff is that the resolution of the solution becomes worse"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Took  1.851 s\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "experiment = pybamm.Experiment(\n",
+    "    [\n",
+    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "        \"Charge at 1 A until 4.1 V\",\n",
+    "        \"Hold at 4.1 V until 50 mA\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "    ],\n",
+    "    period=\"10 minutes\",\n",
+    ")\n",
+    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
+    "sol = sim.solve()\n",
+    "print(\"Took \", timer.format(sol.solve_time))\n",
+    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If we increase the period too much, the experiment becomes slower as the solver takes more failing steps"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "At t = 1.88948, , mxstep steps taken before reaching tout.\n",
+      "At t = 1.88948, , mxstep steps taken before reaching tout.\n",
+      "At t = 1.88948, , mxstep steps taken before reaching tout.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Took  2.113 s\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "experiment = pybamm.Experiment(\n",
+    "    [\n",
+    "        \"Discharge at C/10 for 10 hours or until 3.3 V\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "        \"Charge at 1 A until 4.1 V\",\n",
+    "        \"Hold at 4.1 V until 50 mA\",\n",
+    "        \"Rest for 1 hour\",\n",
+    "    ],\n",
+    "    period=\"30 minutes\",\n",
+    ")\n",
+    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
+    "sol = sim.solve()\n",
+    "print(\"Took \", timer.format(sol.solve_time))\n",
+    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can control the period of individual parts of the experiment to get the fastest solution (again, at the cost of resolution)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Took  596.157 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "experiment = pybamm.Experiment(\n",
+    "    [\n",
+    "        \"Discharge at C/10 for 10 hours or until 3.3 V (5 hour period)\",\n",
+    "        \"Rest for 1 hour (30 minute period)\",\n",
+    "        \"Charge at 1 C until 4.1 V (10 minute period)\",\n",
+    "        \"Hold at 4.1 V until 50 mA (10 minute period)\",\n",
+    "        \"Rest for 1 hour (30 minute period)\",\n",
+    "    ],\n",
+    ")\n",
+    "solver = pybamm.CasadiSolver(mode=\"safe\", extra_options_setup={\"max_num_steps\": 1000})\n",
+    "sim = pybamm.Simulation(model, experiment=experiment, solver=solver)\n",
+    "sol = sim.solve()\n",
+    "print(\"Took \", timer.format(sol.solve_time))\n",
+    "plt.plot(sol[\"Time [s]\"].data, sol[\"Terminal voltage [V]\"].data);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As you can see, this kind of optimization requires a lot of manual tuning. We are working on ways to make the experiment class more efficient in general."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Changing the time interval"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally, in some cases, changing the time interval (either the step size or the final time) may affect whether or not the casadi solver can solve the system. \n",
+    "Therefore, if the casadi solver is failing, it may be worth changing the time interval (usually, reducing step size or final time) to see if that allows the solver to solve the model.\n",
+    "Unfortunately, we have not yet been able to isolate a minimum working example to demonstrate this effect."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Handling instabilities"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If the solver is taking a lot of steps, possibly failing with a `max_steps` error, and the error persists with different solvers and options, this suggests a problem with the model itself. This can be due to a few things:\n",
+    "\n",
+    "- A singularity in the model (such as division by zero). Solve up to the time where the model fails, and plot some variables to see if they are going to infinity. You can then narrow down the source of the problem.\n",
+    "- High model stiffness. The first thing to do to tackle this is to non-dimensionalize your model. If you really don't want to do this, or you do it and the problem persists, plot different variables to identify which variables or parameters may be causing problems. To reduce stiffness, all (dimensionless) parameter values should be as close to 1 as possible.\n",
+    "- Non-differentiable functions (see [below](#Smooth-approximations-to-non-differentiable-functions))\n",
+    "\n",
+    "If none of these fixes work, we are interested in finding out why - please get in touch!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Smooth approximations to non-differentiable functions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Some functions, such as `minimum`, `maximum`, `heaviside`, and `abs`, are discontinuous and/or non-differentiable (their derivative is discontinuous). Adaptive solvers can deal with this discontinuity, but will take many more steps close to the discontinuity in order to resolve it. Therefore, using smooth approximations instead can reduce the number of steps taken by the solver, and hence the integration time. See [this post](https://discourse.julialang.org/t/handling-instability-when-solving-ode-problems/9019/5) for more details.\n",
+    "\n",
+    "Here is an example using the `maximum` function. The function `maximum(x,1)` is continuous but non-differentiable at `x=1`, where its derivative jumps from 0 to 1. However, we can approximate it using the [`softplus` function](https://en.wikipedia.org/wiki/Rectifier_(neural_networks)#Softplus), which is smooth everywhere and is sometimes used in neural networks as a smooth approximation to the RELU activation function. The `softplus` function is given by\n",
+    "$$\n",
+    "s(x,y;k) = \\frac{\\log(\\exp(kx)+\\exp(ky))}{k},\n",
+    "$$\n",
+    "where `k` is a strictly positive smoothing (or sharpness) parameter. The larger the value of `k`, the better the approximation but the stiffer the term (exp blows up quickly!). Usually, a value of `k=10` is a good middle ground.\n",
+    "\n",
+    "In PyBaMM, you can either call the `softplus` function directly, or change `pybamm.settings.max_smoothing` to automatically replace all your calls to `pybamm.maximum` with `softplus`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Exact maximum: maximum(x, y)\n",
+      "Softplus (k=10): log(exp(10.0 * x) + exp(10.0 * y)) / 10.0\n",
+      "Softplus (k=20): log(exp(20.0 * x) + exp(20.0 * y)) / 20.0\n",
+      "Softplus (k=30): log(exp(30.0 * x) + exp(30.0 * y)) / 30.0\n",
+      "Exact maximum: maximum(x, y)\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = pybamm.Variable(\"x\")\n",
+    "y = pybamm.Variable(\"y\")\n",
+    "\n",
+    "# Normal maximum\n",
+    "print(\"Exact maximum:\", pybamm.maximum(x,y))\n",
+    "\n",
+    "# Softplus\n",
+    "print(\"Softplus (k=10):\", pybamm.softplus(x,y,10))\n",
+    "\n",
+    "# Changing the setting to call softplus automatically\n",
+    "pybamm.settings.max_smoothing = 20\n",
+    "print(\"Softplus (k=20):\", pybamm.maximum(x,y))\n",
+    "\n",
+    "# All smoothing parameters can be changed at once\n",
+    "pybamm.settings.set_smoothing_parameters(30)\n",
+    "print(\"Softplus (k=30):\", pybamm.maximum(x,y))\n",
+    "\n",
+    "# Change back\n",
+    "pybamm.settings.set_smoothing_parameters(\"exact\")\n",
+    "print(\"Exact maximum:\", pybamm.maximum(x,y))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Note that if both sides are constant then pybamm will use the exact value even if the setting is set to smoothing"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Exact: 1.0\n",
+      "Softplus: 1.0341598589863317\n"
+     ]
+    }
+   ],
+   "source": [
+    "a = pybamm.InputParameter(\"a\")\n",
+    "pybamm.settings.max_smoothing = 20\n",
+    "# Both inputs are constant so uses exact maximum\n",
+    "print(\"Exact:\", pybamm.maximum(0.999,1).evaluate())\n",
+    "# One input is not constant (InputParameter) so uses softplus\n",
+    "print(\"Softplus:\", pybamm.maximum(a,1).evaluate(inputs={\"a\": 0.999}))\n",
+    "pybamm.settings.set_smoothing_parameters(\"exact\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here is the plot of softplus with different values of `k`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x149e86070>"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 720x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pts = pybamm.linspace(0, 2, 100)\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(10,5))\n",
+    "ax.plot(pts.evaluate(), pybamm.maximum(pts,1).evaluate(), lw=2, label=\"exact\")\n",
+    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,5).evaluate(), \":\", lw=2, label=\"softplus (k=5)\")\n",
+    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,10).evaluate(), \":\", lw=2, label=\"softplus (k=10)\")\n",
+    "ax.plot(pts.evaluate(), pybamm.softplus(pts,1,100).evaluate(), \":\", lw=2, label=\"softplus (k=100)\")\n",
+    "ax.legend()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Solving a model with the exact maximum, and smooth approximations, demonstrates a clear speed-up even for a very simple model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Exact: 289.321 us\n",
+      "Smooth, k=5: 259.474 us\n",
+      "Smooth, k=10: 231.891 us\n",
+      "Smooth, k=100: 276.171 us\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2e4330f6019e46d39f03933e14be6d61",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=2.0, step=0.02), Output()), _dom_classes=('w…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "model_exact = pybamm.BaseModel()\n",
+    "model_exact.rhs = {x: pybamm.maximum(x, 1)}\n",
+    "model_exact.initial_conditions = {x: 0.5}\n",
+    "model_exact.variables = {\"x\": x, \"max(x,1)\": pybamm.maximum(x, 1)}\n",
+    "\n",
+    "model_smooth = pybamm.BaseModel()\n",
+    "k = pybamm.InputParameter(\"k\")\n",
+    "model_smooth.rhs = {x: pybamm.softplus(x, 1, k)}\n",
+    "model_smooth.initial_conditions = {x: 0.5}\n",
+    "model_smooth.variables = {\"x\": x, \"max(x,1)\": pybamm.softplus(x, 1, k)}\n",
+    "\n",
+    "solver = pybamm.CasadiSolver(mode=\"fast\")\n",
+    "\n",
+    "# Exact solution\n",
+    "timer = pybamm.Timer()\n",
+    "time = 0\n",
+    "for _ in range(100):\n",
+    "    exact_sol = solver.solve(model_exact, [0, 2])\n",
+    "    # Report integration time, which is the time spent actually doing the integration\n",
+    "    time += exact_sol.integration_time\n",
+    "print(\"Exact:\", timer.format(time/100))\n",
+    "sols = [exact_sol]\n",
+    "\n",
+    "ks = [5, 10, 100]\n",
+    "for k in ks:\n",
+    "    time = 0\n",
+    "    for _ in range(100):\n",
+    "        sol = solver.solve(model_smooth, [0, 2], inputs={\"k\": k})\n",
+    "        time += sol.integration_time\n",
+    "    print(f\"Smooth, k={k}:\", timer.format(time/100))\n",
+    "    sols.append(sol)\n",
+    "\n",
+    "pybamm.dynamic_plot(sols, [\"x\", \"max(x,1)\"], labels=[\"exact\"] + [f\"smooth (k={k})\" for k in ks]);"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Other smooth approximations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here are the other smooth approximations for the other non-smooth functions:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Smooth minimum (softminus):\t log(exp(-10.0 * x) + exp(-10.0 * y)) / -10.0\n",
+      "Smooth heaviside (sigmoid):\t (1.0 + tanh(10.0 * (y - x))) / 2.0\n",
+      "Smooth absolute value: \t\t x * (exp(10.0 * x) - exp(-10.0 * x)) / (exp(10.0 * x) + exp(-10.0 * x))\n"
+     ]
+    }
+   ],
+   "source": [
+    "pybamm.settings.set_smoothing_parameters(10)\n",
+    "print(\"Smooth minimum (softminus):\\t {!s}\".format(pybamm.minimum(x,y)))\n",
+    "print(\"Smooth heaviside (sigmoid):\\t {!s}\".format(x < y))\n",
+    "print(\"Smooth absolute value: \\t\\t {!s}\".format(abs(x)))\n",
+    "pybamm.settings.set_smoothing_parameters(\"exact\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.5"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": true,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": true,
+   "toc_window_display": true
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/examples/notebooks/submodel_cracking_DFN_or_SPM.ipynb b/examples/notebooks/submodel_cracking_DFN_or_SPM.ipynb
new file mode 100644
index 0000000000..e93dac711a
--- /dev/null
+++ b/examples/notebooks/submodel_cracking_DFN_or_SPM.ipynb
@@ -0,0 +1,263 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Using crack submodels in PyBaMM\n",
+    "In this notebook we show how to use the crack submodel with battery DFN or SPM models. To see all of the models and submodels available in PyBaMM, please take a look at the documentation [here](https://pybamm.readthedocs.io/en/latest/source/models/index.html)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
+   "source": [
+    "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
+    "import pybamm\n",
+    "import os\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "os.chdir(pybamm.__path__[0]+'/..')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Then we load the DFN, SPMe or SPM, by choosing one and commenting the others. \n",
+    "\n",
+    "When you load a model in PyBaMM it builds by default. Building the model sets all of the model variables and sets up any variables which are coupled between different submodels: this is the process which couples the submodels together and allows one submodel to access variables from another. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# model = pybamm.lithium_ion.SPMe(\n",
+    "# model = pybamm.lithium_ion.SPM(\n",
+    "model = pybamm.lithium_ion.DFN(\n",
+    "    options = {\n",
+    "        \"particle\": \"Fickian diffusion\",  \n",
+    "        \"particle cracking\": \"both\", # other options are \"positive\", \"negative\" or \"none\"\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Load the parameter set Ai2020 which contains mechanical parameters. Other sets may not contain mechanical parameters should add them manually. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "chemistry = pybamm.parameter_sets.Ai2020\n",
+    "param = pybamm.ParameterValues(chemistry=chemistry)\n",
+    "## It can update the speed of crack propagation using the commands below:\n",
+    "# param.update({\"Negative electrode Cracking rate\":3.9e-20*10})\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can get the default parameters for the model and update them with the parameters required by the cracking model. Eventually, we would like these to be added to their own chemistry (you might need to adjust the path to the parameters file to your system).\n",
+    "Now the model can be processed and solved in the usual way, and we still have access to model defaults such as the default geometry and default spatial methods"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "238bd5b3f4cf4e308993f897fb30f202",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "sim = pybamm.Simulation(\n",
+    "    model,\n",
+    "    parameter_values=param,\n",
+    "    solver=pybamm.CasadiSolver(dt_max=600),\n",
+    ")\n",
+    "solution = sim.solve(t_eval=[0, 3600], inputs={\"C-rate\": 1})\n",
+    "# plot\n",
+    "quick_plot = pybamm.QuickPlot(solution)\n",
+    "quick_plot.dynamic_plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Plot the results as required."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "9fa4ce32ad714c1f9254492e3ba3371c",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=3600.0, step=10.0), Output()), _dom_classes=…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# extract voltage\n",
+    "stress_t_n_surf = solution[\"Negative particle surface tangential stress\"]\n",
+    "x = solution[\"x [m]\"].entries[0:19, 0]\n",
+    "c_s_n = solution['Negative particle concentration']\n",
+    "r_n = solution[\"r_n [m]\"].entries[:, 0, 0]\n",
+    "\n",
+    "# plot\n",
+    "def plot_concentrations(t):\n",
+    "    f, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4 ,figsize=(20,4))\n",
+    "    ax1.plot(x, stress_t_n_surf(t=t,x=x))\n",
+    "    ax1.set_xlabel(r'$x_n$ [m]')\n",
+    "    ax1.set_ylabel('$\\sigma_t/E_n$')\n",
+    "    \n",
+    "    plot_c_n, = ax2.plot(r_n, c_s_n(r=r_n,t=t,x=x[0]))  # can evaluate at arbitrary x (single representative particle)\n",
+    "    ax2.set_ylabel('Negative particle concentration')\n",
+    "    ax2.set_xlabel(r'$r_n$ [m]')\n",
+    "    ax2.set_ylim(0, 1)\n",
+    "    ax2.set_title('Close to current collector')\n",
+    "    ax2.grid()\n",
+    "    \n",
+    "    plot_c_n, = ax3.plot(r_n, c_s_n(r=r_n,t=t,x=x[10]))  # can evaluate at arbitrary x (single representative particle)\n",
+    "    ax3.set_ylabel('Negative particle concentration')\n",
+    "    ax3.set_xlabel(r'$r_n$ [m]')\n",
+    "    ax3.set_ylim(0, 1)  \n",
+    "    ax3.set_title('In the middle')\n",
+    "    ax3.grid()\n",
+    "\n",
+    "    plot_c_n, = ax4.plot(r_n, c_s_n(r=r_n,t=t,x=x[-1]))  # can evaluate at arbitrary x (single representative particle)\n",
+    "    ax4.set_ylabel('Negative particle concentration')\n",
+    "    ax4.set_xlabel(r'$r_n$ [m]')\n",
+    "    ax4.set_ylim(0, 1)  \n",
+    "    ax4.set_title('Close to separator')\n",
+    "    ax4.grid()\n",
+    "    plt.show()\n",
+    "    \n",
+    "import ipywidgets as widgets\n",
+    "widgets.interact(plot_concentrations, t=widgets.FloatSlider(min=0,max=3600,step=10,value=0));"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Plot results using the default functions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "d1dfc6a3da7c4707aa4f7233aceb3f95",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "label = [\"Crack model\"]\n",
+    "output_variables = [\n",
+    "    \"Negative particle crack length\", \n",
+    "    \"Positive particle crack length\",\n",
+    "    \"X-averaged negative particle crack length\",\n",
+    "    \"X-averaged positive particle crack length\"\n",
+    "]\n",
+    "quick_plot = pybamm.QuickPlot(solution, output_variables, label,variable_limits='tight')\n",
+    "quick_plot.dynamic_plot();\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "\n",
+    "[1] M Doyle, TF Fuller and J Newman. \"Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell.\" Journal of the Electrochemical Society 140.6 (1993): 1526-1533.\n",
+    "\n",
+    "[2] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2019). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/notebooks/using-model-options_thermal-example.ipynb b/examples/notebooks/using-model-options_thermal-example.ipynb
index 1eb8eced78..3158e4d21c 100644
--- a/examples/notebooks/using-model-options_thermal-example.ipynb
+++ b/examples/notebooks/using-model-options_thermal-example.ipynb
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
diff --git a/examples/scripts/DFN.py b/examples/scripts/DFN.py
index 940e55b0c3..9c50dbc7ef 100644
--- a/examples/scripts/DFN.py
+++ b/examples/scripts/DFN.py
@@ -30,7 +30,7 @@
 
 # solve model
 t_eval = np.linspace(0, 3600, 100)
-solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-3)
+solver = pybamm.CasadiSolver(mode="fast", atol=1e-6, rtol=1e-3)
 solution = solver.solve(model, t_eval)
 
 # plot
diff --git a/examples/scripts/SPMe_step.py b/examples/scripts/SPMe_step.py
index b0fb747af9..c1b0743b7e 100644
--- a/examples/scripts/SPMe_step.py
+++ b/examples/scripts/SPMe_step.py
@@ -27,7 +27,7 @@
 
 # solve model
 t_eval = np.linspace(0, 3600, 100)
-solver = model.default_solver
+solver = pybamm.CasadiSolver()
 solution = solver.solve(model, t_eval)
 
 # step model
@@ -35,7 +35,7 @@
 time = 0
 timescale = model.timescale_eval
 end_time = solution.t[-1] * timescale
-step_solver = model.default_solver
+step_solver = pybamm.CasadiSolver()
 step_solution = None
 while time < end_time:
     step_solution = step_solver.step(step_solution, model, dt=dt, npts=10)
diff --git a/examples/scripts/calendar_ageing.py b/examples/scripts/calendar_ageing.py
index 6d8aa529e8..3d37f296d5 100644
--- a/examples/scripts/calendar_ageing.py
+++ b/examples/scripts/calendar_ageing.py
@@ -6,7 +6,7 @@
 models = [
     pb.lithium_ion.SPM({"sei": "reaction limited"}),
     pb.lithium_ion.SPM(
-        {"sei": "reaction limited", "surface form": "algebraic"}, name="Algebraic SPM",
+        {"sei": "reaction limited", "surface form": "algebraic"}, name="Algebraic SPM"
     ),
     pb.lithium_ion.DFN({"sei": "reaction limited"}),
 ]
diff --git a/examples/scripts/compare_comsol/compare_comsol_DFN.py b/examples/scripts/compare_comsol/compare_comsol_DFN.py
index 54542215fb..427f149d4e 100644
--- a/examples/scripts/compare_comsol/compare_comsol_DFN.py
+++ b/examples/scripts/compare_comsol/compare_comsol_DFN.py
@@ -140,9 +140,9 @@ def myinterp(t):
 
 # Make new solution with same t and y
 comsol_solution = pybamm.Solution(pybamm_solution.t, pybamm_solution.y)
-# Update model scales to match the pybamm model
-comsol_model.timescale = pybamm_model.timescale
-comsol_model.length_scales = pybamm_model.length_scales
+# Update solution scales to match the pybamm model
+comsol_model.timescale_eval = pybamm_model.timescale_eval
+comsol_model.length_scales_eval = pybamm_model.length_scales_eval
 comsol_solution.model = comsol_model
 
 # plot
diff --git a/examples/scripts/compare_lithium_ion_particle_distribution.py b/examples/scripts/compare_lithium_ion_particle_distribution.py
index 04ead95b71..4bd5fc7382 100644
--- a/examples/scripts/compare_lithium_ion_particle_distribution.py
+++ b/examples/scripts/compare_lithium_ion_particle_distribution.py
@@ -16,17 +16,22 @@
 params = [models[0].default_parameter_values, models[1].default_parameter_values]
 
 
-def negative_distribution(x):
-    return 1 + 2 * x / models[1].param.l_n
+def negative_radius(x):
+    "Negative particle radius as a function of through-cell position (x_n [m])"
+    R_n_0 = params[0]["Negative particle radius [m]"]
+    grading = 1 + 2 * x / models[1].param.L_n
+    return grading * R_n_0
 
 
-def positive_distribution(x):
-    return 1 + 2 * (1 - x) / models[1].param.l_p
+def positive_radius(x):
+    "Positive particle radius as a function of through-cell position (x_p [m])"
+    R_p_0 = params[0]["Positive particle radius [m]"]
+    grading = 1 + 2 * (models[1].param.L_x - x) / models[1].param.L_p
+    return grading * R_p_0
 
 
-params[1]["Negative particle distribution in x"] = negative_distribution
-params[1]["Positive particle distribution in x"] = positive_distribution
-
+params[1]["Negative particle radius [m]"] = negative_radius
+params[1]["Positive particle radius [m]"] = positive_radius
 
 # set up and solve simulations
 t_eval = np.linspace(0, 3600, 100)
@@ -45,8 +50,8 @@ def positive_distribution(x):
     "Electrolyte potential [V]",
     "Positive electrode potential [V]",
     "Terminal voltage [V]",
-    "Negative particle distribution in x",
-    "Positive particle distribution in x",
+    "Negative particle radius",
+    "Positive particle radius",
 ]
 
 # plot
diff --git a/examples/scripts/compare_particle_shape.py b/examples/scripts/compare_particle_shape.py
index 0b09e868fe..393dd85211 100644
--- a/examples/scripts/compare_particle_shape.py
+++ b/examples/scripts/compare_particle_shape.py
@@ -27,8 +27,6 @@
             {
                 "Negative electrode surface area to volume ratio [m-1]": 170000,
                 "Positive electrode surface area to volume ratio [m-1]": 200000,
-                "Negative surface area per unit volume distribution in x": 1,
-                "Positive surface area per unit volume distribution in x": 1,
             },
             check_already_exists=False,
         )
diff --git a/examples/scripts/compare_spectral_volume.py b/examples/scripts/compare_spectral_volume.py
index 5e5e984903..537289938a 100644
--- a/examples/scripts/compare_spectral_volume.py
+++ b/examples/scripts/compare_spectral_volume.py
@@ -8,8 +8,10 @@
 
 # load model
 # don't use new_copy
-models = [pybamm.lithium_ion.DFN(name="Finite Volume"),
-          pybamm.lithium_ion.DFN(name="Spectral Volume")]
+models = [
+    pybamm.lithium_ion.DFN(name="Finite Volume"),
+    pybamm.lithium_ion.DFN(name="Spectral Volume"),
+]
 
 # create geometry
 geometries = [m.default_geometry for m in models]
@@ -24,32 +26,31 @@
 var = pybamm.standard_spatial_vars
 var_pts = {var.x_n: 1, var.x_s: 1, var.x_p: 1, var.r_n: 1, var.r_p: 1}
 # the Finite Volume method also works on spectral meshes
-meshes = [pybamm.Mesh(
-    geometry,
-    {
-        "negative particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "positive particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "negative electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "separator": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "positive electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
-        ),
-        "current collector": pybamm.SubMesh0D,
-    },
-    var_pts) for geometry in geometries]
+meshes = [
+    pybamm.Mesh(
+        geometry,
+        {
+            "negative particle": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "positive particle": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "negative electrode": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "separator": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "positive electrode": pybamm.MeshGenerator(
+                pybamm.SpectralVolume1DSubMesh, {"order": order}
+            ),
+            "current collector": pybamm.SubMesh0D,
+        },
+        var_pts,
+    )
+    for geometry in geometries
+]
 
 # discretise model
 disc_fv = pybamm.Discretisation(meshes[0], models[0].default_spatial_methods)
@@ -61,8 +62,8 @@
         "negative electrode": pybamm.SpectralVolume(order=order),
         "separator": pybamm.SpectralVolume(order=order),
         "positive electrode": pybamm.SpectralVolume(order=order),
-        "current collector": pybamm.ZeroDimensionalSpatialMethod()
-    }
+        "current collector": pybamm.ZeroDimensionalSpatialMethod(),
+    },
 )
 
 disc_fv.process_model(models[0])
diff --git a/examples/scripts/conservation_lithium.py b/examples/scripts/conservation_lithium.py
new file mode 100644
index 0000000000..8840edb88b
--- /dev/null
+++ b/examples/scripts/conservation_lithium.py
@@ -0,0 +1,48 @@
+#
+# Check conservation of lithium
+#
+
+import pybamm
+import matplotlib.pyplot as plt
+
+pybamm.set_logging_level("INFO")
+
+model = pybamm.lithium_ion.DFN()
+
+experiment = pybamm.Experiment(
+    [
+        "Discharge at 1C until 3.2 V",
+        "Rest for 2 hours",
+        "Charge at C/3 until 4 V",
+        "Charge at 4 V until 5 mA",
+        "Rest for 2 hours",
+    ]
+    * 3
+)
+
+sim = pybamm.Simulation(model, experiment=experiment)
+sim.solve()
+solution = sim.solution
+
+t = solution["Time [s]"].entries
+Ne = solution["Total concentration in electrolyte [mol]"].entries
+Np = solution["Total lithium in positive electrode [mol]"].entries
+Nn = solution["Total lithium in negative electrode [mol]"].entries
+Ntot = Np + Nn + Ne
+
+fig, ax = plt.subplots(1, 2, figsize=(12, 5))
+
+ax[0].plot(t, Ntot / Ntot[0] - 1)
+ax[0].set_xlabel("Time (s)")
+ax[0].set_ylabel("Variation of total lithium as fraction of initial value")
+
+ax[1].plot(t, Np + Nn, label="total")
+ax[1].plot(t, Np, label="positive")
+ax[1].plot(t, Nn, label="negative")
+ax[1].set_xlabel("Time (s)")
+ax[1].set_ylabel("Total lithium in electrode (mol)")
+ax[1].legend()
+
+fig.tight_layout()
+
+plt.show()
diff --git a/examples/scripts/experimental_protocols/cccv.py b/examples/scripts/experimental_protocols/cccv.py
index cfaf6f81d3..f6b98dcb21 100644
--- a/examples/scripts/experimental_protocols/cccv.py
+++ b/examples/scripts/experimental_protocols/cccv.py
@@ -34,8 +34,8 @@
     ax.set_xlim([0, 13])
 ax.legend()
 
-# Save time, voltage, current, discharge capacity and temperature to csv and matlab
-# formats
+# Save time, voltage, current, discharge capacity, temperature, and electrolyte
+# concentration to csv and matlab formats
 sim.solution.save_data(
     "output.mat",
     [
@@ -44,9 +44,19 @@
         "Terminal voltage [V]",
         "Discharge capacity [A.h]",
         "X-averaged cell temperature [K]",
+        "Electrolyte concentration [mol.m-3]",
     ],
     to_format="matlab",
+    short_names={
+        "Time [h]": "t",
+        "Current [A]": "I",
+        "Terminal voltage [V]": "V",
+        "Discharge capacity [A.h]": "Q",
+        "X-averaged cell temperature [K]": "T",
+        "Electrolyte concentration [mol.m-3]": "c_e",
+    },
 )
+# We can only save 0D variables to csv
 sim.solution.save_data(
     "output.csv",
     [
diff --git a/pybamm/CITATIONS.txt b/pybamm/CITATIONS.txt
index 206f9cfc94..452d75f9d6 100644
--- a/pybamm/CITATIONS.txt
+++ b/pybamm/CITATIONS.txt
@@ -24,7 +24,6 @@
 
 }
 
-
 @article{doyle1993modeling,
   title={Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell},
   author={Doyle, M and Fuller, TF and Newman, J},
@@ -78,12 +77,15 @@ year={2019},
 publisher={The Electrochemical Society}
 }
 
-@article{Mohtat2020,
-author = {Mohtat, Peyman and Siegel, Jason B and Stefanopoulou, Anna G},
-title = {{High C-rate Differential Expansion and Voltage Model for Li-ion Batteries}},
-journal = {Submitted for publication},
-year = {2019},
-publisher={ECSarXiv}
+@article{mohtat2020differential,
+  title={Differential Expansion and Voltage Model for Li-ion Batteries at Practical Charging Rates},
+  author={Mohtat, Peyman and Lee, Suhak and Sulzer, Valentin and Siegel, Jason B and Stefanopoulou, Anna G},
+  journal={Journal of The Electrochemical Society},
+  volume={167},
+  number={11},
+  pages={110561},
+  year={2020},
+  publisher={IOP Publishing}
 }
 
 @article{scikits-odes,
@@ -194,6 +196,17 @@ archivePrefix={arXiv},
 primaryClass={physics.app-ph},
 }
 
+@article{Ai2020JES,
+  title={Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells},
+  author={Ai, Weilong and Kraft, Ludwig and Sturm, Johannes and Jossen, Andreas and Wu, Billy},
+  journal={Journal of The Electrochemical Society},
+  volume={167},
+  number={1},
+  pages={013512},
+  year={2019},
+  publisher={IOP Publishing}
+}
+
 @article{subramanian2005,
   title={Efficient macro-micro scale coupled modeling of batteries},
   author={Subramanian, Venkat R and Diwakar, Vinten D and Tapriyal, Deepak},
@@ -204,3 +217,60 @@ primaryClass={physics.app-ph},
   year={2005},
   publisher={IOP Publishing}
 }
+
+@article{brosaplanella2020TSPMe,
+title={Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods}
+journal={Submitted for publication},
+author={Brosa Planella, Ferran and Sheikh, Muhammad and Widanage, Dhammika W},
+year={2020},
+eprint={2011.01611},
+archivePrefix={arXiv},
+primaryClass={physics.chem-ph},
+}
+
+@article{lain2019design,
+  title={Design Strategies for High Power vs. High Energy Lithium Ion Cells},
+  author={Lain, Michael J and Brandon, James and Kendrick, Emma},
+  journal={Batteries},
+  volume={5},
+  number={4},
+  pages={64},
+  year={2019},
+  publisher={Multidisciplinary Digital Publishing Institute}
+}
+
+@article{prada2013simplified,
+  title={A simplified electrochemical and thermal aging model of LiFePO4-graphite Li-ion batteries: power and capacity fade simulations},
+  author={Prada, Eric and Di Domenico, D and Creff, Y and Bernard, J and Sauvant-Moynot, Val{\'e}rie and Huet, Fran{\c{c}}ois},
+  journal={Journal of The Electrochemical Society},
+  volume={160},
+  number={4},
+  pages={A616},
+  year={2013},
+  publisher={IOP Publishing}
+}
+
+@article{deshpande2012battery,
+  title={Battery cycle life prediction with coupled chemical degradation and fatigue mechanics},
+  author={Deshpande, Rutooj and Verbrugge, Mark and Cheng, Yang-Tse and Wang, John and Liu, Ping},
+  journal={Journal of the Electrochemical Society},
+  volume={159},
+  number={10},
+  pages={A1730},
+  year={2012},
+  publisher={IOP Publishing}
+}
+
+@article{Ai_2019,
+	doi = {10.1149/2.0122001jes},
+	url = {https://doi.org/10.1149%2F2.0122001jes},
+	year = 2019,
+	month = {oct},
+	publisher = {The Electrochemical Society},
+	volume = {167},
+	number = {1},
+	pages = {013512},
+	author = {Weilong Ai and Ludwig Kraft and Johannes Sturm and Andreas Jossen and Billy Wu},
+	title = {Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells},
+	journal = {Journal of The Electrochemical Society},
+}
diff --git a/pybamm/__init__.py b/pybamm/__init__.py
index 8fb1d06f41..295d0b83ff 100644
--- a/pybamm/__init__.py
+++ b/pybamm/__init__.py
@@ -111,6 +111,7 @@ def version(formatted=False):
 
 if system() != "Windows":
     from .expression_tree.operations.evaluate import EvaluatorJax
+    from .expression_tree.operations.evaluate import JaxCooMatrix
 
 from .expression_tree.operations.jacobian import Jacobian
 from .expression_tree.operations.convert_to_casadi import CasadiConverter
@@ -147,6 +148,7 @@ def version(formatted=False):
     porosity,
     thermal,
     tortuosity,
+    particle_cracking,
 )
 from .models.submodels.interface import sei
 
@@ -164,14 +166,16 @@ def version(formatted=False):
 #
 from .parameters.parameter_values import ParameterValues
 from .parameters import constants
-from .parameters.geometric_parameters import GeometricParameters
-from .parameters.electrical_parameters import ElectricalParameters
-from .parameters.thermal_parameters import ThermalParameters
+from .parameters.geometric_parameters import geometric_parameters, GeometricParameters
+from .parameters.electrical_parameters import (
+    electrical_parameters,
+    ElectricalParameters,
+)
+from .parameters.thermal_parameters import thermal_parameters, ThermalParameters
 from .parameters.lithium_ion_parameters import LithiumIonParameters
 from .parameters.lead_acid_parameters import LeadAcidParameters
 from .parameters import parameter_sets
 
-
 #
 # Mesh and Discretisation classes
 #
diff --git a/pybamm/discretisations/discretisation.py b/pybamm/discretisations/discretisation.py
index 5c792767fe..38592dccb5 100644
--- a/pybamm/discretisations/discretisation.py
+++ b/pybamm/discretisations/discretisation.py
@@ -492,6 +492,19 @@ def process_boundary_conditions(self, model):
         for key, bcs in model.boundary_conditions.items():
             processed_bcs[key.id] = {}
 
+            # check if the boundary condition at the origin for sphere domains is other
+            # than no flux
+            if key not in model.external_variables:
+                for subdomain in key.domain:
+                    if self.mesh[subdomain].coord_sys == "spherical polar":
+                        if bcs["left"][0].value != 0 or bcs["left"][1] != "Neumann":
+                            raise pybamm.ModelError(
+                                "Boundary condition at r = 0 must be a homogeneous "
+                                "Neumann condition for {} coordinates".format(
+                                    self.mesh[subdomain].coord_sys
+                                )
+                            )
+
             # Handle any boundary conditions applied on the tabs
             if any("tab" in side for side in list(bcs.keys())):
                 bcs = self.check_tab_conditions(key, bcs)
diff --git a/pybamm/expression_tree/array.py b/pybamm/expression_tree/array.py
index 95622571b4..cd068d0b0d 100644
--- a/pybamm/expression_tree/array.py
+++ b/pybamm/expression_tree/array.py
@@ -105,6 +105,10 @@ def _base_evaluate(self, t=None, y=None, y_dot=None, inputs=None):
         """ See :meth:`pybamm.Symbol._base_evaluate()`. """
         return self._entries
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return True
+
 
 def linspace(start, stop, num=50, **kwargs):
     """
diff --git a/pybamm/expression_tree/binary_operators.py b/pybamm/expression_tree/binary_operators.py
index ef49658ad5..501bce7391 100644
--- a/pybamm/expression_tree/binary_operators.py
+++ b/pybamm/expression_tree/binary_operators.py
@@ -138,7 +138,23 @@ def format(self, left, right):
 
     def __str__(self):
         """ See :meth:`pybamm.Symbol.__str__()`. """
-        return "{!s} {} {!s}".format(self.left, self.name, self.right)
+        # Possibly add brackets for clarity
+        if isinstance(self.left, pybamm.BinaryOperator) and not (
+            (self.left.name == self.name)
+            or (self.left.name == "*" and self.name == "/")
+            or (self.left.name == "+" and self.name == "-")
+            or self.name == "+"
+        ):
+            left_str = "({!s})".format(self.left)
+        else:
+            left_str = "{!s}".format(self.left)
+        if isinstance(self.right, pybamm.BinaryOperator) and not (
+            (self.name == "*" and self.right.name in ["*", "/"]) or self.name == "+"
+        ):
+            right_str = "({!s})".format(self.right)
+        else:
+            right_str = "{!s}".format(self.right)
+        return "{} {} {}".format(left_str, self.name, right_str)
 
     def get_children_domains(self, ldomain, rdomain):
         "Combine domains from children in appropriate way"
@@ -218,6 +234,10 @@ def evaluates_on_edges(self, dimension):
             dimension
         )
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return self.left.is_constant() and self.right.is_constant()
+
 
 class Power(BinaryOperator):
     """A node in the expression tree representing a `**` power operator
@@ -828,18 +848,58 @@ def _binary_evaluate(self, left, right):
 
 def minimum(left, right):
     """
-    Returns the smaller of two objects. Not to be confused with :meth:`pybamm.min`,
-    which returns min function of child.
+    Returns the smaller of two objects, possibly with a smoothing approximation.
+    Not to be confused with :meth:`pybamm.min`, which returns min function of child.
     """
-    return pybamm.simplify_if_constant(Minimum(left, right), keep_domains=True)
+    k = pybamm.settings.min_smoothing
+    # Return exact approximation if that is the setting or the outcome is a constant
+    # (i.e. no need for smoothing)
+    if k == "exact" or (pybamm.is_constant(left) and pybamm.is_constant(right)):
+        out = Minimum(left, right)
+    else:
+        out = pybamm.softminus(left, right, k)
+    return pybamm.simplify_if_constant(out, keep_domains=True)
 
 
 def maximum(left, right):
     """
-    Returns the larger of two objects. Not to be confused with :meth:`pybamm.max`,
-    which returns max function of child.
+    Returns the larger of two objects, possibly with a smoothing approximation.
+    Not to be confused with :meth:`pybamm.max`, which returns max function of child.
+    """
+    k = pybamm.settings.max_smoothing
+    # Return exact approximation if that is the setting or the outcome is a constant
+    # (i.e. no need for smoothing)
+    if k == "exact" or (pybamm.is_constant(left) and pybamm.is_constant(right)):
+        out = Maximum(left, right)
+    else:
+        out = pybamm.softplus(left, right, k)
+    return pybamm.simplify_if_constant(out, keep_domains=True)
+
+
+def softminus(left, right, k):
+    """
+    Softplus approximation to the minimum function. k is the smoothing parameter,
+    set by `pybamm.settings.min_smoothing`. The recommended value is k=10.
+    """
+    return pybamm.log(pybamm.exp(-k * left) + pybamm.exp(-k * right)) / -k
+
+
+def softplus(left, right, k):
+    """
+    Softplus approximation to the maximum function. k is the smoothing parameter,
+    set by `pybamm.settings.max_smoothing`. The recommended value is k=10.
+    """
+    return pybamm.log(pybamm.exp(k * left) + pybamm.exp(k * right)) / k
+
+
+def sigmoid(left, right, k):
+    """
+    Sigmoidal approximation to the heaviside function. k is the smoothing parameter,
+    set by `pybamm.settings.heaviside_smoothing`. The recommended value is k=10.
+    Note that the concept of deciding which side to pick when left=right does not apply
+    for this smooth approximation. When left=right, the value is (left+right)/2.
     """
-    return pybamm.simplify_if_constant(Maximum(left, right), keep_domains=True)
+    return (1 + pybamm.tanh(k * (right - left))) / 2
 
 
 def source(left, right, boundary=False):
diff --git a/pybamm/expression_tree/broadcasts.py b/pybamm/expression_tree/broadcasts.py
index 127c69a6c5..026f1d6ba6 100644
--- a/pybamm/expression_tree/broadcasts.py
+++ b/pybamm/expression_tree/broadcasts.py
@@ -107,11 +107,15 @@ def check_and_set_domains(
                 """Primary broadcast from current collector domain must be to electrode
                 or separator or particle domains"""
             )
-        elif child.domain[0] in [
-            "negative electrode",
-            "separator",
-            "positive electrode",
-        ] and broadcast_domain[0] not in ["negative particle", "positive particle"]:
+        elif (
+            child.domain[0]
+            in [
+                "negative electrode",
+                "separator",
+                "positive electrode",
+            ]
+            and broadcast_domain[0] not in ["negative particle", "positive particle"]
+        ):
             raise pybamm.DomainError(
                 """Primary broadcast from electrode or separator must be to particle
                 domains"""
@@ -203,11 +207,15 @@ def check_and_set_domains(
                 """Secondary broadcast from particle domain must be to electrode or
                 separator domains"""
             )
-        elif child.domain[0] in [
-            "negative electrode",
-            "separator",
-            "positive electrode",
-        ] and broadcast_domain != ["current collector"]:
+        elif (
+            child.domain[0]
+            in [
+                "negative electrode",
+                "separator",
+                "positive electrode",
+            ]
+            and broadcast_domain != ["current collector"]
+        ):
             raise pybamm.DomainError(
                 """Secondary broadcast from electrode or separator must be to
                 current collector domains"""
diff --git a/pybamm/expression_tree/concatenations.py b/pybamm/expression_tree/concatenations.py
index 456029314a..56b768732f 100644
--- a/pybamm/expression_tree/concatenations.py
+++ b/pybamm/expression_tree/concatenations.py
@@ -34,6 +34,14 @@ def __init__(self, *children, name=None, check_domain=True, concat_fun=None):
             name, children, domain=domain, auxiliary_domains=auxiliary_domains
         )
 
+    def __str__(self):
+        """ See :meth:`pybamm.Symbol.__str__()`. """
+        out = self.name + "("
+        for child in self.children:
+            out += "{!s}, ".format(child)
+        out = out[:-2] + ")"
+        return out
+
     def get_children_domains(self, children):
         # combine domains from children
         domain = []
@@ -103,6 +111,10 @@ def _evaluate_for_shape(self):
                 [child.evaluate_for_shape() for child in self.children]
             )
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return all(child.is_constant() for child in self.children)
+
 
 class NumpyConcatenation(Concatenation):
     """A node in the expression tree representing a concatenation of equations, when we
@@ -130,7 +142,7 @@ def __init__(self, *children):
                 children[i] = child * pybamm.Vector([1])
         super().__init__(
             *children,
-            name="numpy concatenation",
+            name="numpy_concatenation",
             check_domain=False,
             concat_fun=np.concatenate
         )
@@ -189,7 +201,7 @@ def __init__(self, children, full_mesh, copy_this=None):
         children = list(children)
 
         # Allow the base class to sort the domains into the correct order
-        super().__init__(*children, name="domain concatenation")
+        super().__init__(*children, name="domain_concatenation")
 
         # ensure domain is sorted according to mesh keys
         domain_dict = {d: full_mesh.domain_order.index(d) for d in self.domain}
@@ -349,5 +361,5 @@ class SparseStack(Concatenation):
     def __init__(self, *children):
         children = list(children)
         super().__init__(
-            *children, name="sparse stack", check_domain=False, concat_fun=vstack
+            *children, name="sparse_stack", check_domain=False, concat_fun=vstack
         )
diff --git a/pybamm/expression_tree/exceptions.py b/pybamm/expression_tree/exceptions.py
index 41995623c6..81b55c9826 100644
--- a/pybamm/expression_tree/exceptions.py
+++ b/pybamm/expression_tree/exceptions.py
@@ -17,8 +17,8 @@ class OptionError(Exception):
 
 class GeometryError(Exception):
     """
-        Geometry error: Raised if the an unimplemented geometry is used.
-     """
+    Geometry error: Raised if the an unimplemented geometry is used.
+    """
 
     pass
 
diff --git a/pybamm/expression_tree/functions.py b/pybamm/expression_tree/functions.py
index a8eadd22dd..993e715bba 100644
--- a/pybamm/expression_tree/functions.py
+++ b/pybamm/expression_tree/functions.py
@@ -4,6 +4,7 @@
 import autograd
 import numbers
 import numpy as np
+from scipy import special
 import pybamm
 
 
@@ -58,6 +59,14 @@ def __init__(
             name, children=children, domain=domain, auxiliary_domains=auxiliary_domains
         )
 
+    def __str__(self):
+        """ See :meth:`pybamm.Symbol.__str__()`. """
+        out = "{}(".format(self.name[10:-1])
+        for child in self.children:
+            out += "{!s}, ".format(child)
+        out = out[:-2] + ")"
+        return out
+
     def get_children_domains(self, children_list):
         """Obtains the unique domain of the children. If the
         children have different domains then raise an error"""
@@ -173,6 +182,10 @@ def evaluates_on_edges(self, dimension):
         """ See :meth:`pybamm.Symbol.evaluates_on_edges()`. """
         return any(child.evaluates_on_edges(dimension) for child in self.children)
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return all(child.is_constant() for child in self.children)
+
     def _evaluate_for_shape(self):
         """
         Default behaviour: has same shape as all child
@@ -450,3 +463,24 @@ def _function_diff(self, children, idx):
 def arctan(child):
     " Returns hyperbolic tan function of child. "
     return pybamm.simplify_if_constant(Arctan(child), keep_domains=True)
+
+
+class Erf(SpecificFunction):
+    """ Error function """
+
+    def __init__(self, child):
+        super().__init__(special.erf, child)
+
+    def _function_diff(self, children, idx):
+        """ See :meth:`pybamm.Function._function_diff()`. """
+        return 2 / np.sqrt(np.pi) * Exponential(-children[0] ** 2)
+
+
+def erf(child):
+    " Returns error function of child. "
+    return pybamm.simplify_if_constant(Erf(child), keep_domains=True)
+
+
+def erfc(child):
+    " Returns complementary error function of child. "
+    return pybamm.simplify_if_constant(1 - Erf(child), keep_domains=True)
diff --git a/pybamm/expression_tree/input_parameter.py b/pybamm/expression_tree/input_parameter.py
index e63242cf81..bbc78b7a8f 100644
--- a/pybamm/expression_tree/input_parameter.py
+++ b/pybamm/expression_tree/input_parameter.py
@@ -36,6 +36,10 @@ def set_expected_size(self, size):
         "Specify the size that the input parameter should be"
         self._expected_size = size
 
+        # We also need to update the saved size and shape
+        self._saved_size = size
+        self._saved_shape = (size, 1)
+
     def _evaluate_for_shape(self):
         """
         Returns the scalar 'NaN' to represent the shape of a parameter.
diff --git a/pybamm/expression_tree/operations/convert_to_casadi.py b/pybamm/expression_tree/operations/convert_to_casadi.py
index e47031e4fe..c78eaf28d5 100644
--- a/pybamm/expression_tree/operations/convert_to_casadi.py
+++ b/pybamm/expression_tree/operations/convert_to_casadi.py
@@ -5,6 +5,7 @@
 import casadi
 import numpy as np
 from scipy.interpolate import PchipInterpolator, CubicSpline
+from scipy import special
 
 
 class CasadiConverter(object):
@@ -129,6 +130,8 @@ def _convert(self, symbol, t, y, y_dot, inputs):
                 return casadi.log(*converted_children)
             elif symbol.function == np.sign:
                 return casadi.sign(*converted_children)
+            elif symbol.function == special.erf:
+                return casadi.erf(*converted_children)
             elif isinstance(symbol.function, (PchipInterpolator, CubicSpline)):
                 return casadi.interpolant("LUT", "bspline", [symbol.x], symbol.y)(
                     *converted_children
diff --git a/pybamm/expression_tree/operations/evaluate.py b/pybamm/expression_tree/operations/evaluate.py
index 7aa14e60ac..614cd59fb7 100644
--- a/pybamm/expression_tree/operations/evaluate.py
+++ b/pybamm/expression_tree/operations/evaluate.py
@@ -9,12 +9,106 @@
 
 import numbers
 from platform import system
+
 if system() != "Windows":
     import jax
 
     from jax.config import config
+
     config.update("jax_enable_x64", True)
 
+    class JaxCooMatrix:
+        """
+        A sparse matrix in COO format, with internal arrays using jax device arrays
+
+        This matrix only has two operations supported, a multiply with a scalar, and a
+        dot product with a dense vector. It can also be converted to a dense 2D jax
+        device array
+
+        Parameters
+        ----------
+
+        row: arraylike
+            1D array holding row indices of non-zero entries
+        col: arraylike
+            1D array holding col indices of non-zero entries
+        data: arraylike
+            1D array holding non-zero entries
+        shape: 2-element tuple (x, y)
+            where x is the number of rows, and y the number of columns of the matrix
+        """
+
+        def __init__(self, row, col, data, shape):
+            self.row = jax.numpy.array(row)
+            self.col = jax.numpy.array(col)
+            self.data = jax.numpy.array(data)
+            self.shape = shape
+            self.nnz = len(self.data)
+
+        def toarray(self):
+            """convert sparse matrix to a dense 2D array"""
+            result = jax.numpy.zeros(self.shape, dtype=self.data.dtype)
+            return result.at[self.row, self.col].add(self.data)
+
+        def dot_product(self, b):
+            """
+            dot product of matrix with a dense column vector b
+
+            Parameters
+            ----------
+            b: jax device array
+                must have shape (n, 1)
+            """
+            # assume b is a column vector
+            result = jax.numpy.zeros((self.shape[0], 1), dtype=b.dtype)
+            return result.at[self.row].add(self.data.reshape(-1, 1) * b[self.col])
+
+        def scalar_multiply(self, b):
+            """
+            multiply of matrix with a scalar b
+
+            Parameters
+            ----------
+            b: Number or 1 element jax device array
+                scalar value to multiply
+            """
+            # assume b is a scalar or ndarray with 1 element
+            return JaxCooMatrix(
+                self.row, self.col,
+                (self.data * b).reshape(-1),
+                self.shape
+            )
+
+        def multiply(self, b):
+            """
+            general matrix multiply not supported
+            """
+            raise NotImplementedError
+
+        def __matmul__(self, b):
+            """see self.dot_product"""
+            return self.dot_product(b)
+
+    def create_jax_coo_matrix(value):
+        """
+        Creates a JaxCooMatrix from a scipy.sparse matrix
+
+        Parameters
+        ----------
+
+        value: scipy.sparse matrix
+            the sparse matrix to be converted
+        """
+        scipy_coo = value.tocoo()
+        row = jax.numpy.asarray(scipy_coo.row)
+        col = jax.numpy.asarray(scipy_coo.col)
+        data = jax.numpy.asarray(scipy_coo.data)
+        return JaxCooMatrix(row, col, data, value.shape)
+else:
+
+    def create_jax_coo_matrix(value):  # pragma: no cover
+        raise NotImplementedError('Jax is not available on Windows')
+
 
 def id_to_python_variable(symbol_id, constant=False):
     """
@@ -31,7 +125,15 @@ def id_to_python_variable(symbol_id, constant=False):
     return var_format.format(symbol_id).replace("-", "m")
 
 
-def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
+def is_scalar(arg):
+    is_number = isinstance(arg, numbers.Number)
+    if is_number:
+        return True
+    else:
+        return np.all(np.array(arg.shape) == 1)
+
+
+def find_symbols(symbol, constant_symbols, variable_symbols, output_jax=False):
     """
     This function converts an expression tree to a dictionary of node id's and strings
     specifying valid python code to calculate that nodes value, given y and t.
@@ -42,7 +144,7 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
     `variable_symbols`
 
     Note that it is important that the arguments `constant_symbols` and
-    `variable_symbols` be and *ordered* dict, since the final ordering of the code lines
+    `variable_symbols` be an *ordered* dict, since the final ordering of the code lines
     are important for the calculations. A dict is specified rather than a list so that
     identical subtrees (which give identical id's) are not recalculated in the code
 
@@ -57,22 +159,29 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
     variable_symbol: collections.OrderedDict
         The output dictionary of variable (with y or t) symbol ids to lines of code
 
-    to_dense: bool
-        If True, all constants and expressions are converted to using dense matrices
+    output_jax: bool
+        If True, only numpy and jax operations will be used in the generated code,
+        raises NotImplNotImplementedError if any SparseStack or Mat-Mat multiply
+        operations are used
 
     """
+    # constant symbols that are not numbers are stored in a list of constants, which are
+    # passed into the generated function constant symbols that are numbers are written
+    # directly into the code
     if symbol.is_constant():
         value = symbol.evaluate()
         if not isinstance(value, numbers.Number):
-            if to_dense and scipy.sparse.issparse(value):
-                constant_symbols[symbol.id] = value.toarray()
+            if output_jax and scipy.sparse.issparse(value):
+                # convert any remaining sparse matrices to our custom coo matrix
+                constant_symbols[symbol.id] = create_jax_coo_matrix(value)
+
             else:
                 constant_symbols[symbol.id] = value
         return
 
     # process children recursively
     for child in symbol.children:
-        find_symbols(child, constant_symbols, variable_symbols, to_dense)
+        find_symbols(child, constant_symbols, variable_symbols, output_jax)
 
     # calculate the variable names that will hold the result of calculating the
     # children variables
@@ -94,31 +203,52 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
         if isinstance(symbol, pybamm.Multiplication):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
             dummy_eval_right = symbol.children[1].evaluate_for_shape()
-            if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply({1})"\
-                    .format(children_vars[0], children_vars[1])
-            elif not to_dense and scipy.sparse.issparse(dummy_eval_right):
-                symbol_str = "{1}.multiply({0})"\
-                    .format(children_vars[0], children_vars[1])
+            if scipy.sparse.issparse(dummy_eval_left):
+                if output_jax and is_scalar(dummy_eval_right):
+                    symbol_str = "{0}.scalar_multiply({1})"\
+                        .format(children_vars[0], children_vars[1])
+                else:
+                    symbol_str = "{0}.multiply({1})"\
+                        .format(children_vars[0], children_vars[1])
+            elif scipy.sparse.issparse(dummy_eval_right):
+                if output_jax and is_scalar(dummy_eval_left):
+                    symbol_str = "{1}.scalar_multiply({0})"\
+                        .format(children_vars[0], children_vars[1])
+                else:
+                    symbol_str = "{1}.multiply({0})"\
+                        .format(children_vars[0], children_vars[1])
             else:
                 symbol_str = "{0} * {1}".format(children_vars[0], children_vars[1])
         elif isinstance(symbol, pybamm.Division):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
-            if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply(1/{1})"\
-                    .format(children_vars[0], children_vars[1])
+            dummy_eval_right = symbol.children[1].evaluate_for_shape()
+            if scipy.sparse.issparse(dummy_eval_left):
+                if output_jax and is_scalar(dummy_eval_right):
+                    symbol_str = "{0}.scalar_multiply(1/{1})"\
+                        .format(children_vars[0], children_vars[1])
+                else:
+                    symbol_str = "{0}.multiply(1/{1})"\
+                        .format(children_vars[0], children_vars[1])
             else:
                 symbol_str = "{0} / {1}".format(children_vars[0], children_vars[1])
 
         elif isinstance(symbol, pybamm.Inner):
             dummy_eval_left = symbol.children[0].evaluate_for_shape()
             dummy_eval_right = symbol.children[1].evaluate_for_shape()
-            if not to_dense and scipy.sparse.issparse(dummy_eval_left):
-                symbol_str = "{0}.multiply({1})"\
-                    .format(children_vars[0], children_vars[1])
-            elif not to_dense and scipy.sparse.issparse(dummy_eval_right):
-                symbol_str = "{1}.multiply({0})"\
-                    .format(children_vars[0], children_vars[1])
+            if scipy.sparse.issparse(dummy_eval_left):
+                if output_jax and is_scalar(dummy_eval_right):
+                    symbol_str = "{0}.scalar_multiply({1})"\
+                        .format(children_vars[0], children_vars[1])
+                else:
+                    symbol_str = "{0}.multiply({1})"\
+                        .format(children_vars[0], children_vars[1])
+            elif scipy.sparse.issparse(dummy_eval_right):
+                if output_jax and is_scalar(dummy_eval_left):
+                    symbol_str = "{1}.scalar_multiply({0})"\
+                        .format(children_vars[0], children_vars[1])
+                else:
+                    symbol_str = "{1}.multiply({0})"\
+                        .format(children_vars[0], children_vars[1])
             else:
                 symbol_str = "{0} * {1}".format(children_vars[0], children_vars[1])
 
@@ -126,6 +256,19 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
             symbol_str = "np.minimum({},{})".format(children_vars[0], children_vars[1])
         elif isinstance(symbol, pybamm.Maximum):
             symbol_str = "np.maximum({},{})".format(children_vars[0], children_vars[1])
+
+        elif isinstance(symbol, pybamm.MatrixMultiplication):
+            dummy_eval_left = symbol.children[0].evaluate_for_shape()
+            dummy_eval_right = symbol.children[1].evaluate_for_shape()
+            if output_jax and (
+                    scipy.sparse.issparse(dummy_eval_left) and
+                    scipy.sparse.issparse(dummy_eval_right)
+            ):
+                raise NotImplementedError('sparse mat-mat multiplication not supported '
+                                          'for output_jax == True')
+            else:
+                symbol_str = children_vars[0] + " " + symbol.name + " " \
+                    + children_vars[1]
         else:
             symbol_str = children_vars[0] + " " + symbol.name + " " + children_vars[1]
 
@@ -165,10 +308,12 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
                 symbol_str = "{}".format(",".join(children_vars))
 
         elif isinstance(symbol, pybamm.SparseStack):
-            if not to_dense and len(children_vars) > 1:
-                symbol_str = "scipy.sparse.vstack(({}))".format(",".join(children_vars))
-            elif len(children_vars) > 1:
-                symbol_str = "np.vstack(({}))".format(",".join(children_vars))
+            if len(children_vars) > 1:
+                if output_jax:
+                    raise NotImplementedError
+                else:
+                    symbol_str = "scipy.sparse.vstack(({}))".format(
+                        ",".join(children_vars))
             else:
                 symbol_str = "{}".format(",".join(children_vars))
 
@@ -223,7 +368,7 @@ def find_symbols(symbol, constant_symbols, variable_symbols, to_dense=False):
     variable_symbols[symbol.id] = symbol_str
 
 
-def to_python(symbol, debug=False, to_dense=False):
+def to_python(symbol, debug=False, output_jax=False):
     """
     This function converts an expression tree into a dict of constant input values, and
     valid python code that acts like the tree's :func:`pybamm.Symbol.evaluate` function
@@ -243,14 +388,15 @@ def to_python(symbol, debug=False, to_dense=False):
         the expression tree
     str:
         valid python code that will evaluate all the variable nodes in the tree.
-    to_dense: bool
-        If True, all constants and expressions are converted to using dense matrices
+    output_jax: bool
+        If True, only numpy and jax operations will be used in the generated code.
+        Raises NotImplNotImplementedError if any SparseStack or Mat-Mat multiply
+        operations are used
 
     """
-
     constant_values = OrderedDict()
     variable_symbols = OrderedDict()
-    find_symbols(symbol, constant_values, variable_symbols, to_dense)
+    find_symbols(symbol, constant_values, variable_symbols, output_jax)
 
     line_format = "{} = {}"
 
@@ -260,7 +406,7 @@ def to_python(symbol, debug=False, to_dense=False):
                 line_format.format(id_to_python_variable(symbol_id, False), symbol_line)
             )
             + line_format.format(id_to_python_variable(symbol_id, False), symbol_line)
-            + "; print(type({0}),{0}.shape)".format(
+            + "; print(type({0}),np.shape({0}))".format(
                 id_to_python_variable(symbol_id, False)
             )
             for symbol_id, symbol_line in variable_symbols.items()
@@ -294,18 +440,20 @@ def __init__(self, symbol):
         # extract constants in generated function
         for i, symbol_id in enumerate(constants.keys()):
             const_name = id_to_python_variable(symbol_id, True)
-            python_str = '{} = constants[{}]\n'.format(const_name, i) + python_str
+            python_str = "{} = constants[{}]\n".format(const_name, i) + python_str
 
         # constants passed in as an ordered dict, convert to list
         self._constants = list(constants.values())
 
         # indent code
-        python_str = '   ' + python_str
-        python_str = python_str.replace('\n', '\n   ')
+        python_str = "   " + python_str
+        python_str = python_str.replace("\n", "\n   ")
 
         # add function def to first line
-        python_str = 'def evaluate(constants, t=None, y=None, '\
-            'y_dot=None, inputs=None, known_evals=None):\n' + python_str
+        python_str = (
+            "def evaluate(constants, t=None, y=None, "
+            "y_dot=None, inputs=None, known_evals=None):\n" + python_str
+        )
 
         # calculate the final variable that will output the result of calling `evaluate`
         # on `symbol`
@@ -315,21 +463,18 @@ def __init__(self, symbol):
 
         # add return line
         if symbol.is_constant() and isinstance(result_value, numbers.Number):
-            python_str = python_str + '\n   return ' + str(result_value)
+            python_str = python_str + "\n   return " + str(result_value)
         else:
-            python_str = python_str + '\n   return ' + result_var
+            python_str = python_str + "\n   return " + result_var
 
         # store a copy of examine_jaxpr
-        python_str = python_str + \
-            '\nself._evaluate = evaluate'
+        python_str = python_str + "\nself._evaluate = evaluate"
 
         self._python_str = python_str
         self._symbol = symbol
 
         # compile and run the generated python code,
-        compiled_function = compile(
-            python_str, result_var, "exec"
-        )
+        compiled_function = compile(python_str, result_var, "exec")
         exec(compiled_function)
 
     def evaluate(self, t=None, y=None, y_dot=None, inputs=None, known_evals=None):
@@ -359,11 +504,6 @@ class EvaluatorJax:
     so any sparse matrices and operations involved sparse matrices are converted to
     their dense equivilents before compilation
 
-    Raises
-    ------
-    RuntimeError
-        if any sparse matrices are present in the expression tree
-
     Parameters
     ----------
 
@@ -374,31 +514,45 @@ class EvaluatorJax:
     """
 
     def __init__(self, symbol):
-        constants, python_str = pybamm.to_python(symbol, debug=False, to_dense=True)
+        constants, python_str = pybamm.to_python(symbol, debug=False, output_jax=True)
 
         # replace numpy function calls to jax numpy calls
-        python_str = python_str.replace('np.', 'jax.numpy.')
+        python_str = python_str.replace("np.", "jax.numpy.")
 
         # convert all numpy constants to device vectors
         for symbol_id in constants:
             if isinstance(constants[symbol_id], np.ndarray):
                 constants[symbol_id] = jax.device_put(constants[symbol_id])
 
-        # extract constants in generated function
-        for i, symbol_id in enumerate(constants.keys()):
-            const_name = id_to_python_variable(symbol_id, True)
-            python_str = '{} = constants[{}]\n'.format(const_name, i) + python_str
+        # get a list of constant arguments to input to the function
+        arg_list = [
+            id_to_python_variable(symbol_id, True)
+            for symbol_id in constants.keys()
+        ]
 
-        # constants passed in as an ordered dict, convert to list
-        self._constants = list(constants.values())
+        # get a list of hashable arguments to make static
+        # a jax device array is not hashable
+        static_argnums = (
+            i for i, c in enumerate(constants.values())
+            if not (
+                isinstance(c, jax.interpreters.xla.DeviceArray)
+            )
+        )
+
+        # store constants
+        self._constants = tuple(constants.values())
 
         # indent code
-        python_str = '   ' + python_str
-        python_str = python_str.replace('\n', '\n   ')
+        python_str = "   " + python_str
+        python_str = python_str.replace("\n", "\n   ")
 
         # add function def to first line
-        python_str = 'def evaluate_jax(constants, t=None, y=None, '\
-            'y_dot=None, inputs=None, known_evals=None):\n' + python_str
+        args = 't=None, y=None, y_dot=None, inputs=None, known_evals=None'
+        if arg_list:
+            args = ','.join(arg_list) + ', ' + args
+        python_str = (
+            "def evaluate_jax({}):\n".format(args) + python_str
+        )
 
         # calculate the final variable that will output the result of calling `evaluate`
         # on `symbol`
@@ -408,25 +562,29 @@ def __init__(self, symbol):
 
         # add return line
         if symbol.is_constant() and isinstance(result_value, numbers.Number):
-            python_str = python_str + '\n   return ' + str(result_value)
+            python_str = python_str + "\n   return " + str(result_value)
         else:
-            python_str = python_str + '\n   return ' + result_var
+            python_str = python_str + "\n   return " + result_var
 
         # store a copy of examine_jaxpr
-        python_str = python_str + \
-            '\nself._evaluate_jax = evaluate_jax'
+        python_str = python_str + "\nself._evaluate_jax = evaluate_jax"
+
+        # store the final generated code
+        self._python_str = python_str
 
         # compile and run the generated python code,
-        compiled_function = compile(
-            python_str, result_var, "exec"
-        )
+        compiled_function = compile(python_str, result_var, "exec")
         exec(compiled_function)
 
-        self._jit_evaluate = jax.jit(self._evaluate_jax, static_argnums=(0, 4, 5))
+        n = len(arg_list)
+        static_argnums = tuple(static_argnums)
+        self._jit_evaluate = jax.jit(self._evaluate_jax,
+                                     static_argnums=static_argnums)
 
         # store a jit version of evaluate_jax's jacobian
-        jacobian_evaluate = jax.jacfwd(self._evaluate_jax, argnums=2)
-        self._jac_evaluate = jax.jit(jacobian_evaluate, static_argnums=(0, 4, 5))
+        jacobian_evaluate = jax.jacfwd(self._evaluate_jax, argnums=1 + n)
+        self._jac_evaluate = jax.jit(jacobian_evaluate,
+                                     static_argnums=static_argnums)
 
     def get_jacobian(self):
         return EvaluatorJaxJacobian(self._jac_evaluate, self._constants)
@@ -438,7 +596,7 @@ def debug(self, t=None, y=None, y_dot=None, inputs=None, known_evals=None):
 
         # execute code
         jaxpr = jax.make_jaxpr(self._evaluate_jax)(
-            self._constants, t, y, y_dot, inputs, known_evals
+            *self._constants, t, y, y_dot, inputs, known_evals
         ).jaxpr
         print("invars:", jaxpr.invars)
         print("outvars:", jaxpr.outvars)
@@ -456,7 +614,7 @@ def evaluate(self, t=None, y=None, y_dot=None, inputs=None, known_evals=None):
         if y is not None and y.ndim == 1:
             y = y.reshape(-1, 1)
 
-        result = self._jit_evaluate(self._constants, t, y, y_dot, inputs, known_evals)
+        result = self._jit_evaluate(*self._constants, t, y, y_dot, inputs, known_evals)
 
         # don't need known_evals, but need to reproduce Symbol.evaluate signature
         if known_evals is not None:
@@ -479,7 +637,7 @@ def evaluate(self, t=None, y=None, y_dot=None, inputs=None, known_evals=None):
             y = y.reshape(-1, 1)
 
         # execute code
-        result = self._jac_evaluate(self._constants, t, y, y_dot, inputs, known_evals)
+        result = self._jac_evaluate(*self._constants, t, y, y_dot, inputs, known_evals)
         result = result.reshape(result.shape[0], -1)
 
         # don't need known_evals, but need to reproduce Symbol.evaluate signature
diff --git a/pybamm/expression_tree/parameter.py b/pybamm/expression_tree/parameter.py
index eca440ebd2..83ce18a0dc 100644
--- a/pybamm/expression_tree/parameter.py
+++ b/pybamm/expression_tree/parameter.py
@@ -35,6 +35,10 @@ def _evaluate_for_shape(self):
         """
         return np.nan
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return True
+
 
 class FunctionParameter(pybamm.Symbol):
     """A node in the expression tree representing a function parameter
@@ -60,7 +64,10 @@ class FunctionParameter(pybamm.Symbol):
     """
 
     def __init__(
-        self, name, inputs, diff_variable=None,
+        self,
+        name,
+        inputs,
+        diff_variable=None,
     ):
         # assign diff variable
         self.diff_variable = diff_variable
diff --git a/pybamm/expression_tree/scalar.py b/pybamm/expression_tree/scalar.py
index fffc461960..5bde1f147e 100644
--- a/pybamm/expression_tree/scalar.py
+++ b/pybamm/expression_tree/scalar.py
@@ -24,9 +24,6 @@ class Scalar(pybamm.Symbol):
     """
 
     def __init__(self, value, name=None, domain=[]):
-        """
-
-        """
         # set default name if not provided
         self.value = value
         if name is None:
@@ -62,3 +59,7 @@ def _jac(self, variable):
     def new_copy(self):
         """ See :meth:`pybamm.Symbol.new_copy()`. """
         return Scalar(self.value, self.name, self.domain)
+
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return True
diff --git a/pybamm/expression_tree/symbol.py b/pybamm/expression_tree/symbol.py
index e0db67aa98..5f6fb3a134 100644
--- a/pybamm/expression_tree/symbol.py
+++ b/pybamm/expression_tree/symbol.py
@@ -61,6 +61,10 @@ def evaluate_for_shape_using_domain(domain, auxiliary_domains=None, typ="vector"
     return create_object_of_size(_domain_size * _auxiliary_domain_sizes, typ)
 
 
+def is_constant(symbol):
+    return isinstance(symbol, numbers.Number) or symbol.is_constant()
+
+
 class Symbol(anytree.NodeMixin):
     """Base node class for the expression tree
 
@@ -174,8 +178,8 @@ def domain(self, domain):
 
     @property
     def auxiliary_domains(self):
-        "Returns domains that are not the primary domain"
-        return {k: v for k, v in self._domains.items() if k != "primary"}
+        "Returns auxiliary domains"
+        return self._auxiliary_domains
 
     @auxiliary_domains.setter
     def auxiliary_domains(self, auxiliary_domains):
@@ -193,6 +197,7 @@ def auxiliary_domains(self, auxiliary_domains):
         if len(set(values)) != len(values):
             raise pybamm.DomainError("All auxiliary domains must be different")
 
+        self._auxiliary_domains = auxiliary_domains
         self._domains.update(auxiliary_domains)
 
     @property
@@ -203,10 +208,16 @@ def secondary_domain(self):
     def copy_domains(self, symbol):
         "Copy the domains from a given symbol, bypassing checks"
         self._domains = symbol.domains
+        self._domain = self._domains["primary"]
+        self._auxiliary_domains = {
+            k: v for k, v in self._domains.items() if k != "primary"
+        }
 
     def clear_domains(self):
         "Clear domains, bypassing checks"
         self._domains = {"primary": []}
+        self._domain = []
+        self._auxiliary_domains = {}
 
     def get_children_auxiliary_domains(self, children):
         "Combine auxiliary domains from children, at all levels"
@@ -292,13 +303,13 @@ def visualise(self, filename):
             DotExporter(
                 new_node, nodeattrfunc=lambda node: 'label="{}"'.format(node.label)
             ).to_picture(filename)
-        except FileNotFoundError:
+        except FileNotFoundError:  # pragma: no cover
             # raise error but only through logger so that test passes
             pybamm.logger.error("Please install graphviz>=2.42.2 to use dot exporter")
 
     def relabel_tree(self, symbol, counter):
-        """ Finds all children of a symbol and assigns them a new id so that they can be
-                visualised properly using the graphviz output
+        """Finds all children of a symbol and assigns them a new id so that they can be
+        visualised properly using the graphviz output
         """
         name = symbol.name
         if name == "div":
@@ -434,38 +445,63 @@ def __rpow__(self, other):
         return pybamm.simplify_if_constant(pybamm.Power(other, self), keep_domains=True)
 
     def __lt__(self, other):
-        """return a :class:`NotEqualHeaviside` object"""
-        return pybamm.simplify_if_constant(
-            pybamm.NotEqualHeaviside(self, other), keep_domains=True
-        )
+        """return a :class:`NotEqualHeaviside` object, or a smooth approximation"""
+        k = pybamm.settings.heaviside_smoothing
+        # Return exact approximation if that is the setting or the outcome is a constant
+        # (i.e. no need for smoothing)
+        if k == "exact" or (is_constant(self) and is_constant(other)):
+            out = pybamm.NotEqualHeaviside(self, other)
+        else:
+            out = pybamm.sigmoid(self, other, k)
+        return pybamm.simplify_if_constant(out, keep_domains=True)
 
     def __le__(self, other):
-        """return a :class:`EqualHeaviside` object"""
-        return pybamm.simplify_if_constant(
-            pybamm.EqualHeaviside(self, other), keep_domains=True
-        )
+        """return a :class:`EqualHeaviside` object, or a smooth approximation"""
+        k = pybamm.settings.heaviside_smoothing
+        # Return exact approximation if that is the setting or the outcome is a constant
+        # (i.e. no need for smoothing)
+        if k == "exact" or (is_constant(self) and is_constant(other)):
+            out = pybamm.EqualHeaviside(self, other)
+        else:
+            out = pybamm.sigmoid(self, other, k)
+        return pybamm.simplify_if_constant(out, keep_domains=True)
 
     def __gt__(self, other):
-        """return a :class:`NotEqualHeaviside` object"""
-        return pybamm.simplify_if_constant(
-            pybamm.NotEqualHeaviside(other, self), keep_domains=True
-        )
+        """return a :class:`NotEqualHeaviside` object, or a smooth approximation"""
+        k = pybamm.settings.heaviside_smoothing
+        # Return exact approximation if that is the setting or the outcome is a constant
+        # (i.e. no need for smoothing)
+        if k == "exact" or (is_constant(self) and is_constant(other)):
+            out = pybamm.NotEqualHeaviside(other, self)
+        else:
+            out = pybamm.sigmoid(other, self, k)
+        return pybamm.simplify_if_constant(out, keep_domains=True)
 
     def __ge__(self, other):
-        """return a :class:`EqualHeaviside` object"""
-        return pybamm.simplify_if_constant(
-            pybamm.EqualHeaviside(other, self), keep_domains=True
-        )
+        """return a :class:`EqualHeaviside` object, or a smooth approximation"""
+        k = pybamm.settings.heaviside_smoothing
+        # Return exact approximation if that is the setting or the outcome is a constant
+        # (i.e. no need for smoothing)
+        if k == "exact" or (is_constant(self) and is_constant(other)):
+            out = pybamm.EqualHeaviside(other, self)
+        else:
+            out = pybamm.sigmoid(other, self, k)
+        return pybamm.simplify_if_constant(out, keep_domains=True)
 
     def __neg__(self):
         """return a :class:`Negate` object"""
         return pybamm.simplify_if_constant(pybamm.Negate(self), keep_domains=True)
 
     def __abs__(self):
-        """return an :class:`AbsoluteValue` object"""
-        return pybamm.simplify_if_constant(
-            pybamm.AbsoluteValue(self), keep_domains=True
-        )
+        """return an :class:`AbsoluteValue` object, or a smooth approximation"""
+        k = pybamm.settings.abs_smoothing
+        # Return exact approximation if that is the setting or the outcome is a constant
+        # (i.e. no need for smoothing)
+        if k == "exact" or is_constant(self):
+            out = pybamm.AbsoluteValue(self)
+        else:
+            out = pybamm.smooth_absolute_value(self, k)
+        return pybamm.simplify_if_constant(out, keep_domains=True)
 
     def __mod__(self, other):
         """return an :class:`Modulo` object"""
@@ -602,24 +638,15 @@ def _evaluate_for_shape(self):
 
     def is_constant(self):
         """returns true if evaluating the expression is not dependent on `t` or `y`
-        or `u`
+        or `inputs`
 
         See Also
         --------
         evaluate : evaluate the expression
 
         """
-        # if any of the nodes are instances of any of these types, then the whole
-        # expression depends on either t or y or u
-        search_types = (
-            pybamm.Variable,
-            pybamm.StateVector,
-            pybamm.Time,
-            pybamm.InputParameter,
-        )
-
-        # do the search, return true if no relevent nodes are found
-        return not self.has_symbol_of_classes(search_types)
+        # Default behaviour is False
+        return False
 
     def evaluate_ignoring_errors(self, t=0):
         """
@@ -736,37 +763,43 @@ def size(self):
         """
         Size of an object, found by evaluating it with appropriate t and y
         """
-        return np.prod(self.shape)
+        try:
+            return self._saved_size
+        except AttributeError:
+            self._saved_size = np.prod(self.shape)
+            return self._saved_size
 
     @property
     def shape(self):
         """
         Shape of an object, found by evaluating it with appropriate t and y.
         """
-        # Default behaviour is to try to evaluate the object directly
-        # Try with some large y, to avoid having to unpack (slow)
         try:
-            y = np.nan * np.ones((1000, 1))
-            evaluated_self = self.evaluate(0, y, y, inputs="shape test")
-        # If that fails, fall back to calculating how big y should really be
-        except ValueError:
-            unpacker = pybamm.SymbolUnpacker(pybamm.StateVector)
-            state_vectors_in_node = unpacker.unpack_symbol(self).values()
-            if state_vectors_in_node == []:
-                y = None
-            else:
+            return self._saved_shape
+        except AttributeError:
+            # Default behaviour is to try to evaluate the object directly
+            # Try with some large y, to avoid having to unpack (slow)
+            try:
+                y = np.nan * np.ones((1000, 1))
+                evaluated_self = self.evaluate(0, y, y, inputs="shape test")
+            # If that fails, fall back to calculating how big y should really be
+            except ValueError:
+                unpacker = pybamm.SymbolUnpacker(pybamm.StateVector)
+                state_vectors_in_node = unpacker.unpack_symbol(self).values()
                 min_y_size = max(
-                    len(x._evaluation_array) for x in state_vectors_in_node
+                    max(len(x._evaluation_array) for x in state_vectors_in_node), 1
                 )
                 # Pick a y that won't cause RuntimeWarnings
                 y = np.nan * np.ones((min_y_size, 1))
-            evaluated_self = self.evaluate(0, y, y, inputs="shape test")
+                evaluated_self = self.evaluate(0, y, y, inputs="shape test")
 
-        # Return shape of evaluated object
-        if isinstance(evaluated_self, numbers.Number):
-            return ()
-        else:
-            return evaluated_self.shape
+            # Return shape of evaluated object
+            if isinstance(evaluated_self, numbers.Number):
+                self._saved_shape = ()
+            else:
+                self._saved_shape = evaluated_self.shape
+
+        return self._saved_shape
 
     @property
     def size_for_testing(self):
diff --git a/pybamm/expression_tree/unary_operators.py b/pybamm/expression_tree/unary_operators.py
index ac244248d5..d5be9ef49c 100644
--- a/pybamm/expression_tree/unary_operators.py
+++ b/pybamm/expression_tree/unary_operators.py
@@ -1,6 +1,7 @@
 #
 # Unary operator classes and methods
 #
+import numbers
 import numpy as np
 import pybamm
 from scipy.sparse import issparse, csr_matrix
@@ -24,6 +25,8 @@ class UnaryOperator(pybamm.Symbol):
     """
 
     def __init__(self, name, child, domain=None, auxiliary_domains=None):
+        if isinstance(child, numbers.Number):
+            child = pybamm.Scalar(child)
         if domain is None:
             domain = child.domain
         if auxiliary_domains is None:
@@ -87,6 +90,10 @@ def evaluates_on_edges(self, dimension):
         """ See :meth:`pybamm.Symbol.evaluates_on_edges()`. """
         return self.child.evaluates_on_edges(dimension)
 
+    def is_constant(self):
+        """ See :meth:`pybamm.Symbol.is_constant()`. """
+        return self.child.is_constant()
+
 
 class Negate(UnaryOperator):
     """A node in the expression tree representing a `-` negation operator
@@ -575,7 +582,9 @@ def _unary_new_copy(self, child):
 
     def _evaluate_for_shape(self):
         """ See :meth:`pybamm.Symbol.evaluate_for_shape_using_domain()` """
-        return pybamm.evaluate_for_shape_using_domain(self.domain)
+        return pybamm.evaluate_for_shape_using_domain(
+            self.domain, self.auxiliary_domains
+        )
 
     def evaluates_on_edges(self, dimension):
         """ See :meth:`pybamm.Symbol.evaluates_on_edges()`. """
@@ -1147,14 +1156,14 @@ def x_average(symbol):
         if a.id == b.id == c.id:
             return a
         else:
-            geo = pybamm.GeometricParameters()
+            geo = pybamm.geometric_parameters
             l_n = geo.l_n
             l_s = geo.l_s
             l_p = geo.l_p
             return (l_n * a + l_s * b + l_p * c) / (l_n + l_s + l_p)
     # Otherwise, use Integral to calculate average value
     else:
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         if symbol.domain == ["negative electrode"]:
             x = pybamm.standard_spatial_vars.x_n
             l = geo.l_n
@@ -1214,7 +1223,7 @@ def z_average(symbol):
         return symbol.orphans[0]
     # Otherwise, use Integral to calculate average value
     else:
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         z = pybamm.standard_spatial_vars.z
         l_z = geo.l_z
         return Integral(symbol, z) / l_z
@@ -1251,7 +1260,7 @@ def yz_average(symbol):
         return symbol.orphans[0]
     # Otherwise, use Integral to calculate average value
     else:
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         y = pybamm.standard_spatial_vars.y
         z = pybamm.standard_spatial_vars.z
         l_y = geo.l_y
@@ -1343,3 +1352,14 @@ def boundary_value(symbol, side):
 def sign(symbol):
     " Returns a :class:`Sign` object. "
     return Sign(symbol)
+
+
+def smooth_absolute_value(symbol, k):
+    """
+    Smooth approximation to the absolute value function. k is the smoothing parameter,
+    set by `pybamm.settings.abs_smoothing`. The recommended value is k=10.
+    """
+    x = symbol
+    exp = pybamm.exp
+    kx = k * symbol
+    return x * (exp(kx) - exp(-kx)) / (exp(kx) + exp(-kx))
diff --git a/pybamm/expression_tree/variable.py b/pybamm/expression_tree/variable.py
index 44055c651d..911e2cd3fa 100644
--- a/pybamm/expression_tree/variable.py
+++ b/pybamm/expression_tree/variable.py
@@ -144,9 +144,7 @@ def get_variable(self):
 
         """
         return Variable(
-            self.name[:-1],
-            domain=self.domain,
-            auxiliary_domains=self.auxiliary_domains,
+            self.name[:-1], domain=self.domain, auxiliary_domains=self.auxiliary_domains
         )
 
     def diff(self, variable):
diff --git a/pybamm/geometry/battery_geometry.py b/pybamm/geometry/battery_geometry.py
index d3e0b68901..7b05b7ea72 100644
--- a/pybamm/geometry/battery_geometry.py
+++ b/pybamm/geometry/battery_geometry.py
@@ -22,7 +22,7 @@ def battery_geometry(include_particles=True, current_collector_dimension=0):
 
     """
     var = pybamm.standard_spatial_vars
-    geo = pybamm.GeometricParameters()
+    geo = pybamm.geometric_parameters
     l_n = geo.l_n
     l_s = geo.l_s
 
diff --git a/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_U.txt b/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_U.txt
new file mode 100644
index 0000000000..987192474c
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_U.txt
@@ -0,0 +1,36880 @@
+0	4.181482004
+1	4.175568142
+2	4.173469674
+3	4.173088135
+4	4.172897365
+5	4.172515826
+6	4.172325056
+7	4.172325056
+8	4.172325056
+9	4.172134286
+10	4.171943516
+11	4.171943516
+12	4.171561977
+13	4.171371207
+14	4.171180437
+15	4.171180437
+16	4.170989668
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diff --git a/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_displacement.txt b/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_displacement.txt
new file mode 100644
index 0000000000..1abab6f79c
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/0.1C_discharge_displacement.txt
@@ -0,0 +1,3745 @@
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\ No newline at end of file
diff --git a/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_T.txt b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_T.txt
new file mode 100644
index 0000000000..0695fd6e77
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_T.txt
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diff --git a/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_U.txt b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_U.txt
new file mode 100644
index 0000000000..e22e747da1
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_U.txt
@@ -0,0 +1,7310 @@
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diff --git a/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_displacement.txt b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_displacement.txt
new file mode 100644
index 0000000000..8ee457ce77
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/0.5C_discharge_displacement.txt
@@ -0,0 +1,788 @@
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+7311.673930367749         4.667763172375133E-6
\ No newline at end of file
diff --git a/pybamm/input/discharge_data/Enertech_cells/1C_discharge_T.txt b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_T.txt
new file mode 100644
index 0000000000..70a12240e8
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_T.txt
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diff --git a/pybamm/input/discharge_data/Enertech_cells/1C_discharge_U.txt b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_U.txt
new file mode 100644
index 0000000000..2b479938f9
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_U.txt
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diff --git a/pybamm/input/discharge_data/Enertech_cells/1C_discharge_displacement.txt b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_displacement.txt
new file mode 100644
index 0000000000..69f31d5e6c
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/1C_discharge_displacement.txt
@@ -0,0 +1,417 @@
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\ No newline at end of file
diff --git a/pybamm/input/discharge_data/Enertech_cells/2C_discharge_T.txt b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_T.txt
new file mode 100644
index 0000000000..cad16f6332
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_T.txt
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diff --git a/pybamm/input/discharge_data/Enertech_cells/2C_discharge_U.txt b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_U.txt
new file mode 100644
index 0000000000..007f4452d3
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_U.txt
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diff --git a/pybamm/input/discharge_data/Enertech_cells/2C_discharge_displacement.txt b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_displacement.txt
new file mode 100644
index 0000000000..14defb39fd
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/2C_discharge_displacement.txt
@@ -0,0 +1,232 @@
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+370                       1.312216898248585E-4
+380                       1.3034259389246375E-4
+390                       1.294767891426281E-4
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+530                       1.1853862179084019E-4
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+560                       1.1644385809999014E-4
+570                       1.1576253972426225E-4
+580                       1.1508964929207718E-4
+590                       1.144251305983098E-4
+600                       1.1376877488228201E-4
+610                       1.1312054812183049E-4
+620                       1.1248018561024425E-4
+630                       1.1184695891621398E-4
+640                       1.1122098817407777E-4
+650                       1.10601848516289E-4
+660                       1.0998927288743432E-4
+670                       1.0938299337574301E-4
+680                       1.087824332237953E-4
+690                       1.0818714099782332E-4
+700                       1.0759736337066356E-4
+710                       1.0701299811698519E-4
+720                       1.0643387836965563E-4
+730                       1.0585998924126545E-4
+740                       1.052907558882347E-4
+750                       1.0472582359534273E-4
+760                       1.0416445339200561E-4
+770                       1.0360500730040596E-4
+780                       1.0304679123311263E-4
+790                       1.0248882105766398E-4
+800                       1.0192977811894203E-4
+810                       1.0136979413602888E-4
+820                       1.008091382837257E-4
+830                       1.0024820005022787E-4
+840                       9.96871846457008E-5
+850                       9.912653830088223E-5
+860                       9.85649554424661E-5
+870                       9.800367945902465E-5
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+890                       9.688361308134323E-5
+900                       9.632491699382897E-5
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+1020                      8.967449176704298E-5
+1030                      8.912634404768621E-5
+1040                      8.857588310659558E-5
+1050                      8.802571207931958E-5
+1060                      8.747489723694343E-5
+1070                      8.692329949776248E-5
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+1090                      8.582849987229408E-5
+1100                      8.528804640282596E-5
+1110                      8.475762092299886E-5
+1120                      8.423907708345045E-5
+1130                      8.373337874952604E-5
+1140                      8.324060814778182E-5
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+1240                      7.820922549915667E-5
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+1270                      7.654915568816267E-5
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+1290                      7.540042165397862E-5
+1300                      7.481343564451337E-5
+1310                      7.42178138131012E-5
+1320                      7.361321393355809E-5
+1330                      7.299873214029068E-5
+1340                      7.237477683032828E-5
+1350                      7.174114204653933E-5
+1360                      7.109754408382196E-5
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+1470                      6.316944396616286E-5
+1480                      6.234969072417153E-5
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+1500                      6.0643760306883094E-5
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+1530                      5.788378461259744E-5
+1540                      5.6896514725261375E-5
+1550                      5.587299558701534E-5
+1560                      5.4816050363609725E-5
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+1580                      5.2588779525584936E-5
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+1600                      5.018883507080342E-5
+1610                      4.890987123168485E-5
+1620                      4.755095889232615E-5
+1630                      4.6111393573034155E-5
+1640                      4.4621970963528206E-5
+1650                      4.311012224680617E-5
+1660                      4.1602412810739076E-5
+1670                      4.010549033525779E-5
+1680                      3.860081992000507E-5
+1690                      3.70807295744637E-5
+1700                      3.5553939250575146E-5
+1710                      3.402416171559471E-5
+1720                      3.24891634999722E-5
+1730                      3.094895615545153E-5
+1740                      2.9398515231903324E-5
+1746.9730657205407        2.8311140722133918E-5
+1750                      2.7835264778208026E-5
+1759.15758780183          2.6384754357783565E-5
diff --git a/pybamm/input/discharge_data/Enertech_cells/stn_2C.txt b/pybamm/input/discharge_data/Enertech_cells/stn_2C.txt
new file mode 100755
index 0000000000..2b924bdb92
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/stn_2C.txt
@@ -0,0 +1,896 @@
+# Negative particle surface tangetial stress close to the separator 
+# for the Enertech cells Ai2020 JES 
+# time [s] and normalised stress sigma_t_surf_n/E_n
+0,-1.0741e-17
+2,0.00031276
+4,0.00043323
+6,0.00051944
+8,0.00058904
+10,0.00064844
+12,0.00070099
+14,0.00074829
+16,0.0007915
+18,0.00083158
+20,0.00086605
+22,0.00089617
+24,0.00092722
+26,0.00095722
+28,0.00098602
+30,0.0010136
+32,0.0010401
+34,0.0010655
+36,0.0010899
+38,0.0011133
+40,0.0011357
+42,0.0011572
+44,0.0011779
+46,0.0011979
+48,0.001217
+50,0.0012354
+52,0.0012532
+54,0.0012678
+56,0.0012777
+58,0.0012907
+60,0.0013042
+62,0.0013175
+64,0.0013308
+66,0.0013436
+68,0.0013563
+70,0.0013685
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+74,0.0013921
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+80,0.0014231
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+84,0.0014328
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diff --git a/pybamm/input/discharge_data/Enertech_cells/stp_2C.txt b/pybamm/input/discharge_data/Enertech_cells/stp_2C.txt
new file mode 100755
index 0000000000..0cf5eb9b13
--- /dev/null
+++ b/pybamm/input/discharge_data/Enertech_cells/stp_2C.txt
@@ -0,0 +1,896 @@
+# Positive particle surface tangetial stress close to the separator 
+# for the Enertech cells Ai2020 JES
+# time [s] and normalised stress sigma_t_surf_p/E_p
+0,2.207e-18
+2,8.026e-05
+4,0.00011677
+6,0.00014216
+8,0.00016234
+10,0.00017923
+12,0.00019457
+14,0.00020834
+16,0.0002196
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+26,0.00026146
+28,0.00026824
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diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/README.md
new file mode 100644
index 0000000000..7609b721ff
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/README.md
@@ -0,0 +1,9 @@
+# Enertech Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_cracking_rate_Ai2020.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_cracking_rate_Ai2020.py
new file mode 100644
index 0000000000..00952608c8
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_cracking_rate_Ai2020.py
@@ -0,0 +1,35 @@
+from pybamm import Parameter, constants, exp
+
+
+def graphite_cracking_rate_Ai2020(T_dim):
+    """
+    graphite particle cracking rate as a function of temperature [1, 2].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+     Battery cycle life prediction with coupled chemical degradation and fatigue
+     mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    Parameters
+    ----------
+    T_dim: :class:`pybamm.Symbol`
+        temperature, [K]
+
+    Returns
+    -------
+    k_cr: :class:`pybamm.Symbol`
+        cracking rate, [m/(Pa.m0.5)^m_cr]
+        where m_cr is another Paris' law constant
+    """
+    k_cr = 3.9e-20
+    T_ref = Parameter("Reference temperature [K]")
+    Eac_cr = Parameter(
+        "Negative electrode activation energy for cracking rate [J.mol-1]"
+    )
+    arrhenius = exp(Eac_cr / constants.R * (1 / T_dim - 1 / T_ref))
+    return k_cr * arrhenius
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_diffusivity_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_diffusivity_Dualfoil1998.py
new file mode 100644
index 0000000000..3f80df4cd7
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_diffusivity_Dualfoil1998.py
@@ -0,0 +1,34 @@
+from pybamm import exp, constants, Parameter
+
+
+def graphite_diffusivity_Dualfoil1998(sto, T):
+    """
+    Graphite diffusivity as a function of stochiometry [1, 2, 3].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016).
+     A new method to model the thickness change of a commercial pouch cell
+     during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature, [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity [m2.s-1]
+    """
+    D_ref = 3.9 * 10 ** (-14)
+    E_D_s = 5000
+    T_ref = Parameter("Reference temperature [K]")
+    arrhenius = exp(E_D_s / constants.R * (1 / T_ref - 1 / T))
+    return D_ref * arrhenius
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_electrolyte_exchange_current_density_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_electrolyte_exchange_current_density_Dualfoil1998.py
new file mode 100644
index 0000000000..d0ada14911
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_electrolyte_exchange_current_density_Dualfoil1998.py
@@ -0,0 +1,37 @@
+from pybamm import exp, constants, Parameter
+
+
+def graphite_electrolyte_exchange_current_density_Dualfoil1998(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    m_ref = (
+        1 * 10 ** (-11) * constants.F
+    )  # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 5000  # activation energy for Temperature Dependent Reaction Constant [J/mol]
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    c_n_max = Parameter("Maximum concentration in negative electrode [mol.m-3]")
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_n_max - c_s_surf) ** 0.5
+    )
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020.csv
new file mode 100644
index 0000000000..12c6231083
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020.csv
@@ -0,0 +1,104 @@
+# Entropy for graphite from Ai2020
+# Just for reference against graphite_entropy_Enertech_Ai2020_function
+# stoichiometry , entropic change [mV.K-1]
+0.0000000e+00,5.2700000e-03
+1.0000000e-02,4.9161311e-02
+2.0000000e-02,1.1269475e-01
+3.0000000e-02,1.9070171e-01
+4.0000000e-02,2.4996395e-01
+5.0000000e-02,2.4670045e-01
+6.0000000e-02,1.9017663e-01
+7.0000000e-02,1.2383313e-01
+8.0000000e-02,7.0147138e-02
+9.0000000e-02,3.1338363e-02
+1.0000000e-01,3.7890420e-03
+1.1000000e-01,-1.6168816e-02
+1.2000000e-01,-3.1205820e-02
+1.3000000e-01,-4.3153828e-02
+1.4000000e-01,-5.3302760e-02
+1.5000000e-01,-6.2626427e-02
+1.6000000e-01,-7.1923436e-02
+1.7000000e-01,-8.1880316e-02
+1.8000000e-01,-9.3048410e-02
+1.9000000e-01,-1.0571601e-01
+2.0000000e-01,-1.1969020e-01
+2.1000000e-01,-1.3411266e-01
+2.2000000e-01,-1.4755409e-01
+2.3000000e-01,-1.5852853e-01
+2.4000000e-01,-1.6615492e-01
+2.5000000e-01,-1.7045348e-01
+2.6000000e-01,-1.7211739e-01
+2.7000000e-01,-1.7206991e-01
+2.8000000e-01,-1.7113903e-01
+2.9000000e-01,-1.6993421e-01
+3.0000000e-01,-1.6885282e-01
+3.1000000e-01,-1.6813185e-01
+3.2000000e-01,-1.6789813e-01
+3.3000000e-01,-1.6820053e-01
+3.4000000e-01,-1.6902097e-01
+3.5000000e-01,-1.7026507e-01
+3.6000000e-01,-1.7173534e-01
+3.7000000e-01,-1.7309697e-01
+3.8000000e-01,-1.7386338e-01
+3.9000000e-01,-1.7345079e-01
+4.0000000e-01,-1.7134817e-01
+4.1000000e-01,-1.6737103e-01
+4.2000000e-01,-1.6183723e-01
+4.3000000e-01,-1.5548923e-01
+4.4000000e-01,-1.4919003e-01
+4.5000000e-01,-1.4360695e-01
+4.6000000e-01,-1.3900773e-01
+4.7000000e-01,-1.3500887e-01
+4.8000000e-01,-1.2994318e-01
+4.9000000e-01,-1.2106473e-01
+5.0000000e-01,-1.1021528e-01
+5.1000000e-01,-1.0348811e-01
+5.2000000e-01,-1.0092885e-01
+5.3000000e-01,-1.0015801e-01
+5.4000000e-01,-9.9965693e-02
+5.5000000e-01,-9.9939815e-02
+5.6000000e-01,-9.9954176e-02
+5.7000000e-01,-9.9972658e-02
+5.8000000e-01,-9.9986619e-02
+5.9000000e-01,-9.9995371e-02
+6.0000000e-01,-1.0000014e-01
+6.1000000e-01,-1.0000230e-01
+6.2000000e-01,-1.0000291e-01
+6.3000000e-01,-1.0000268e-01
+6.4000000e-01,-1.0000209e-01
+6.5000000e-01,-1.0000141e-01
+6.6000000e-01,-1.0000078e-01
+6.7000000e-01,-1.0000027e-01
+6.8000000e-01,-9.9999912e-02
+6.9000000e-01,-9.9999691e-02
+7.0000000e-01,-9.9999591e-02
+7.1000000e-01,-9.9999585e-02
+7.2000000e-01,-9.9999646e-02
+7.3000000e-01,-9.9999746e-02
+7.4000000e-01,-9.9999862e-02
+7.5000000e-01,-9.9999972e-02
+7.6000000e-01,-1.0000006e-01
+7.7000000e-01,-1.0000011e-01
+7.8000000e-01,-1.0000011e-01
+7.9000000e-01,-1.0000006e-01
+8.0000000e-01,-9.9999942e-02
+8.1000000e-01,-9.9999758e-02
+8.2000000e-01,-9.9999503e-02
+8.3000000e-01,-9.9999176e-02
+8.4000000e-01,-9.9998778e-02
+8.5000000e-01,-9.9998308e-02
+8.6000000e-01,-9.9997769e-02
+8.7000000e-01,-9.9997162e-02
+8.8000000e-01,-9.9996490e-02
+8.9000000e-01,-9.9995755e-02
+9.0000000e-01,-9.9994959e-02
+9.1000000e-01,-9.9994107e-02
+9.2000000e-01,-9.9993200e-02
+9.3000000e-01,-9.9992243e-02
+9.4000000e-01,-9.9991237e-02
+9.5000000e-01,-9.9990187e-02
+9.6000000e-01,-9.9989096e-02
+9.7000000e-01,-9.9987965e-02
+9.8000000e-01,-9.9986799e-02
+9.9000000e-01,-9.9985599e-02
+1.0000000e+00,-9.9984369e-02
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020_function.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020_function.py
new file mode 100644
index 0000000000..3a688e53f2
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_entropy_Enertech_Ai2020_function.py
@@ -0,0 +1,52 @@
+def graphite_entropy_Enertech_Ai2020_function(sto, T):
+    """
+        Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
+        a temperature of 298.15K as a function of the stochiometry. The fit is taken
+        from Ref [1], which is only accurate
+       for 0.43 < sto < 0.9936.
+
+        References
+        ----------
+        .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+        Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. # noqa
+        Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES # noqa
+
+    Parameters
+    ----------
+    sto: double
+       Stochiometry of material (li-fraction)
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Entropic change [v.K-1]
+    """
+
+    du_dT = (
+        0.001
+        * (
+            0.005269056
+            + 3.299265709 * sto
+            - 91.79325798 * sto ** 2
+            + 1004.911008 * sto ** 3
+            - 5812.278127 * sto ** 4
+            + 19329.7549 * sto ** 5
+            - 37147.8947 * sto ** 6
+            + 38379.18127 * sto ** 7
+            - 16515.05308 * sto ** 8
+        )
+        / (
+            1
+            - 48.09287227 * sto
+            + 1017.234804 * sto ** 2
+            - 10481.80419 * sto ** 3
+            + 59431.3 * sto ** 4
+            - 195881.6488 * sto ** 5
+            + 374577.3152 * sto ** 6
+            - 385821.1607 * sto ** 7
+            + 165705.8597 * sto ** 8
+        )
+    )
+    # show no temperature dependence
+    return du_dT
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020.csv
new file mode 100644
index 0000000000..8a5bce2874
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020.csv
@@ -0,0 +1,129 @@
+# OCP for graphite from Ai 2020
+# sto,ocp [V]
+# extra point to avoid extrapolation
+0,3.5
+# experimentally measured data
+0.0005,3
+0.00127041,1.04
+0.00152479,1.01
+0.00190595,0.972653837
+0.002223558,0.94249055
+0.004060547,0.816240592
+0.004820151,0.780280928
+0.006463943,0.71896262
+0.00741337,0.691374757
+0.008616506,0.661391781
+0.009123417,0.649962232
+0.010768226,0.6165173
+0.012665046,0.583310858
+0.014118344,0.560830783
+0.017786752,0.512439476
+0.02069469,0.48025136
+0.023983799,0.448495867
+0.030502175,0.39598881
+0.036001135,0.359507681
+0.039606662,0.338477981
+0.059148083,0.256319558
+0.061297942,0.25117361
+0.071349833,0.236055324
+0.080265526,0.231009217
+0.119208079,0.2232966
+0.128120548,0.218284244
+0.134253707,0.213273859
+0.141584594,0.208228362
+0.150874177,0.203209739
+0.160609131,0.198620985
+0.170345957,0.193816376
+0.189747769,0.184166915
+0.209222253,0.176790532
+0.21901773,0.173830441
+0.228756579,0.170963261
+0.238552575,0.167903501
+0.248349231,0.164649979
+0.258084023,0.161491332
+0.267821184,0.15859383
+0.28741535,0.153399157
+0.297209811,0.151002319
+0.307004942,0.14886213
+0.316798396,0.146918911
+0.326534032,0.145328142
+0.336321558,0.144002109
+0.346061758,0.142902125
+0.355856392,0.142014262
+0.365593044,0.141316008
+0.375388012,0.140759105
+0.385120781,0.140314323
+0.394915577,0.139942322
+0.404717479,0.139617851
+0.414512102,0.139325406
+0.424244871,0.139051014
+0.434039331,0.138779297
+0.44377024,0.138517413
+0.453564862,0.138258897
+0.463298139,0.137981293
+0.473034456,0.137672226
+0.482766544,0.137329325
+0.492564552,0.136903224
+0.502302892,0.136390244
+0.512042595,0.135757581
+0.521833161,0.134947101
+0.531572182,0.133923235
+0.541369033,0.132621681
+0.551104831,0.130989474
+0.5608998,0.128964924
+0.570635608,0.126549987
+0.580434806,0.123742878
+0.590235692,0.120770834
+0.599977407,0.117929634
+0.609716266,0.115379983
+0.619517822,0.113205423
+0.629313635,0.111366477
+0.639049108,0.109855495
+0.648790152,0.108578952
+0.658584104,0.107520678
+0.668320248,0.106632536
+0.67805504,0.105893758
+0.687851869,0.105260613
+0.69764938,0.104713189
+0.707389072,0.104254365
+0.717188097,0.103845625
+0.726977148,0.103477119
+0.736776336,0.103153932
+0.746515866,0.102856541
+0.756259106,0.102587443
+0.766055091,0.102338279
+0.775789039,0.102101986
+0.785537861,0.101880905
+0.79532979,0.101676423
+0.805080646,0.101465878
+0.814827099,0.101264171
+0.824570003,0.101062635
+0.834370889,0.10087041
+0.844173289,0.10068096
+0.853913187,0.100489223
+0.86365051,0.100300437
+0.873392073,0.100099718
+0.883126865,0.099877104
+0.892918286,0.099628985
+0.902708516,0.099332616
+0.912443308,0.098958419
+0.922232533,0.098442542
+0.932019724,0.097683643
+0.941812832,0.096492
+0.951602392,0.094510791
+0.961392795,0.091136817
+0.970177652,0.086115186
+0.976051358,0.081078748
+0.980413449,0.07604037
+0.983887804,0.070991535
+0.986792703,0.065898328
+0.989255096,0.060844047
+0.991401407,0.055810118
+0.993359929,0.050670698
+0.995130154,0.045562401
+0.996776304,0.040392663
+0.99822944,0.035261272
+0.999241066,0.030242658
+0.999746961,0.024850768
+0.999936448,0.019251502
+1,0.004994678
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020_function.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020_function.py
new file mode 100644
index 0000000000..ffbda91789
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_ocp_Enertech_Ai2020_function.py
@@ -0,0 +1,49 @@
+def graphite_ocp_Enertech_Ai2020_function(sto):
+    """
+    Graphite  Open Circuit Potential (OCP) as a a function of the
+    stochiometry. The fit is taken from the Enertech cell [1], which is only accurate
+       for 0.0065 < sto < 0.84.
+
+        References
+        ----------
+        .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+        Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+        Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1),
+        013512. DOI: 10.1149/2.0122001JES
+
+    Parameters
+    ----------
+    sto: double
+       Stochiometry of material (li-fraction)
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        OCP [V]
+
+    """
+
+    p1 = -2058.29865
+    p2 = 10040.08960
+    p3 = -20824.86740
+    p4 = 23911.86578
+    p5 = -16576.3692
+    p6 = 7098.09151
+    p7 = -1845.43634
+    p8 = 275.31114
+    p9 = -21.20097
+    p10 = 0.84498
+    u_eq = (
+        p1 * sto ** 9
+        + p2 * sto ** 8
+        + p3 * sto ** 7
+        + p4 * sto ** 6
+        + p5 * sto ** 5
+        + p6 * sto ** 4
+        + p7 * sto ** 3
+        + p8 * sto ** 2
+        + p9 * sto
+        + p10
+    )
+
+    return u_eq
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_volume_change_Ai2020.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_volume_change_Ai2020.py
new file mode 100644
index 0000000000..d2f1cd117a
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/graphite_volume_change_Ai2020.py
@@ -0,0 +1,47 @@
+def graphite_volume_change_Ai2020(sto):
+    """
+    Graphite particle volume change as a function of stochiometry [1, 2].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016).
+     A new method to model the thickness change of a commercial pouch cell
+     during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry, dimensionless
+        should be R-averaged particle concentration
+    Returns
+    -------
+    t_change:class:`pybamm.Symbol`
+        volume change, dimensionless, normalised by particle volume
+    """
+    p1 = 145.907
+    p2 = -681.229
+    p3 = 1334.442
+    p4 = -1415.710
+    p5 = 873.906
+    p6 = -312.528
+    p7 = 60.641
+    p8 = -5.706
+    p9 = 0.386
+    p10 = -4.966e-05
+    t_change = (
+        p1 * sto ** 9
+        + p2 * sto ** 8
+        + p3 * sto ** 7
+        + p4 * sto ** 6
+        + p5 * sto ** 5
+        + p6 * sto ** 4
+        + p7 * sto ** 3
+        + p8 * sto ** 2
+        + p9 * sto
+        + p10
+    )
+    return t_change
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/parameters.csv
new file mode 100644
index 0000000000..c38e9becaa
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ai2020/parameters.csv
@@ -0,0 +1,48 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrode properties,,,
+Negative electrode conductivity [S.m-1],100,Ai 2020,graphite
+Maximum concentration in negative electrode [mol.m-3],28700,Ai 2020,tuned for 1C
+Negative electrode diffusivity [m2.s-1],[function]graphite_diffusivity_Dualfoil1998,Ai 2020,tuned for 1C
+Negative electrode OCP [V],[data]graphite_ocp_Enertech_Ai2020,Ai 2020,
+,,,
+# Microstructure,,,
+Negative electrode porosity,0.33,Ai 2020,
+Negative electrode active material volume fraction,0.61,Ai 2020,
+Negative particle radius [m],5E-6,Ai 2020,
+Negative electrode Bruggeman coefficient (electrolyte),2.914,Ai 2020,theoretical
+Negative electrode Bruggeman coefficient (electrode),0,default,
+,,,
+# Interfacial reactions,,,
+Negative electrode cation signed stoichiometry,-1,,
+Negative electrode electrons in reaction,1,,
+Reference OCP vs SHE in the negative electrode [V],,,
+Negative electrode charge transfer coefficient,0.5,Ai 2020,
+Negative electrode double-layer capacity [F.m-2],0,,
+Negative electrode exchange-current density [A.m-2],[function]graphite_electrolyte_exchange_current_density_Dualfoil1998,,
+,,,
+# Density,,,
+Negative electrode density [kg.m-3],2470,,
+,,,
+# Thermal parameters,,,
+Negative electrode specific heat capacity [J.kg-1.K-1],1080.2,,
+Negative electrode thermal conductivity [W.m-1.K-1],1.04,,
+Negative electrode OCP entropic change [V.K-1],[function]graphite_entropy_Enertech_Ai2020_function,,
+# Negative electrode OCP entropic change [V.K-1],0,,
+,,,
+# Mechanical properties,,,
+Negative electrode Poisson's ratio,0.3,,
+Negative electrode Young's modulus [Pa],15e9,,
+Negative electrode reference concentration for free of deformation [mol.m-3],0,,
+Negative electrode partial molar volume [m3.mol-1],3.1e-6,,
+Negative electrode volume change,[function]graphite_volume_change_Ai2020,Ai 2020,
+,,,
+# Crack model,,,
+Negative electrode initial crack length [m],20e-9,,
+Negative electrode initial crack width [m],15e-9,,
+Negative electrode number of cracks per unit area [m-2],3.18e15,,
+Negative electrode Paris' law constant b,1.12,,
+Negative electrode Paris' law constant m,2.2,,
+Negative electrode cracking rate,[function]graphite_cracking_rate_Ai2020,,
+Negative electrode activation energy for cracking rate [J.mol-1],0,,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py
index 202efcd380..0108c24e99 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py
@@ -3,28 +3,28 @@
 
 def graphite_LGM50_diffusivity_Chen2020(sto, T):
     """
-      LG M50 Graphite diffusivity as a function of stochiometry, in this case the
-      diffusivity is taken to be a constant. The value is taken from [1].
+    LG M50 Graphite diffusivity as a function of stochiometry, in this case the
+    diffusivity is taken to be a constant. The value is taken from [1].
 
-      References
-      ----------
-      .. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
-      Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
-      Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
-      Electrochemical Society 167 (2020): 080534.
+    References
+    ----------
+    .. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
+    Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
+    Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
+    Electrochemical Society 167 (2020): 080534.
 
-      Parameters
-      ----------
-      sto: :class:`pybamm.Symbol`
-         Electrode stochiometry
-      T: :class:`pybamm.Symbol`
-         Dimensional temperature
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+       Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+       Dimensional temperature
 
-      Returns
-      -------
-      :class:`pybamm.Symbol`
-         Solid diffusivity
-   """
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+       Solid diffusivity
+    """
 
     D_ref = 3.3e-14
     E_D_s = 0  # to be implemented
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/parameters.csv
index 36af231e09..257a9f8f6e 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/parameters.csv
@@ -11,7 +11,6 @@ Negative electrode OCP [V],[data]graphite_LGM50_ocp_Chen2020,Chen 2020,
 Negative electrode porosity,0.25,Chen 2020,
 Negative electrode active material volume fraction,0.75,Chen 2020,
 Negative particle radius [m],5.86E-6,Chen 2020,
-Negative particle distribution in x,1,default,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Chen 2020,theoretical
 Negative electrode Bruggeman coefficient (electrode),1.5,default,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_diffusivity_Ecker2015.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_diffusivity_Ecker2015.py
index c792d5490a..91103baedc 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_diffusivity_Ecker2015.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_diffusivity_Ecker2015.py
@@ -28,7 +28,7 @@ def graphite_diffusivity_Ecker2015(sto, T):
     -------
     :class:`pybamm.Symbol`
         Solid diffusivity
-   """
+    """
 
     D_ref = 8.4e-13 * exp(-11.3 * sto) + 8.2e-15
     E_D_s = 3.03e4
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv
index f59ba699ae..771e702884 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv
@@ -13,7 +13,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Ecker2015_function,,
 Negative electrode porosity,0.329,,
 Negative electrode active material volume fraction, 0.372403,,
 Negative particle radius [m],1.37E-05,,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),1.6372789338386007,Solve for permeability factor B=0.162=eps^b,
 Negative electrode Bruggeman coefficient (electrode),0,No Bruggeman correction to the solid conductivity,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_diffusivity_Kim2011.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_diffusivity_Kim2011.py
index c247b5c167..5c76052c25 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_diffusivity_Kim2011.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_diffusivity_Kim2011.py
@@ -23,7 +23,7 @@ def graphite_diffusivity_Kim2011(sto, T):
     -------
     :class:`pybamm.Symbol`
         Solid diffusivity
-   """
+    """
 
     D_ref = 9 * 10 ** (-14)
     E_D_s = 4e3
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_ocp_Kim2011.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_ocp_Kim2011.py
index 0cbab00dde..f6de52db1b 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_ocp_Kim2011.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_ocp_Kim2011.py
@@ -3,15 +3,15 @@
 
 def graphite_ocp_Kim2011(sto):
     """
-       Graphite Open Circuit Potential (OCP) as a function of the stochiometry [1].
+    Graphite Open Circuit Potential (OCP) as a function of the stochiometry [1].
 
-       References
-       ----------
-       .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
-       (2011). Multi-domain modeling of lithium-ion batteries encompassing
-       multi-physics in varied length scales. Journal of The Electrochemical
-       Society, 158(8), A955-A969.
-       """
+    References
+    ----------
+    .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+    (2011). Multi-domain modeling of lithium-ion batteries encompassing
+    multi-physics in varied length scales. Journal of The Electrochemical
+    Society, 158(8), A955-A969.
+    """
 
     u_eq = (
         0.124
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv
index 7322e75402..0469e22fd8 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv
@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Kim2011,
 Negative electrode porosity,0.4,,
 Negative electrode active material volume fraction,0.51,,
 Negative particle radius [m],5.083E-7,,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),2,,
 Negative electrode Bruggeman coefficient (electrode),2,,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_entropic_change_Moura2016.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_entropic_change_Moura2016.py
index f0f1f11ee2..b629a321ec 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_entropic_change_Moura2016.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_entropic_change_Moura2016.py
@@ -3,18 +3,18 @@
 
 def graphite_entropic_change_Moura2016(sto, c_n_max):
     """
-        Graphite entropic change in open circuit potential (OCP) at a temperature of
-        298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code
-        [1].
+    Graphite entropic change in open circuit potential (OCP) at a temperature of
+    298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code
+    [1].
 
-        References
-        ----------
-        .. [1] https://github.com/scott-moura/fastDFN
+    References
+    ----------
+    .. [1] https://github.com/scott-moura/fastDFN
 
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_mcmb2528_diffusivity_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_mcmb2528_diffusivity_Dualfoil1998.py
index a4ec9f9f6d..5a9a868386 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_mcmb2528_diffusivity_Dualfoil1998.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/graphite_mcmb2528_diffusivity_Dualfoil1998.py
@@ -21,7 +21,7 @@ def graphite_mcmb2528_diffusivity_Dualfoil1998(sto, T):
     -------
     :class:`pybamm.Symbol`
         Solid diffusivity
-   """
+    """
 
     D_ref = 3.9 * 10 ** (-14)
     E_D_s = 42770
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv
index 12fba05b21..6d6511094a 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv
@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Ramadass2004,
 Negative electrode porosity,0.485,Ramadass,electrolyte volume fraction
 Negative electrode active material volume fraction,0.49,Ramadass,
 Negative particle radius [m],2e-06,Ramadass,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),4,Guess,
 Negative electrode Bruggeman coefficient (electrode),4,Ramadass,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_diffusivity_PeymanMPM.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_diffusivity_PeymanMPM.py
index d54e50e9e8..16880068e8 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_diffusivity_PeymanMPM.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_diffusivity_PeymanMPM.py
@@ -21,7 +21,7 @@ def graphite_diffusivity_PeymanMPM(sto, T):
     -------
     :class:`pybamm.Symbol`
         Solid diffusivity
-   """
+    """
 
     D_ref = 5.0 * 10 ** (-15)
     E_D_s = 42770
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_entropic_change_PeymanMPM.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_entropic_change_PeymanMPM.py
index 5724f8503a..5d9178c09e 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_entropic_change_PeymanMPM.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_entropic_change_PeymanMPM.py
@@ -1,17 +1,17 @@
 def graphite_entropic_change_PeymanMPM(sto, c_n_max):
     """
-        Graphite entropic change in open circuit potential (OCP) at a temperature of
-        298.15K as a function of the stochiometry taken from [1]
+    Graphite entropic change in open circuit potential (OCP) at a temperature of
+    298.15K as a function of the stochiometry taken from [1]
 
-        References
-        ----------
-        .. [1] K.E. Thomas, J. Newman, "Heats of mixing and entropy in porous insertion
-               electrode", J. of Power Sources 119 (2003) 844-849
+    References
+    ----------
+    .. [1] K.E. Thomas, J. Newman, "Heats of mixing and entropy in porous insertion
+           electrode", J. of Power Sources 119 (2003) 844-849
 
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_ocp_PeymanMPM.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_ocp_PeymanMPM.py
index f2e8528e2b..02a5bba688 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_ocp_PeymanMPM.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/graphite_ocp_PeymanMPM.py
@@ -3,13 +3,13 @@
 
 def graphite_ocp_PeymanMPM(sto):
     """
-       Graphite Open Circuit Potential (OCP) as a function of the
-       stochiometry. The fit is taken from Peyman MPM [1].
+    Graphite Open Circuit Potential (OCP) as a function of the
+    stochiometry. The fit is taken from Peyman MPM [1].
 
-       References
-       ----------
-       .. [1] Peyman Mohtat et al, MPM (to be submitted)
-       """
+    References
+    ----------
+    .. [1] Peyman Mohtat et al, MPM (to be submitted)
+    """
 
     u_eq = (
         0.063
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/parameters.csv
index 7f4b9188fb..315908eecb 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/parameters.csv
@@ -12,7 +12,6 @@ Negative electrode OCP [V],[function]graphite_ocp_PeymanMPM,Peyman MPM,
 Negative electrode porosity,0.3,Peyman MPM,
 Negative electrode active material volume fraction,0.61,Peyman MPM,rest is binder
 Negative particle radius [m],2.5E-06,Peyman MPM,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrode),1.5,Peyman MPM,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Peyman MPM,
 Negative electrode tortuosity, 0.16,
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_entropic_change_Moura2016.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_entropic_change_Moura2016.py
index f0f1f11ee2..b629a321ec 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_entropic_change_Moura2016.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_entropic_change_Moura2016.py
@@ -3,18 +3,18 @@
 
 def graphite_entropic_change_Moura2016(sto, c_n_max):
     """
-        Graphite entropic change in open circuit potential (OCP) at a temperature of
-        298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code
-        [1].
+    Graphite entropic change in open circuit potential (OCP) at a temperature of
+    298.15K as a function of the stochiometry taken from Scott Moura's FastDFN code
+    [1].
 
-        References
-        ----------
-        .. [1] https://github.com/scott-moura/fastDFN
+    References
+    ----------
+    .. [1] https://github.com/scott-moura/fastDFN
 
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_diffusivity_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_diffusivity_Dualfoil1998.py
index a4ec9f9f6d..5a9a868386 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_diffusivity_Dualfoil1998.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_diffusivity_Dualfoil1998.py
@@ -21,7 +21,7 @@ def graphite_mcmb2528_diffusivity_Dualfoil1998(sto, T):
     -------
     :class:`pybamm.Symbol`
         Solid diffusivity
-   """
+    """
 
     D_ref = 3.9 * 10 ** (-14)
     E_D_s = 42770
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_ocp_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_ocp_Dualfoil1998.py
index 60004b3c1a..5ed6f91755 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_ocp_Dualfoil1998.py
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/graphite_mcmb2528_ocp_Dualfoil1998.py
@@ -3,15 +3,15 @@
 
 def graphite_mcmb2528_ocp_Dualfoil1998(sto):
     """
-       Graphite MCMB 2528 Open Circuit Potential (OCP) as a function of the
-       stochiometry. The fit is taken from Dualfoil [1]. Dualfoil states that the data
-       was measured by Chris Bogatu at Telcordia and PolyStor materials, 2000. However,
-       we could not find any other records of this measurment.
+    Graphite MCMB 2528 Open Circuit Potential (OCP) as a function of the
+    stochiometry. The fit is taken from Dualfoil [1]. Dualfoil states that the data
+    was measured by Chris Bogatu at Telcordia and PolyStor materials, 2000. However,
+    we could not find any other records of this measurment.
 
-       References
-       ----------
-       .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
-       """
+    References
+    ----------
+    .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+    """
 
     u_eq = (
         0.194
diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/parameters.csv b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/parameters.csv
index 02f5ad6747..abc612b06d 100644
--- a/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/parameters.csv
@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_mcmb2528_ocp_Dualfoil1998,
 Negative electrode porosity,0.3,Scott Moura FastDFN,electrolyte volume fraction
 Negative electrode active material volume fraction,0.6,,
 Negative particle radius [m],1E-05,Scott Moura FastDFN,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Scott Moura FastDFN,
 Negative electrode Bruggeman coefficient (electrode),1.5,Scott Moura FastDFN,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_electrolyte_exchange_current_density_kashkooli2017.py b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_electrolyte_exchange_current_density_kashkooli2017.py
new file mode 100644
index 0000000000..083c352806
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_electrolyte_exchange_current_density_kashkooli2017.py
@@ -0,0 +1,37 @@
+from pybamm import exp, constants, Parameter
+
+
+def LFP_electrolyte_exchange_current_density_kashkooli2017(c_e, c_s_surf, T):  # , 1
+    """
+    Exchange-current density for Butler-Volmer reactions between LFP and electrolyte
+
+    References
+    ----------
+    .. [1] Kashkooli, A. G., Amirfazli, A., Farhad, S., Lee, D. U., Felicelli, S., Park,
+    H. W., ... & Chen, Z. (2017). Representative volume element model of lithium-ion
+    battery electrodes based on X-ray nano-tomography. Journal of Applied
+    Electrochemistry, 47(3), 281-293.
+
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+
+    m_ref = 6 * 10 ** (-7)  # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 39570
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+    c_p_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_p_max - c_s_surf) ** 0.5
+    )
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_ocp_ashfar2017.py b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_ocp_ashfar2017.py
new file mode 100644
index 0000000000..9695acfe4b
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/LFP_ocp_ashfar2017.py
@@ -0,0 +1,24 @@
+from pybamm import exp
+
+
+def LFP_ocp_ashfar2017(sto):
+    """
+    Open-circuit potential for LFP
+
+    References
+    ----------
+    .. [1] Afshar, S., Morris, K., & Khajepour, A. (2017). Efficient electrochemical
+    model for lithium-ion cells. arXiv preprint arXiv:1709.03970.
+
+    Parameters
+    ----------
+    sto : :class:`pybamm.Symbol`
+       Stochiometry of material (li-fraction)
+
+    """
+
+    c1 = -150 * sto
+    c2 = -30 * (1 - sto)
+    k = 3.4077 - 0.020269 * sto + 0.5 * exp(c1) - 0.9 * exp(c2)
+
+    return k
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/README.md b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/README.md
new file mode 100644
index 0000000000..e1a3841858
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/README.md
@@ -0,0 +1,7 @@
+# Lithium Iron Phosphate cathode parameters
+
+Parameters for an LFP cathode, from the paper
+
+> Prada, E., Di Domenico, D., Creff, Y., Bernard, J., Sauvant-Moynot, V., & Huet, F. (2013). A simplified electrochemical and thermal aging model of LiFePO4-graphite Li-ion batteries: power and capacity fade simulations. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.053304jes), 160(4), A616.
+
+and references therein. The functions used for OCP and exchange-current density are from separate references (documented within the functions), to provide better fit to data
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/parameters.csv
new file mode 100644
index 0000000000..f2de48cd58
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/parameters.csv
@@ -0,0 +1,34 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with # will be ignored,,,
+,,,
+# Electrode properties,,,
+Positive electrode conductivity [S.m-1],0.33795074,"Calculation, consistant with Hosseinzadeh 2018",
+Maximum concentration in positive electrode [mol.m-3],22806,Prada Thermal Aging,
+Positive electrode diffusivity [m2.s-1],5.90E-18,Prada Fast Charging,
+Positive electrode OCP [V],[function]LFP_ocp_ashfar2017,,
+,,,
+# Microstructure,,,
+Positive electrode porosity,0.12728395,Calculation minimized to Severson,
+Positive electrode active material volume fraction,0.28485556,Calculation minimized to Severson,
+Positive particle radius [m],1.00E-08,Calculation minimized to Severson,
+Positive electrode Bruggeman coefficient (electrode),1.5,,
+Positive electrode Bruggeman coefficient (electrolyte),1.5,,
+,,,
+# Interfacial reactions,,,
+Positive electrode cation signed stoichiometry,-1,,
+Positive electrode electrons in reaction,1,,
+Reference OCP vs SHE in the positive electrode [V],,adjust,
+Positive electrode charge transfer coefficient,0.5,adjust,
+Positive electrode double-layer capacity [F.m-2],0.2,adjust,
+,,,
+# Density,,,
+Positive electrode density [kg.m-3],2341.17,default,
+,,,
+,,,
+# Thermal parameters,,,
+Positive electrode specific heat capacity [J.kg-1.K-1],1100,,
+Positive electrode thermal conductivity [W.m-1.K-1],2.1,,
+Positive electrode OCP entropic change [V.K-1],0,,
+,,,
+# exchange-current density,,,
+Positive electrode exchange-current density [A.m-2],[function]LFP_electrolyte_exchange_current_density_kashkooli2017,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv
index 3e13409322..13cb9769b5 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv
@@ -13,7 +13,6 @@ Positive electrode OCP [V],[function]nco_ocp_Ecker2015_function,,
 Positive electrode porosity,0.296,,
 Positive electrode active material volume fraction, 0.40832,,
 Positive particle radius [m],6.5E-06,,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),1.5442267190786427,Solve for permeability factor B=0.1526=eps^b,
 Positive electrode Bruggeman coefficient (electrode),0,No Bruggeman correction to solid conductivity,
 Positive electrode exchange-current density [A.m-2],[function]nco_electrolyte_exchange_current_density_Ecker2015,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/NMC_entropic_change_PeymanMPM.py b/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/NMC_entropic_change_PeymanMPM.py
index 60fa6ecaa5..afb7762473 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/NMC_entropic_change_PeymanMPM.py
+++ b/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/NMC_entropic_change_PeymanMPM.py
@@ -3,20 +3,20 @@
 
 def NMC_entropic_change_PeymanMPM(sto, c_p_max):
     """
-        Nickel Manganese Cobalt (NMC) entropic change in open circuit potential (OCP) at
-        a temperature of 298.15K as a function of the OCP. The fit is taken from [1].
-
-        References
-        ----------
-        .. [1] W. Le, I. Belharouak, D. Vissers, K. Amine, "In situ thermal study of
-        li1+ x [ni1/ 3co1/ 3mn1/ 3] 1- x o2 using isothermal micro-clorimetric
-        techniques",
-        J. of the Electrochemical Society 153 (11) (2006) A2147–A2151.
-
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+    Nickel Manganese Cobalt (NMC) entropic change in open circuit potential (OCP) at
+    a temperature of 298.15K as a function of the OCP. The fit is taken from [1].
+
+    References
+    ----------
+    .. [1] W. Le, I. Belharouak, D. Vissers, K. Amine, "In situ thermal study of
+    li1+ x [ni1/ 3co1/ 3mn1/ 3] 1- x o2 using isothermal micro-clorimetric
+    techniques",
+    J. of the Electrochemical Society 153 (11) (2006) A2147–A2151.
+
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/parameters.csv
index 94d301c422..ef0ac497f6 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/parameters.csv
@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]NMC_ocp_PeymanMPM,,
 Positive electrode porosity,0.3,Peyman MPM,
 Positive electrode active material volume fraction,0.445,Peyman MPM,rest is binder
 Positive particle radius [m],3.5E-06,Peyman MPM,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrode),1.5,Peyman MPM,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Peyman MPM,
 Positive electrode tortuosity,0.16,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/README.md
new file mode 100644
index 0000000000..bd1c479e41
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/README.md
@@ -0,0 +1,9 @@
+# Lithium Cobalt Oxide cathode parameters
+
+Parameters for a lithium Cobalt Oxide cathode, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_cracking_rate_Ai2020.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_cracking_rate_Ai2020.py
new file mode 100644
index 0000000000..e445d697c2
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_cracking_rate_Ai2020.py
@@ -0,0 +1,35 @@
+from pybamm import Parameter, constants, exp
+
+
+def lico2_cracking_rate_Ai2020(T_dim):
+    """
+    lico2 particle cracking rate as a function of temperature [1, 2].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+     Battery cycle life prediction with coupled chemical degradation and fatigue
+     mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    Parameters
+    ----------
+    T: :class:`pybamm.Symbol`
+        temperature, [K]
+
+    Returns
+    -------
+    k_cr: :class:`pybamm.Symbol`
+        cracking rate, [m/(Pa.m0.5)^m_cr]
+        where m_cr is another Paris' law constant
+    """
+    k_cr = 3.9e-20
+    T_ref = Parameter("Reference temperature [K]")
+    Eac_cr = Parameter(
+        "Positive electrode activation energy for cracking rate [J.mol-1]"
+    )
+    arrhenius = exp(Eac_cr / constants.R * (1 / T_dim - 1 / T_ref))
+    return k_cr * arrhenius
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_diffusivity_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_diffusivity_Dualfoil1998.py
new file mode 100644
index 0000000000..7cd095336a
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_diffusivity_Dualfoil1998.py
@@ -0,0 +1,29 @@
+from pybamm import exp, constants, Parameter
+
+
+def lico2_diffusivity_Dualfoil1998(sto, T):
+    """
+    LiCo2 diffusivity as a function of stochiometry, in this case the
+    diffusivity is taken to be a constant. The value is taken from Dualfoil [1].
+
+    References
+    ----------
+    .. [1] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature, [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity [m2.s-1]
+    """
+    D_ref = 5.387 * 10 ** (-15)
+    E_D_s = 5000
+    T_ref = Parameter("Reference temperature [K]")
+    arrhenius = exp(E_D_s / constants.R * (1 / T_ref - 1 / T))
+    return D_ref * arrhenius
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_electrolyte_exchange_current_density_Dualfoil1998.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_electrolyte_exchange_current_density_Dualfoil1998.py
new file mode 100644
index 0000000000..3fec659a0e
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_electrolyte_exchange_current_density_Dualfoil1998.py
@@ -0,0 +1,36 @@
+from pybamm import exp, constants, Parameter
+
+
+def lico2_electrolyte_exchange_current_density_Dualfoil1998(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between lico2 and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    m_ref = 1 * 10 ** (-11) * constants.F  # need to match the unit from m/s
+    # (A/m2)(mol/m3)**1.5 - includes ref concentrations
+    E_r = 5000
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    c_p_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_p_max - c_s_surf) ** 0.5
+    )
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020.csv b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020.csv
new file mode 100644
index 0000000000..e3484e6b4f
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020.csv
@@ -0,0 +1,12 @@
+# Entropy for lico2	from Ai 2020
+# Just for reference against lico2_entropic_change_Ai2020_function
+# stoichiometry , entropic change [mV.K-1]
+0.450912106, 	-0.165164656
+0.519320066, 	-0.235038471
+0.587728027, 	-0.299562966
+0.657960199, 	-0.369445652
+0.725456053, 	-0.433965712
+0.794776119, 	-0.538614535
+0.86318408, 	-0.56034448
+0.932504146, 	-0.464393844
+1, 	-0.507521064
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020_function.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020_function.py
new file mode 100644
index 0000000000..fb5357bf08
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_entropic_change_Ai2020_function.py
@@ -0,0 +1,49 @@
+def lico2_entropic_change_Ai2020_function(sto, T):
+    """
+        Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
+        a temperature of 298.15K as a function of the stochiometry. The fit is taken
+        from Ref [1], which is only accurate
+       for 0.43 < sto < 0.9936.
+
+        References
+        ----------
+        .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+        Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity
+        in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society,
+         167(1), 013512. DOI: 10.1149/2.0122001JES
+
+    Parameters
+    ----------
+    sto: double
+       Stochiometry of material (li-fraction)
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Entropic change [V.K-1]
+    """
+
+    # Since the equation for LiCo2 from this ref. has the stretch factor,
+    # should this too? If not, the "bumps" in the OCV don't line up.
+    p1 = -3.20392657
+    p2 = 14.5719049
+    p3 = -27.9047599
+    p4 = 29.1744564
+    p5 = -17.992018
+    p6 = 6.54799331
+    p7 = -1.30382445
+    p8 = 0.109667298
+
+    du_dT = (
+        p1 * sto ** 7
+        + p2 * sto ** 6
+        + p3 * sto ** 5
+        + p4 * sto ** 4
+        + p5 * sto ** 3
+        + p6 * sto ** 2
+        + p7 * sto
+        + p8
+    )
+    # show no temperature dependence
+    return du_dT
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020.csv b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020.csv
new file mode 100644
index 0000000000..ffd7886e2b
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020.csv
@@ -0,0 +1,448 @@
+# OCP for lico2 from Rieger 2016 
+# stoichiometry , OCP [V]
+0.43,4.3
+0.436639784,4.279907753
+0.437906143,4.276472669
+0.439172502,4.273800938
+0.44043886,4.271129206
+0.441705219,4.268648313
+0.442971578,4.266167419
+0.444237937,4.263686526
+0.445504296,4.261205633
+0.446770655,4.258724739
+0.448037014,4.256243846
+0.449303373,4.253762952
+0.450569732,4.251282059
+0.45183609,4.248992003
+0.453102449,4.24651111
+0.454368808,4.244221054
+0.455635167,4.24174016
+0.456901526,4.239259267
+0.458167885,4.236969211
+0.459434244,4.234679156
+0.460700603,4.232198262
+0.461966961,4.229717369
+0.46323332,4.227236475
+0.464499679,4.225137258
+0.465766038,4.222656364
+0.467032397,4.220366309
+0.468298756,4.217885415
+0.469565115,4.21559536
+0.470831474,4.213305304
+0.472097833,4.211015249
+0.473364191,4.208534355
+0.47463055,4.2062443
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+0.479695986,4.197084078
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diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020_function.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020_function.py
new file mode 100644
index 0000000000..42ecd15ea2
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_ocp_Ai2020_function.py
@@ -0,0 +1,47 @@
+def lico2_ocp_Ai2020_function(sto):
+    """
+     Lithium Cobalt Oxide (LiCO2) Open Circuit Potential (OCP) as a a function of the
+     stochiometry. The fit is taken from the Enertech cell [1], which is only accurate
+        for 0.435 < sto < 0.9651.
+
+     References
+     ----------
+     .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical
+     Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells.
+     Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES
+
+     Parameters
+     ----------
+     sto: double
+        Stochiometry of material (li-fraction)
+
+    Returns
+     -------
+     :class:`pybamm.Symbol`
+         OCP [V]
+
+    """
+
+    p1 = -107897.40
+    p2 = 677406.28
+    p3 = -1873803.91
+    p4 = 2996535.44
+    p5 = -3052331.36
+    p6 = 2053377.31
+    p7 = -912135.88
+    p8 = 257964.35
+    p9 = -42146.98
+    p10 = 3035.67
+    u_eq = (
+        p1 * sto ** 9
+        + p2 * sto ** 8
+        + p3 * sto ** 7
+        + p4 * sto ** 6
+        + p5 * sto ** 5
+        + p6 * sto ** 4
+        + p7 * sto ** 3
+        + p8 * sto ** 2
+        + p9 * sto
+        + p10
+    )
+    return u_eq
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_volume_change_Ai2020.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_volume_change_Ai2020.py
new file mode 100644
index 0000000000..e36b9cd036
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/lico2_volume_change_Ai2020.py
@@ -0,0 +1,31 @@
+from pybamm import Parameter
+
+
+def lico2_volume_change_Ai2020(sto):
+    """
+    lico2 particle volume change as a function of stochiometry [1, 2].
+
+    References
+    ----------
+     .. [1] > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+     Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in
+     Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512
+      DOI: 10.1149/2.0122001JES.
+     .. [2] > Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016).
+     A new method to model the thickness change of a commercial pouch cell
+     during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+    Parameters
+    ----------
+    sto: :class:`pybamm.Symbol`
+        Electrode stochiometry, dimensionless
+        should be R-averaged particle concentration
+    Returns
+    -------
+    t_change:class:`pybamm.Symbol`
+        volume change, dimensionless, normalised by particle volume
+    """
+    omega = Parameter("Positive electrode partial molar volume [m3.mol-1]")
+    c_p_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")
+    t_change = omega * c_p_max * sto
+    return t_change
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/parameters.csv
new file mode 100644
index 0000000000..88df496316
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ai2020/parameters.csv
@@ -0,0 +1,49 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrode properties,,,
+Positive electrode conductivity [S.m-1],10,Ai 2020,lithium cobalt oxide
+Maximum concentration in positive electrode [mol.m-3],49943,Ai 2020,
+Positive electrode diffusivity [m2.s-1],[function]lico2_diffusivity_Dualfoil1998,,
+Positive electrode OCP [V],[data]lico2_ocp_Ai2020,,
+,,,
+# Microstructure,,,
+Positive electrode porosity,0.32,Ai 2020,electrolyte volume fraction
+Positive electrode active material volume fraction,0.62,,assuming zero binder volume fraction
+Positive particle radius [m],3E-06,Ai 2020,
+Positive electrode surface area to volume ratio [m-1],620000,Ai 2020,
+Positive electrode Bruggeman coefficient (electrolyte),1.83,Ai 2020,
+Positive electrode Bruggeman coefficient (electrode),0,Ai 2020,
+,,,
+# Interfacial reactions,,,
+Positive electrode cation signed stoichiometry,-1,,
+Positive electrode electrons in reaction,1,,
+Reference OCP vs SHE in the positive electrode [V],,,
+Positive electrode charge transfer coefficient,0.5,Ai 2020,
+Negative electrode double-layer capacity [F.m-2],0,,#??
+Positive electrode exchange-current density [A.m-2],[function]lico2_electrolyte_exchange_current_density_Dualfoil1998,,
+,,,
+# Density,,,
+Positive electrode density [kg.m-3],2470,,
+,,,
+# Thermal parameters,,,
+Positive electrode specific heat capacity [J.kg-1.K-1],1080.2,,
+Positive electrode thermal conductivity [W.m-1.K-1],1.58,,
+Positive electrode OCP entropic change [V.K-1],[function]lico2_entropic_change_Ai2020_function,,
+# Positive electrode OCP entropic change [V.K-1],0,,
+,,,
+# mechanical properties,,,
+Positive electrode Poisson's ratio,0.2,,
+Positive electrode Young's modulus [Pa],375e9,,
+Positive electrode reference concentration for free of deformation [mol.m-3],0,,
+Positive electrode partial molar volume [m3.mol-1],-7.28e-7,,
+Positive electrode volume change,[function]lico2_volume_change_Ai2020,Ai 2020,
+,,,
+# Crack model,,,
+Positive electrode initial crack length [m],20e-9,,
+Positive electrode initial crack width [m],15e-9,,
+Positive electrode number of cracks per unit area [m-2],3.18e15,,
+Positive electrode Paris' law constant b,1.12,,
+Positive electrode Paris' law constant m,2.2,,
+Positive electrode cracking rate,[function]lico2_cracking_rate_Ai2020,,
+Positive electrode activation energy for cracking rate [J.mol-1],0,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/lico2_entropic_change_Moura2016.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/lico2_entropic_change_Moura2016.py
index 9f3baeb4e6..3938d7dcd6 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/lico2_entropic_change_Moura2016.py
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/lico2_entropic_change_Moura2016.py
@@ -3,18 +3,18 @@
 
 def lico2_entropic_change_Moura2016(sto, c_p_max):
     """
-        Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
-        a temperature of 298.15K as a function of the stochiometry. The fit is taken
-        from Scott Moura's FastDFN code [1].
-
-        References
-        ----------
-        .. [1] https://github.com/scott-moura/fastDFN
-
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+    Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
+    a temperature of 298.15K as a function of the stochiometry. The fit is taken
+    from Scott Moura's FastDFN code [1].
+
+    References
+    ----------
+    .. [1] https://github.com/scott-moura/fastDFN
+
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/parameters.csv
index 93d0b43ed0..99cec014e3 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/parameters.csv
@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]lico2_ocp_Dualfoil1998,,
 Positive electrode porosity,0.3,Scott Moura FastDFN,electrolyte volume fraction
 Positive electrode active material volume fraction,0.5,,
 Positive particle radius [m],1E-05,Scott Moura FastDFN,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Scott Moura FastDFN,
 Positive electrode Bruggeman coefficient (electrode),1.5,Scott Moura FastDFN,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_entropic_change_Moura2016.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_entropic_change_Moura2016.py
index 9f3baeb4e6..3938d7dcd6 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_entropic_change_Moura2016.py
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_entropic_change_Moura2016.py
@@ -3,18 +3,18 @@
 
 def lico2_entropic_change_Moura2016(sto, c_p_max):
     """
-        Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
-        a temperature of 298.15K as a function of the stochiometry. The fit is taken
-        from Scott Moura's FastDFN code [1].
-
-        References
-        ----------
-        .. [1] https://github.com/scott-moura/fastDFN
-
-          Parameters
-          ----------
-          sto : :class:`pybamm.Symbol`
-               Stochiometry of material (li-fraction)
+    Lithium Cobalt Oxide (LiCO2) entropic change in open circuit potential (OCP) at
+    a temperature of 298.15K as a function of the stochiometry. The fit is taken
+    from Scott Moura's FastDFN code [1].
+
+    References
+    ----------
+    .. [1] https://github.com/scott-moura/fastDFN
+
+      Parameters
+      ----------
+      sto : :class:`pybamm.Symbol`
+           Stochiometry of material (li-fraction)
 
     """
 
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_ocp_Ramadass2004.py b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_ocp_Ramadass2004.py
index 7a5e34a622..8541121a84 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_ocp_Ramadass2004.py
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/lico2_ocp_Ramadass2004.py
@@ -1,4 +1,3 @@
-
 def lico2_ocp_Ramadass2004(sto):
     """
     Lithium Cobalt Oxide (LiCO2) Open Circuit Potential (OCP) as a a function of the
@@ -21,12 +20,20 @@ def lico2_ocp_Ramadass2004(sto):
     stretch = 1.13
     sto = stretch * sto
 
-    u_eq = ((- 4.656 + 88.669 * (sto ** 2)
-             - 401.119 * (sto ** 4) + 342.909 * (sto ** 6)
-             - 462.471 * (sto ** 8) + 433.434 * (sto ** 10)) / (
-                 - 1 + 18.933 * (sto ** 2) - 79.532 * (sto ** 4)
-                 + 37.311 * (sto ** 6) - 73.083 * (sto ** 8)
-                 + 95.96 * (sto ** 10))
-            )
+    u_eq = (
+        -4.656
+        + 88.669 * (sto ** 2)
+        - 401.119 * (sto ** 4)
+        + 342.909 * (sto ** 6)
+        - 462.471 * (sto ** 8)
+        + 433.434 * (sto ** 10)
+    ) / (
+        -1
+        + 18.933 * (sto ** 2)
+        - 79.532 * (sto ** 4)
+        + 37.311 * (sto ** 6)
+        - 73.083 * (sto ** 8)
+        + 95.96 * (sto ** 10)
+    )
 
     return u_eq
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/parameters.csv
index 8d26275f26..08954e4444 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/parameters.csv
@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]lico2_ocp_Ramadass2004,,
 Positive electrode porosity,0.385,Ramadass,electrolyte volume fraction
 Positive electrode active material volume fraction,0.59,Ramadass,
 Positive particle radius [m],2e-06,Ramadass,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),4,Ramadass,
 Positive electrode Bruggeman coefficient (electrode),4,Ramadass,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/nca_Kim2011/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/nca_Kim2011/parameters.csv
index 0a0f00fe42..767566934b 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/nca_Kim2011/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/nca_Kim2011/parameters.csv
@@ -11,7 +11,6 @@ Positive electrode OCP [V],[data]nca_ocp_Kim2011_data,
 Positive electrode porosity,0.4,,
 Positive electrode active material volume fraction,0.41,,
 Positive particle radius [m],1.633E-6,,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),2,,
 Positive electrode Bruggeman coefficient (electrode),2,,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/nmc_LGM50_diffusivity_Chen2020.py b/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/nmc_LGM50_diffusivity_Chen2020.py
index ec95615e09..d5b52e55a0 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/nmc_LGM50_diffusivity_Chen2020.py
+++ b/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/nmc_LGM50_diffusivity_Chen2020.py
@@ -3,27 +3,27 @@
 
 def nmc_LGM50_diffusivity_Chen2020(sto, T):
     """
-       NMC diffusivity as a function of stoichiometry, in this case the
-       diffusivity is taken to be a constant. The value is taken from [1].
+     NMC diffusivity as a function of stoichiometry, in this case the
+     diffusivity is taken to be a constant. The value is taken from [1].
 
-       References
-       ----------
-      .. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
-      Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
-      Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
-      Electrochemical Society 167 (2020): 080534.
+     References
+     ----------
+    .. [1] Chang-Hui Chen, Ferran Brosa Planella, Kieran O’Regan, Dominika Gastol, W.
+    Dhammika Widanage, and Emma Kendrick. "Development of Experimental Techniques for
+    Parameterization of Multi-scale Lithium-ion Battery Models." Journal of the
+    Electrochemical Society 167 (2020): 080534.
 
-       Parameters
-       ----------
-       sto: :class:`pybamm.Symbol`
-         Electrode stochiometry
-       T: :class:`pybamm.Symbol`
-          Dimensional temperature
+     Parameters
+     ----------
+     sto: :class:`pybamm.Symbol`
+       Electrode stochiometry
+     T: :class:`pybamm.Symbol`
+        Dimensional temperature
 
-       Returns
-       -------
-       :class:`pybamm.Symbol`
-          Solid diffusivity
+     Returns
+     -------
+     :class:`pybamm.Symbol`
+        Solid diffusivity
     """
 
     D_ref = 4e-15
diff --git a/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/parameters.csv b/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/parameters.csv
index 997f4ba416..c49b71cf93 100644
--- a/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/parameters.csv
@@ -11,7 +11,6 @@ Positive electrode OCP [V],[data]nmc_LGM50_ocp_Chen2020,Chen 2020,
 Positive electrode porosity,0.335,Chen 2020,
 Positive electrode active material volume fraction,0.665,Chen 2020,
 Positive particle radius [m],5.22E-6,Chen 2020,
-Positive particle distribution in x,1,default,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Chen 2020,theoretical
 Positive electrode Bruggeman coefficient (electrode),1.5,default,
 ,,,
diff --git a/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/README.md b/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/README.md
new file mode 100644
index 0000000000..8c1bc70405
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/README.md
@@ -0,0 +1,5 @@
+# Pouch cell parameters
+
+Parameters for an A123 LFP cell, from the paper
+
+> Lain, M. J., Brandon, J., & Kendrick, E. (2019). Design Strategies for High Power vs. High Energy Lithium Ion Cells. [Batteries](https://doi.org/10.3390/batteries5040064), 5(4), 64.
diff --git a/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/parameters.csv b/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/parameters.csv
new file mode 100644
index 0000000000..3056894a56
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cells/A123_Lain2019/parameters.csv
@@ -0,0 +1,37 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Macroscale geometry,,,
+Negative current collector thickness [m],1.00E-05,Lain 2019,
+Negative electrode thickness [m],3.60E-05,Lain 2019,
+Separator thickness [m],1.80E-05,Lain 2019,
+Positive electrode thickness [m],8.10E-05,Lain 2019,
+Positive current collector thickness [m],1.90E-05,Lain 2019,
+Electrode height [m],6.49E-02,A123 18650 datasheet,Not needed for 1D
+Electrode width [m],1.78,fit to Severson 2019,Not needed for 1D
+Negative tab width [m],0.04,default,Not needed for 1D
+Negative tab centre y-coordinate [m],0.06,default,Not needed for 1D
+Negative tab centre z-coordinate [m],0.137,default,Not needed for 1D
+Positive tab width [m],0.04,default,Not needed for 1D
+Positive tab centre y-coordinate [m],0.147,default,Not needed for 1D
+Positive tab centre z-coordinate [m],0.137,default,Not needed for 1D
+,,,
+# Current collector properties ,,,
+Negative current collector conductivity [S.m-1],58411000,CRC Handbook,copper
+Positive current collector conductivity [S.m-1],36914000,CRC Handbook,aluminium
+,,,
+# Density,,,
+Negative current collector density [kg.m-3],8960,CRC Handbook,copper
+Positive current collector density [kg.m-3],2700,CRC Handbook,aluminium
+,,,
+# Specific heat capacity,,,
+Negative current collector specific heat capacity [J.kg-1.K-1],385,CRC Handbook,copper
+Positive current collector specific heat capacity [J.kg-1.K-1],897,CRC Handbook,aluminium
+,,,
+# Thermal conductivity,,,
+Negative current collector thermal conductivity [W.m-1.K-1],401,CRC Handbook,copper
+Positive current collector thermal conductivity [W.m-1.K-1],237,CRC Handbook,aluminium
+,,,
+# Electrical,,,
+Cell capacity [A.h],1.1,Lain 2019,
+Typical current [A],30,Lain 2019,
diff --git a/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/README.md
new file mode 100644
index 0000000000..af5ffdd828
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/README.md
@@ -0,0 +1,9 @@
+# Enertech cell parameters
+
+Parameters for the Enertech cell, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/parameters.csv
new file mode 100644
index 0000000000..a11764f2ab
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/cells/Enertech_Ai2020/parameters.csv
@@ -0,0 +1,36 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Macroscale geometry,,,
+Negative current collector thickness [m],10E-6,Ai 2020,
+Negative electrode thickness [m],76.5E-6,Ai 2020,
+Separator thickness [m],25E-6,Ai 2020,
+Positive electrode thickness [m],68E-6,Ai 2020,
+Positive current collector thickness [m],15E-6,Ai 2020,
+Electrode height [m],51E-3,Ai 2020,Not needed for 1D
+Electrode width [m],47E-3,Ai 2020,Not needed for 1D
+Cell cooling surface area [m2],60.484E-4,Ai 2020, pouch
+Cell volume [m3],1.5341E-5,Ai 2020, pouch
+Cell emissivity,0.95,Ai 2020,estimation
+Cell thermal expansion coefficien [m.K-1], 1.1E-6,Ai 2020,
+,,,
+# Current collector properties ,,,
+Negative current collector conductivity [S.m-1],58411000,CRC Handbook,copper
+Positive current collector conductivity [S.m-1],36914000,CRC Handbook,aluminium
+,,,
+# Density,,,
+Negative current collector density [kg.m-3],8960,CRC Handbook,copper
+Positive current collector density [kg.m-3],2700,CRC Handbook,aluminium
+,,,
+# Specific heat capacity,,,
+Negative current collector specific heat capacity [J.kg-1.K-1],385,CRC Handbook,copper
+Positive current collector specific heat capacity [J.kg-1.K-1],897,CRC Handbook,aluminium
+,,,
+# Thermal conductivity,,,
+Negative current collector thermal conductivity [W.m-1.K-1],401,CRC Handbook,copper
+Positive current collector thermal conductivity [W.m-1.K-1],237,CRC Handbook,aluminium
+,,,
+# Electrical,,,
+Cell capacity [A.h], 2.28,Ai 2020,2.28/34
+Typical current [A], 2.28,Ai 2020,
+Current function [A], 2.28,default current function,
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/cells/UMBL_Mohtat2020/parameters.csv b/pybamm/input/parameters/lithium-ion/cells/UMBL_Mohtat2020/parameters.csv
index bfe0cb39ba..7f2492965d 100644
--- a/pybamm/input/parameters/lithium-ion/cells/UMBL_Mohtat2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/cells/UMBL_Mohtat2020/parameters.csv
@@ -10,7 +10,7 @@ Positive current collector thickness [m],2.5E-05,Scott Moura FastDFN,no info fro
 Electrode height [m],1,KOKAM SLPB78205130H,Not needed for 1D
 Electrode width [m],0.2050,KOKAM SLPB78205130H,Not needed for 1D
 Cell cooling surface area [m2],0.41,,pouch
-Cell volume [m3]3.92E-5,,pouch
+Cell volume [m3],3.92E-5,,pouch
 ,,,
 # Current collector properties ,,,
 Negative current collector conductivity [S.m-1],59600000,LIONSIMBA,carbon
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/README.md
new file mode 100644
index 0000000000..a81234481f
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/README.md
@@ -0,0 +1,9 @@
+# LiPF6 electrolyte parameters
+
+Parameters for a LiPF6 electrolyte, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/dlnf_dlnc_Ai2020.py b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/dlnf_dlnc_Ai2020.py
new file mode 100644
index 0000000000..51ae614ec1
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/dlnf_dlnc_Ai2020.py
@@ -0,0 +1,34 @@
+from pybamm import Parameter
+
+
+def dlnf_dlnc_Ai2020(c_e, T, T_ref=298.3, t_plus=0.38):
+    """
+    Activity dependence of LiPF6 in EC:DMC as a function of ion concentration.
+
+    References
+    ----------
+    .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+    Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity
+    in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society,
+    167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+    Parameters
+    ----------
+    c_e: :class:`pybamm.Symbol`
+        Dimensional electrolyte concentration, mol/m^3
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature, K
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        1 + dlnf/dlnc
+    """
+    T_ref = Parameter("Reference temperature [K]")
+    t_plus = Parameter("Cation transference number")
+    dlnf_dlnc = (
+        0.601
+        - 0.24 * (c_e / 1000) ** 0.5
+        + 0.982 * (1 - 0.0052 * (T - T_ref)) * (c_e / 1000) ** 1.5
+    ) / (1 - t_plus)
+    return dlnf_dlnc
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_conductivity_Ai2020.py b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_conductivity_Ai2020.py
new file mode 100644
index 0000000000..a6d0bf07dc
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_conductivity_Ai2020.py
@@ -0,0 +1,40 @@
+def electrolyte_conductivity_Ai2020(c_e, T):
+    """
+    Conductivity of LiPF6 in EC:DMC as a function of ion concentration.
+    Concentration should be in dm3 in the function.
+
+    References
+    ----------
+    .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+    Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity
+    in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society,
+    167(1), 013512. DOI: 10.1149/2.0122001JES.
+    .. [2] Torchio, Marcello, et al. "Lionsimba: a matlab framework based
+    on a finite volume model suitable for li-ion battery design, simulation,
+    and control." Journal of The Electrochemical Society 163.7 (2016): A1192.
+
+    Parameters
+    ----------
+    c_e: :class:`pybamm.Symbol`
+        Dimensional electrolyte concentration
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    sigma_e = (
+        1e-4
+        * c_e
+        * (
+            (-10.5 + 0.668 * 1e-3 * c_e + 0.494 * 1e-6 * c_e ** 2)
+            + (0.074 - 1.78 * 1e-5 * c_e - 8.86 * 1e-10 * c_e ** 2) * T
+            + (-6.96 * 1e-5 + 2.8 * 1e-8 * c_e) * T ** 2
+        )
+        ** 2
+    )
+
+    return sigma_e
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_diffusivity_Ai2020.py b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_diffusivity_Ai2020.py
new file mode 100644
index 0000000000..3201839779
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/electrolyte_diffusivity_Ai2020.py
@@ -0,0 +1,28 @@
+def electrolyte_diffusivity_Ai2020(c_e, T):
+    """
+    Diffusivity of LiPF6 in EC:DMC as a function of ion concentration.
+
+    References
+    ----------
+    .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+    Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity
+    in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society,
+    167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+    Parameters
+    ----------
+    c_e: :class:`pybamm.Symbol`
+        Dimensional electrolyte concentration, mol/m^3
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature, K
+
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    D_c_e = 10 ** (-8.43 - 54 / (T - 229 - 5e-3 * c_e) - 0.22e-3 * c_e)
+
+    return D_c_e
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/parameters.csv
new file mode 100644
index 0000000000..5d18c26c9a
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/parameters.csv
@@ -0,0 +1,9 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrolyte properties,,,
+Typical electrolyte concentration [mol.m-3],1000,Ai 2020,
+Cation transference number,0.38,Ai 2020,
+1 + dlnf/dlnc,[function]dlnf_dlnc_Ai2020,,
+Electrolyte diffusivity [m2.s-1],[function]electrolyte_diffusivity_Ai2020,, 
+Electrolyte conductivity [S.m-1],[function]electrolyte_conductivity_Ai2020,,
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_conductivity_Nyman2008.py b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_conductivity_Nyman2008.py
index defa74e43b..f8885591f4 100644
--- a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_conductivity_Nyman2008.py
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_conductivity_Nyman2008.py
@@ -1,6 +1,3 @@
-from pybamm import exp, constants
-
-
 def electrolyte_conductivity_Nyman2008(c_e, T):
     """
     Conductivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
@@ -27,7 +24,6 @@ def electrolyte_conductivity_Nyman2008(c_e, T):
         0.1297 * (c_e / 1000) ** 3 - 2.51 * (c_e / 1000) ** 1.5 + 3.329 * (c_e / 1000)
     )
 
-    E_k_e = 34700
-    arrhenius = exp(E_k_e / constants.R * (1 / 298.15 - 1 / T))
+    # Nyman et al. (2008) does not provide temperature dependence
 
-    return sigma_e * arrhenius
+    return sigma_e
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_diffusivity_Nyman2008.py b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_diffusivity_Nyman2008.py
index bee3152dcf..2a832539d6 100644
--- a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_diffusivity_Nyman2008.py
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/electrolyte_diffusivity_Nyman2008.py
@@ -1,6 +1,3 @@
-from pybamm import exp, constants
-
-
 def electrolyte_diffusivity_Nyman2008(c_e, T):
     """
     Diffusivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
@@ -24,7 +21,7 @@ def electrolyte_diffusivity_Nyman2008(c_e, T):
     """
 
     D_c_e = 8.794e-11 * (c_e / 1000) ** 2 - 3.972e-10 * (c_e / 1000) + 4.862e-10
-    E_D_e = 37040
-    arrhenius = exp(E_D_e / constants.R * (1 / 298.15 - 1 / T))
 
-    return D_c_e * arrhenius
+    # Nyman et al. (2008) does not provide temperature dependence
+
+    return D_c_e
diff --git a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/parameters.csv b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/parameters.csv
index c6e77e42a6..238c6fb4c8 100644
--- a/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/electrolytes/lipf6_Nyman2008/parameters.csv
@@ -1,9 +1,9 @@
-Name [units],Value,Reference,Notes
-# Empty rows and rows starting with ‘#’ will be ignored,,,
-,,,
-# Electrolyte properties,,,
-Typical electrolyte concentration [mol.m-3],1000,Chen 2020,
-Cation transference number,0.2594,Chen 2020,
-1 + dlnf/dlnc,1,,
-Electrolyte diffusivity [m2.s-1],[function]electrolyte_diffusivity_Nyman2008,Nyman 2008," "
-Electrolyte conductivity [S.m-1],[function]electrolyte_conductivity_Nyman2008,Nyman 2008," "
\ No newline at end of file
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrolyte properties,,,
+Typical electrolyte concentration [mol.m-3],1000,Chen 2020,
+Cation transference number,0.2594,Chen 2020,
+1 + dlnf/dlnc,1,,
+Electrolyte diffusivity [m2.s-1],[function]electrolyte_diffusivity_Nyman2008,Nyman 2008, 
+Electrolyte conductivity [S.m-1],[function]electrolyte_conductivity_Nyman2008,Nyman 2008, 
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/README.md
new file mode 100644
index 0000000000..7609b721ff
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/README.md
@@ -0,0 +1,9 @@
+# Enertech Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/parameters.csv
new file mode 100644
index 0000000000..7c9c919863
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ai2020/parameters.csv
@@ -0,0 +1,19 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Temperature
+Reference temperature [K],298.15,25C,
+Total heat transfer coefficient [W.m-2.K-1],35,default,
+Ambient temperature [K],298.15,,
+,,,
+# Electrical
+Number of electrodes connected in parallel to make a cell,34,,
+Number of cells connected in series to make a battery,1,,
+Lower voltage cut-off [V],3,,
+Upper voltage cut-off [V],4.2,,
+,,,
+# Initial conditions
+Initial concentration in negative electrode [mol.m-3],24108,Ai 2020,
+Initial concentration in positive electrode [mol.m-3],21725,Ai 2020,
+Initial concentration in electrolyte [mol.m-3],1000,Ai 2020,
+Initial temperature [K],298.15,,
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
index 685cdbf661..e9dd8657c3 100644
--- a/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv
@@ -16,4 +16,4 @@ Upper voltage cut-off [V],4.4,,
 Initial concentration in negative electrode [mol.m-3],29866,Chen 2020,
 Initial concentration in positive electrode [mol.m-3],17038,Chen 2020,
 Initial concentration in electrolyte [mol.m-3],1000,Chen 2020,
-Initial temperature [K],298.15,,
\ No newline at end of file
+Initial temperature [K],298.15,,
diff --git a/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/README.md b/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/README.md
new file mode 100644
index 0000000000..997e2e9233
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/README.md
@@ -0,0 +1,7 @@
+# 1C discharge from full
+
+Discharge lithium-ion battery from full charge at 4C, using the initial conditions from the paper
+
+> Prada, E., Di Domenico, D., Creff, Y., Bernard, J., Sauvant-Moynot, V., & Huet, F. (2013). A simplified electrochemical and thermal aging model of LiFePO4-graphite Li-ion batteries: power and capacity fade simulations. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.053304jes), 160(4), A616.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/parameters.csv b/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/parameters.csv
new file mode 100644
index 0000000000..b6abadce83
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/experiments/4C_discharge_from_full_Prada2013/parameters.csv
@@ -0,0 +1,21 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Temperature,,,
+Reference temperature [K],298.15,25C,
+Heat transfer coefficient [W.m-2.K-1],10,,
+Ambient temperature [K],298.15,,
+,,,
+,,,
+# Electrical,,,
+Number of electrodes connected in parallel to make a cell,1,,
+Number of cells connected in series to make a battery,1,,
+Lower voltage cut-off [V],2,,
+Upper voltage cut-off [V],4.4,,
+Current function [A],4.4,,
+,,,
+# Initial conditions,,,
+Initial concentration in negative electrode [mol.m-3],28831.45783,Minimized to Severson Data,
+Initial concentration in positive electrode [mol.m-3],35.3766672,Minimized to Severson Data,
+Initial concentration in electrolyte [mol.m-3],1200,Lain,
+Initial temperature [K],298.15,,
diff --git a/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/README.md b/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/README.md
new file mode 100644
index 0000000000..7609b721ff
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/README.md
@@ -0,0 +1,9 @@
+# Enertech Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020). Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society, 167(1), 013512. DOI: 10.1149/2.0122001JES.
+
+> Rieger, B., Erhard, S. V., Rumpf, K., & Jossen, A. (2016). A new method to model the thickness change of a commercial pouch cell during discharge. Journal of The Electrochemical Society, 163(8), A1566-A1575.
+
+and references therein.
diff --git a/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/parameters.csv b/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/parameters.csv
new file mode 100644
index 0000000000..a3f3f787fd
--- /dev/null
+++ b/pybamm/input/parameters/lithium-ion/separators/separator_Ai2020/parameters.csv
@@ -0,0 +1,9 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+Separator porosity,0.5,Ai 2020,
+Separator Bruggeman coefficient (electrolyte),1.5,Ai 2020,theoretical
+Separator Bruggeman coefficient (electrode),0,default,
+Separator density [kg.m-3],2470,default,cell parameter
+Separator specific heat capacity [J.kg-1.K-1],1080.2,default,cell parameter
+Separator thermal conductivity [W.m-1.K-1],0.334,default,cell parameter 
\ No newline at end of file
diff --git a/pybamm/input/parameters/lithium-ion/separators/separator_Ecker2015/parameters.csv b/pybamm/input/parameters/lithium-ion/separators/separator_Ecker2015/parameters.csv
index b1f6cf21a9..d51a852b4d 100644
--- a/pybamm/input/parameters/lithium-ion/separators/separator_Ecker2015/parameters.csv
+++ b/pybamm/input/parameters/lithium-ion/separators/separator_Ecker2015/parameters.csv
@@ -4,3 +4,6 @@ Name [units],Value,Reference,Notes
 Separator porosity,0.508,,
 Separator Bruggeman coefficient (electrolyte),1.9804586773134942, Solve for permeability factor B=0.304=eps^b,
 Separator Bruggeman coefficient (electrode),0,No Bruggeman correction to solid conductivity,
+Separator density [kg.m-3],397,default,
+Separator specific heat capacity [J.kg-1.K-1],700,default,
+Separator thermal conductivity [W.m-1.K-1],0.16,default,
\ No newline at end of file
diff --git a/pybamm/install_odes.py b/pybamm/install_odes.py
index 1e9ccc1052..2f5333c868 100644
--- a/pybamm/install_odes.py
+++ b/pybamm/install_odes.py
@@ -135,11 +135,7 @@ def main(arguments=None):
     )
 
     # Check is sundials is already installed
-    SUNDIALS_LIB_DIRS = [
-        join(os.getenv("HOME"), ".local"),
-        "/usr/local",
-        "/usr",
-    ]
+    SUNDIALS_LIB_DIRS = [join(os.getenv("HOME"), ".local"), "/usr/local", "/usr"]
 
     if args.sundials_libs:
         SUNDIALS_LIB_DIRS.insert(0, args.sundials_libs)
diff --git a/pybamm/meshes/meshes.py b/pybamm/meshes/meshes.py
index 6f273afcc6..3eb88a1d2b 100644
--- a/pybamm/meshes/meshes.py
+++ b/pybamm/meshes/meshes.py
@@ -94,7 +94,18 @@ def __init__(self, geometry, submesh_types, var_pts):
                 else:
                     for lim, sym in spatial_limits.items():
                         if isinstance(sym, pybamm.Symbol):
-                            sym_eval = sym.evaluate()
+                            try:
+                                sym_eval = sym.evaluate()
+                            except NotImplementedError as error:
+                                if sym.has_symbol_of_classes(pybamm.Parameter):
+                                    raise pybamm.DiscretisationError(
+                                        "Parameter values have not yet been set for "
+                                        "geometry. Make sure that something like "
+                                        "`param.process_geometry(geometry)` has been "
+                                        "run."
+                                    )
+                                else:
+                                    raise error
                         elif isinstance(sym, numbers.Number):
                             sym_eval = sym
                         geometry[domain][spatial_variable][lim] = sym_eval
diff --git a/pybamm/meshes/one_dimensional_submeshes.py b/pybamm/meshes/one_dimensional_submeshes.py
index ae12a3f2f0..f4f0bdd66f 100644
--- a/pybamm/meshes/one_dimensional_submeshes.py
+++ b/pybamm/meshes/one_dimensional_submeshes.py
@@ -340,8 +340,7 @@ def __init__(self, lims, npts, edges=None, order=2):
 
         # default: Spectral Volumes of equal size
         if edges is None:
-            edges = np.linspace(spatial_lims["min"], spatial_lims["max"],
-                                npts + 1)
+            edges = np.linspace(spatial_lims["min"], spatial_lims["max"], npts + 1)
         # check that npts + 1 equals number of user-supplied edges
         elif (npts + 1) != len(edges):
             raise pybamm.GeometryError(
@@ -369,16 +368,30 @@ def __init__(self, lims, npts, edges=None, order=2):
 
         coord_sys = spatial_var.coord_sys
 
-        cv_edges = np.array([edges[0]] + [
-            x
-            for (a, b) in zip(edges[:-1], edges[1:])
-            for x in np.flip(
-                a + 0.5 * (b - a) * (1 + np.sin(np.pi * np.array(
-                    [((order + 1) - 1 - 2 * i) / (2 * (order + 1) - 2)
-                     for i in range(order + 1)]
-                )))
-            )[1:]
-        ])
+        cv_edges = np.array(
+            [edges[0]]
+            + [
+                x
+                for (a, b) in zip(edges[:-1], edges[1:])
+                for x in np.flip(
+                    a
+                    + 0.5
+                    * (b - a)
+                    * (
+                        1
+                        + np.sin(
+                            np.pi
+                            * np.array(
+                                [
+                                    ((order + 1) - 1 - 2 * i) / (2 * (order + 1) - 2)
+                                    for i in range(order + 1)
+                                ]
+                            )
+                        )
+                    )
+                )[1:]
+            ]
+        )
 
         self.sv_edges = edges
         self.sv_nodes = (edges[:-1] + edges[1:]) / 2
diff --git a/pybamm/models/base_model.py b/pybamm/models/base_model.py
index d693dcb4c2..8809bff549 100644
--- a/pybamm/models/base_model.py
+++ b/pybamm/models/base_model.py
@@ -1,9 +1,11 @@
 #
 # Base model class
 #
+import casadi
 import numbers
 import pybamm
 import warnings
+from collections import OrderedDict
 
 
 class BaseModel(object):
@@ -648,6 +650,155 @@ def info(self, symbol_name):
 
         print(div)
 
+    def export_casadi_objects(self, variable_names, input_parameter_order=None):
+        """
+        Export the constituent parts of the model (rhs, algebraic, initial conditions,
+        etc) as casadi objects.
+
+        Parameters
+        ----------
+        variable_names : list
+            Variables to be exported alongside the model structure
+        input_parameter_order : list, optional
+            Order in which the input parameters should be stacked. If None, the order
+            returned by :meth:`BaseModel.input_parameters` is used
+
+        Returns
+        -------
+        casadi_dict : dict
+            Dictionary of {str: casadi object} pairs representing the model in casadi
+            format
+        """
+        # Discretise model if it isn't already discretised
+        # This only works with purely 0D models, as otherwise the mesh and spatial
+        # method should be specified by the user
+        if self.is_discretised is False:
+            try:
+                disc = pybamm.Discretisation()
+                disc.process_model(self)
+            except pybamm.DiscretisationError as e:
+                raise pybamm.DiscretisationError(
+                    "Cannot automatically discretise model, model should be "
+                    "discretised before exporting casadi functions ({})".format(e)
+                )
+
+        # Create casadi functions for the model
+        t_casadi = casadi.MX.sym("t")
+        y_diff = casadi.MX.sym("y_diff", self.concatenated_rhs.size)
+        y_alg = casadi.MX.sym("y_alg", self.concatenated_algebraic.size)
+        y_casadi = casadi.vertcat(y_diff, y_alg)
+
+        # Read inputs
+        inputs_wrong_order = {}
+        for input_param in self.input_parameters:
+            name = input_param.name
+            inputs_wrong_order[name] = casadi.MX.sym(name, input_param._expected_size)
+        # Read external variables
+        external_casadi = {}
+        for external_varaiable in self.external_variables:
+            name = external_varaiable.name
+            ev_size = external_varaiable._evaluate_for_shape().shape[0]
+            external_casadi[name] = casadi.MX.sym(name, ev_size)
+        # Sort according to input_parameter_order
+        if input_parameter_order is None:
+            inputs = inputs_wrong_order
+        else:
+            inputs = {name: inputs_wrong_order[name] for name in input_parameter_order}
+        # Set up external variables and inputs
+        # Put external variables first like the integrator expects
+        ext_and_in = {**external_casadi, **inputs}
+        inputs_stacked = casadi.vertcat(*[p for p in ext_and_in.values()])
+
+        # Convert initial conditions to casadi form
+        y0 = self.concatenated_initial_conditions.to_casadi(
+            t_casadi, y_casadi, inputs=inputs
+        )
+        x0 = y0[: self.concatenated_rhs.size]
+        z0 = y0[self.concatenated_rhs.size :]
+
+        # Convert rhs and algebraic to casadi form and calculate jacobians
+        rhs = self.concatenated_rhs.to_casadi(t_casadi, y_casadi, inputs=ext_and_in)
+        jac_rhs = casadi.jacobian(rhs, y_casadi)
+        algebraic = self.concatenated_algebraic.to_casadi(
+            t_casadi, y_casadi, inputs=inputs
+        )
+        jac_algebraic = casadi.jacobian(algebraic, y_casadi)
+
+        # For specified variables, convert to casadi
+        variables = OrderedDict()
+        for name in variable_names:
+            var = self.variables[name]
+            variables[name] = var.to_casadi(t_casadi, y_casadi, inputs=ext_and_in)
+
+        casadi_dict = {
+            "t": t_casadi,
+            "x": y_diff,
+            "z": y_alg,
+            "inputs": inputs_stacked,
+            "rhs": rhs,
+            "algebraic": algebraic,
+            "jac_rhs": jac_rhs,
+            "jac_algebraic": jac_algebraic,
+            "variables": variables,
+            "x0": x0,
+            "z0": z0,
+        }
+
+        return casadi_dict
+
+    def generate(
+        self, filename, variable_names, input_parameter_order=None, cg_options=None
+    ):
+        """
+        Generate the model in C, using CasADi.
+
+        Parameters
+        ----------
+        filename : str
+            Name of the file to which to save the code
+        variable_names : list
+            Variables to be exported alongside the model structure
+        input_parameter_order : list, optional
+            Order in which the input parameters should be stacked. If None, the order
+            returned by :meth:`BaseModel.input_parameters` is used
+        cg_options : dict
+            Options to pass to the code generator.
+            See https://web.casadi.org/docs/#generating-c-code
+        """
+        model = self.export_casadi_objects(variable_names, input_parameter_order)
+
+        # Read the exported objects
+        t, x, z, p = model["t"], model["x"], model["z"], model["inputs"]
+        x0, z0 = model["x0"], model["z0"]
+        rhs, alg = model["rhs"], model["algebraic"]
+        variables = model["variables"]
+        jac_rhs, jac_alg = model["jac_rhs"], model["jac_algebraic"]
+
+        # Create functions
+        rhs_fn = casadi.Function("rhs_", [t, x, z, p], [rhs])
+        alg_fn = casadi.Function("alg_", [t, x, z, p], [alg])
+        jac_rhs_fn = casadi.Function("jac_rhs", [t, x, z, p], [jac_rhs])
+        jac_alg_fn = casadi.Function("jac_alg", [t, x, z, p], [jac_alg])
+        # Call these functions to initialize initial conditions
+        # (initial conditions are not yet consistent at this stage)
+        x0_fn = casadi.Function("x0", [p], [x0])
+        z0_fn = casadi.Function("z0", [p], [z0])
+        # Variables
+        variables_stacked = casadi.vertcat(*variables.values())
+        variables_fn = casadi.Function("variables", [t, x, z, p], [variables_stacked])
+
+        # Write C files
+        cg_options = cg_options or {}
+        C = casadi.CodeGenerator(filename, cg_options)
+        C.add(rhs_fn)
+        C.add(alg_fn)
+        C.add(jac_rhs_fn)
+        C.add(jac_alg_fn)
+        C.add(x0_fn)
+        C.add(z0_fn)
+        C.add(variables_fn)
+        C.generate()
+
     @property
     def default_parameter_values(self):
         return pybamm.ParameterValues({})
diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py
index 22c3a033d8..cd6df85048 100644
--- a/pybamm/models/full_battery_models/base_battery_model.py
+++ b/pybamm/models/full_battery_models/base_battery_model.py
@@ -24,26 +24,24 @@ class BaseBatteryModel(pybamm.BaseModel):
                 model with prescribed cell volume and cross-sectional area, and
                 (if thermal effects are included) solves a lumped thermal model
                 with prescribed surface area for cooling.
-            * "dimensionality" : int, optional
-                Sets the dimension of the current collector problem. Can be 0
-                (default), 1 or 2.
-            * "surface form" : bool or str, optional
-                Whether to use the surface formulation of the problem. Can be False
-                (default), "differential" or "algebraic".
             * "convection" : bool or str, optional
                 Whether to include the effects of convection in the model. Can be
                 False (default), "differential" or "algebraic". Must be 'False' for
                 lithium-ion models.
-            * "side reactions" : list, optional
-                Contains a list of any side reactions to include. Default is []. If this
-                list is not empty (i.e. side reactions are included in the model), then
-                "surface form" cannot be 'False'.
-            * "interfacial surface area" : str, optional
-                Sets the model for the interfacial surface area. Can be "constant"
-                (default) or "varying". Not currently implemented in any of the models.
             * "current collector" : str, optional
                 Sets the current collector model to use. Can be "uniform" (default),
                 "potential pair" or "potential pair quite conductive".
+            * "dimensionality" : int, optional
+                Sets the dimension of the current collector problem. Can be 0
+                (default), 1 or 2.
+            * "external submodels" : list
+                A list of the submodels that you would like to supply an external
+                variable for instead of solving in PyBaMM. The entries of the lists
+                are strings that correspond to the submodel names in the keys
+                of `self.submodels`.
+            * "interfacial surface area" : str, optional
+                Sets the model for the interfacial surface area. Can be "constant"
+                (default) or "varying". Not currently implemented in any of the models.
             * "particle" : str, optional
                 Sets the submodel to use to describe behaviour within the particle.
                 Can be "Fickian diffusion" (default), "uniform profile",
@@ -54,14 +52,14 @@ class BaseBatteryModel(pybamm.BaseModel):
                 (default) or "user". For the "user" option the surface area per
                 unit volume can be passed as a parameter, and is therefore not
                 necessarily consistent with the particle shape.
-            * "thermal" : str, optional
-                Sets the thermal model to use. Can be "isothermal" (default), "lumped",
-                "x-lumped", or "x-full".
-            * "external submodels" : list
-                A list of the submodels that you would like to supply an external
-                variable for instead of solving in PyBaMM. The entries of the lists
-                are strings that correspond to the submodel names in the keys
-                of `self.submodels`.
+            * "particle cracking" : str, optional
+                Sets the model to account for mechanical effects and particle
+                cracking. Can be None, "no cracking", "anode", "cathode" or "both".
+                All options other than None account for the effects of swelling
+                of electrode particles, cell thickness change, and stress-assisted
+                diffusion. The options "anode", "cathode" or "both" additionally account
+                for crack propagation in the anode, cathode or both electrodes,
+                respectively.
             * "sei" : str
                 Set the sei submodel to be used. Options are:
 
@@ -103,6 +101,16 @@ class BaseBatteryModel(pybamm.BaseModel):
                         * (\\phi_s - \\phi_e - U - R_{sei} * L_{sei} * \\frac{I}{aL})
             * "sei porosity change" : bool
                 Whether to include porosity change due to SEI formation (default False)
+            * "side reactions" : list, optional
+                Contains a list of any side reactions to include. Default is []. If this
+                list is not empty (i.e. side reactions are included in the model), then
+                "surface form" cannot be 'False'.
+            * "surface form" : bool or str, optional
+                Whether to use the surface formulation of the problem. Can be False
+                (default), "differential" or "algebraic".
+            * "thermal" : str, optional
+                Sets the thermal model to use. Can be "isothermal" (default), "lumped",
+                "x-lumped", or "x-full".
 
     **Extends:** :class:`pybamm.BaseModel`
     """
@@ -198,12 +206,14 @@ def options(self, extra_options):
             "current collector": "uniform",
             "particle": "Fickian diffusion",
             "particle shape": "spherical",
+            "electrolyte conductivity": "default",
             "thermal": "isothermal",
             "cell geometry": None,
             "external submodels": [],
             "sei": None,
             "sei porosity change": False,
             "working electrode": None,
+            "particle cracking": None,
         }
         # Change the default for cell geometry based on which thermal option is provided
         extra_options = extra_options or {}
@@ -340,6 +350,17 @@ def options(self, extra_options):
                 )
             )
 
+        if options["particle cracking"] not in [
+            None,
+            "no cracking",
+            "anode",
+            "cathode",
+            "both",
+        ]:
+            raise pybamm.OptionError(
+                "Unknown particle cracking '{}'".format(options["particle cracking"])
+            )
+
         if options["dimensionality"] == 0:
             if options["current collector"] not in ["uniform"]:
                 raise pybamm.OptionError(
@@ -375,6 +396,19 @@ def options(self, extra_options):
                 "placed at the top of the cell."
             )
 
+        if options["electrolyte conductivity"] not in [
+            "default",
+            "full",
+            "leading order",
+            "composite",
+            "integrated",
+        ]:
+            raise pybamm.OptionError(
+                "electrolyte conductivity model '{}' not recognised".format(
+                    options["electrolyte conductivity"]
+                )
+            )
+
         self._options = options
 
     def set_standard_output_variables(self):
@@ -786,6 +820,8 @@ def set_voltage_variables(self):
 
         # Battery-wide variables
         V_dim = self.variables["Terminal voltage [V]"]
+        eta_e_av = self.variables.get("X-averaged electrolyte ohmic losses", 0)
+        eta_c_av = self.variables.get("X-averaged concentration overpotential", 0)
         eta_e_av_dim = self.variables.get("X-averaged electrolyte ohmic losses [V]", 0)
         eta_c_av_dim = self.variables.get(
             "X-averaged concentration overpotential [V]", 0
@@ -793,7 +829,6 @@ def set_voltage_variables(self):
         num_cells = pybamm.Parameter(
             "Number of cells connected in series to make a battery"
         )
-
         self.variables.update(
             {
                 "X-averaged battery open circuit voltage [V]": ocv_av_dim * num_cells,
@@ -809,6 +844,41 @@ def set_voltage_variables(self):
                 "Battery voltage [V]": V_dim * num_cells,
             }
         )
+        # Variables for calculating the equivalent circuit model (ECM) resistance
+        # Need to compare OCV to initial value to capture this as an overpotential
+        ocv_init = self.param.U_p(
+            self.param.c_p_init(1), self.param.T_init
+        ) - self.param.U_n(self.param.c_n_init(0), self.param.T_init)
+        ocv_init_dim = (
+            self.param.U_p_ref
+            - self.param.U_n_ref
+            + self.param.potential_scale * ocv_init
+        )
+        eta_ocv = ocv - ocv_init
+        eta_ocv_dim = ocv_dim - ocv_init_dim
+        # Current collector current density for working out euiqvalent resistance
+        # based on Ohm's Law
+        i_cc = self.variables["Current collector current density"]
+        i_cc_dim = self.variables["Current collector current density [A.m-2]"]
+        # Gather all overpotentials
+        v_ecm = -(eta_ocv + eta_r_av + eta_c_av + eta_e_av + delta_phi_s_av)
+        v_ecm_dim = -(
+            eta_ocv_dim
+            + eta_r_av_dim
+            + eta_c_av_dim
+            + eta_e_av_dim
+            + delta_phi_s_av_dim
+        )
+        # Current collector area for turning resistivity into resistance
+        A_cc = self.param.A_cc
+        self.variables.update(
+            {
+                "Change in measured open circuit voltage": eta_ocv,
+                "Change in measured open circuit voltage [V]": eta_ocv_dim,
+                "Local ECM resistance": v_ecm / (i_cc * A_cc),
+                "Local ECM resistance [Ohm]": v_ecm_dim / (i_cc_dim * A_cc),
+            }
+        )
 
         # Cut-off voltage
         voltage = self.variables["Terminal voltage"]
diff --git a/pybamm/models/full_battery_models/lead_acid/basic_full.py b/pybamm/models/full_battery_models/lead_acid/basic_full.py
index 74b7829ad2..91b922a0b1 100644
--- a/pybamm/models/full_battery_models/lead_acid/basic_full.py
+++ b/pybamm/models/full_battery_models/lead_acid/basic_full.py
@@ -176,7 +176,7 @@ def __init__(self, name="Basic full model"):
         # Current in the electrolyte
         ######################
         i_e = (param.kappa_e(c_e, T) * tor * param.gamma_e / param.C_e) * (
-            param.chi(c_e) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
+            param.chi(c_e, T) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
         )
         self.algebraic[phi_e] = pybamm.div(i_e) - j
         self.boundary_conditions[phi_e] = {
diff --git a/pybamm/models/full_battery_models/lead_acid/higher_order.py b/pybamm/models/full_battery_models/lead_acid/higher_order.py
index 24a0b02eb7..1e95ca288e 100644
--- a/pybamm/models/full_battery_models/lead_acid/higher_order.py
+++ b/pybamm/models/full_battery_models/lead_acid/higher_order.py
@@ -62,9 +62,7 @@ def __init__(self, options=None, name="Composite model", build=True):
     def set_current_collector_submodel(self):
         cc = pybamm.current_collector
 
-        if self.options["current collector"] in [
-            "uniform",
-        ]:
+        if self.options["current collector"] in ["uniform"]:
             submodel = cc.Uniform(self.param)
         elif self.options["current collector"] == "potential pair quite conductive":
             if self.options["dimensionality"] == 1:
diff --git a/pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py b/pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py
index 3371f4bd6b..a6696938b2 100644
--- a/pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py
+++ b/pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py
@@ -25,8 +25,8 @@ def __init__(self, options=None, name="Unnamed lithium-ion model", build=False):
             "negative electrode": self.param.L_x,
             "separator": self.param.L_x,
             "positive electrode": self.param.L_x,
-            "negative particle": self.param.R_n,
-            "positive particle": self.param.R_p,
+            "negative particle": self.param.R_n_typ,
+            "positive particle": self.param.R_p_typ,
             "current collector y": self.param.L_y,
             "current collector z": self.param.L_z,
         }
@@ -40,9 +40,9 @@ def set_standard_output_variables(self):
         self.variables.update(
             {
                 "r_n": var.r_n,
-                "r_n [m]": var.r_n * self.param.R_n,
+                "r_n [m]": var.r_n * self.param.R_n_typ,
                 "r_p": var.r_p,
-                "r_p [m]": var.r_p * self.param.R_p,
+                "r_p [m]": var.r_p * self.param.R_p_typ,
             }
         )
 
@@ -92,3 +92,23 @@ def set_other_reaction_submodels_to_zero(self):
         self.submodels["positive oxygen interface"] = pybamm.interface.NoReaction(
             self.param, "Positive", "lithium-ion oxygen"
         )
+
+    def set_crack_submodel(self):
+        if self.options["particle cracking"] is None:
+            return
+
+        if self.options["particle cracking"] == "no cracking":
+            n = pybamm.particle_cracking.NoCracking(self.param, "Negative")
+            p = pybamm.particle_cracking.NoCracking(self.param, "Positive")
+        elif self.options["particle cracking"] == "cathode":
+            n = pybamm.particle_cracking.NoCracking(self.param, "Negative")
+            p = pybamm.particle_cracking.CrackPropagation(self.param, "Positive")
+        elif self.options["particle cracking"] == "anode":
+            n = pybamm.particle_cracking.CrackPropagation(self.param, "Negative")
+            p = pybamm.particle_cracking.NoCracking(self.param, "Positive")
+        else:
+            n = pybamm.particle_cracking.CrackPropagation(self.param, "Negative")
+            p = pybamm.particle_cracking.CrackPropagation(self.param, "Positive")
+
+        self.submodels["negative particle cracking"] = n
+        self.submodels["positive particle cracking"] = p
diff --git a/pybamm/models/full_battery_models/lithium_ion/basic_dfn.py b/pybamm/models/full_battery_models/lithium_ion/basic_dfn.py
index 4e246d6fa1..e11b109dba 100644
--- a/pybamm/models/full_battery_models/lithium_ion/basic_dfn.py
+++ b/pybamm/models/full_battery_models/lithium_ion/basic_dfn.py
@@ -167,14 +167,18 @@ def __init__(self, name="Doyle-Fuller-Newman model"):
         self.boundary_conditions[c_s_n] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_n * j_n / param.a_n / param.D_n(c_s_surf_n, T),
+                -param.C_n * j_n / param.a_R_n / param.D_n(c_s_surf_n, T),
                 "Neumann",
             ),
         }
         self.boundary_conditions[c_s_p] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_p * j_p / param.a_p / param.gamma_p / param.D_p(c_s_surf_p, T),
+                -param.C_p
+                * j_p
+                / param.a_R_p
+                / param.gamma_p
+                / param.D_p(c_s_surf_p, T),
                 "Neumann",
             ),
         }
@@ -240,7 +244,7 @@ def __init__(self, name="Doyle-Fuller-Newman model"):
         # Current in the electrolyte
         ######################
         i_e = (param.kappa_e(c_e, T) * tor * param.gamma_e / param.C_e) * (
-            param.chi(c_e) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
+            param.chi(c_e, T) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
         )
         self.algebraic[phi_e] = pybamm.div(i_e) - j
         self.boundary_conditions[phi_e] = {
diff --git a/pybamm/models/full_battery_models/lithium_ion/basic_dfn_half_cell.py b/pybamm/models/full_battery_models/lithium_ion/basic_dfn_half_cell.py
index cb98a2dec9..11b06cf34b 100644
--- a/pybamm/models/full_battery_models/lithium_ion/basic_dfn_half_cell.py
+++ b/pybamm/models/full_battery_models/lithium_ion/basic_dfn_half_cell.py
@@ -32,9 +32,7 @@ class BasicDFNHalfCell(BaseModel):
     **Extends:** :class:`pybamm.lithium_ion.BaseModel`
     """
 
-    def __init__(
-        self, name="Doyle-Fuller-Newman half cell model", options=None,
-    ):
+    def __init__(self, name="Doyle-Fuller-Newman half cell model", options=None):
         super().__init__({}, name)
         pybamm.citations.register("marquis2019asymptotic")
         # `param` is a class containing all the relevant parameters and functions for
@@ -235,7 +233,7 @@ def __init__(
             self.boundary_conditions[c_s_n] = {
                 "left": (pybamm.Scalar(0), "Neumann"),
                 "right": (
-                    -param.C_n * j_n / param.a_n / param.D_n(c_s_surf_n, T),
+                    -param.C_n * j_n / param.a_R_n / param.D_n(c_s_surf_n, T),
                     "Neumann",
                 ),
             }
@@ -271,7 +269,7 @@ def __init__(
                 "right": (
                     -param.C_p
                     * j_p
-                    / param.a_p
+                    / param.a_R_p
                     / param.gamma_p
                     / param.D_p(c_s_surf_p, T),
                     "Neumann",
@@ -377,7 +375,7 @@ def __init__(
         # Current in the electrolyte
         ######################
         i_e = (param.kappa_e(c_e, T) * tor * param.gamma_e / param.C_e) * (
-            param.chi(c_e) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
+            param.chi(c_e, T) * pybamm.grad(c_e) / c_e - pybamm.grad(phi_e)
         )
         self.algebraic[phi_e] = pybamm.div(i_e) - j
 
@@ -438,8 +436,8 @@ def __init__(
             "Negative particle concentration": c_s_n,
             "Negative particle surface concentration [mol.m-3]": param.c_n_max
             * c_s_surf_n,
-            "X-averaged negative particle surface concentration [mol.m-3]":
-            param.c_n_max * c_s_surf_n_av,
+            "X-averaged negative particle surface concentration "
+            "[mol.m-3]": param.c_n_max * c_s_surf_n_av,
             "Negative particle concentration [mol.m-3]": param.c_n_max * c_s_n,
             "Electrolyte concentration": c_e,
             "Electrolyte concentration [mol.m-3]": param.c_e_typ * c_e,
@@ -448,8 +446,8 @@ def __init__(
             "Positive particle concentration": c_s_p,
             "Positive particle surface concentration [mol.m-3]": param.c_p_max
             * c_s_surf_p,
-            "X-averaged positive particle surface concentration [mol.m-3]":
-            param.c_p_max * c_s_surf_p_av,
+            "X-averaged positive particle surface concentration "
+            "[mol.m-3]": param.c_p_max * c_s_surf_p_av,
             "Positive particle concentration [mol.m-3]": param.c_p_max * c_s_p,
             "Current [A]": I,
             "Negative electrode potential": phi_s_n,
diff --git a/pybamm/models/full_battery_models/lithium_ion/basic_spm.py b/pybamm/models/full_battery_models/lithium_ion/basic_spm.py
index 8e027d0e76..18019287d0 100644
--- a/pybamm/models/full_battery_models/lithium_ion/basic_spm.py
+++ b/pybamm/models/full_battery_models/lithium_ion/basic_spm.py
@@ -89,14 +89,18 @@ def __init__(self, name="Single Particle Model"):
         self.boundary_conditions[c_s_n] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_n * j_n / param.a_n / param.D_n(c_s_surf_n, T),
+                -param.C_n * j_n / param.a_R_n / param.D_n(c_s_surf_n, T),
                 "Neumann",
             ),
         }
         self.boundary_conditions[c_s_p] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_p * j_p / param.a_p / param.gamma_p / param.D_p(c_s_surf_p, T),
+                -param.C_p
+                * j_p
+                / param.a_R_p
+                / param.gamma_p
+                / param.D_p(c_s_surf_p, T),
                 "Neumann",
             ),
         }
@@ -170,4 +174,3 @@ def __init__(self, name="Single Particle Model"):
 
     def new_copy(self, build=False):
         return pybamm.BaseModel.new_copy(self)
-
diff --git a/pybamm/models/full_battery_models/lithium_ion/dfn.py b/pybamm/models/full_battery_models/lithium_ion/dfn.py
index ea8b7c31c1..568dbe6ab2 100644
--- a/pybamm/models/full_battery_models/lithium_ion/dfn.py
+++ b/pybamm/models/full_battery_models/lithium_ion/dfn.py
@@ -44,6 +44,7 @@ def __init__(self, options=None, name="Doyle-Fuller-Newman model", build=True):
         self.set_electrolyte_submodel()
         self.set_thermal_submodel()
         self.set_current_collector_submodel()
+        self.set_crack_submodel()
         self.set_sei_submodel()
 
         if build:
@@ -121,6 +122,13 @@ def set_electrolyte_submodel(self):
             self.param
         )
 
+        if self.options["electrolyte conductivity"] not in ["default", "full"]:
+            raise pybamm.OptionError(
+                "electrolyte conductivity '{}' not suitable for DFN".format(
+                    self.options["electrolyte conductivity"]
+                )
+            )
+
         if self.options["surface form"] is False:
             self.submodels[
                 "electrolyte conductivity"
diff --git a/pybamm/models/full_battery_models/lithium_ion/spm.py b/pybamm/models/full_battery_models/lithium_ion/spm.py
index 313a3d930a..f87f5d005f 100644
--- a/pybamm/models/full_battery_models/lithium_ion/spm.py
+++ b/pybamm/models/full_battery_models/lithium_ion/spm.py
@@ -44,6 +44,7 @@ def __init__(self, options=None, name="Single Particle Model", build=True):
         self.set_positive_electrode_submodel()
         self.set_thermal_submodel()
         self.set_current_collector_submodel()
+        self.set_crack_submodel()
         self.set_sei_submodel()
 
         if build:
@@ -136,6 +137,13 @@ def set_electrolyte_submodel(self):
 
         surf_form = pybamm.electrolyte_conductivity.surface_potential_form
 
+        if self.options["electrolyte conductivity"] not in ["default", "leading order"]:
+            raise pybamm.OptionError(
+                "electrolyte conductivity '{}' not suitable for SPM".format(
+                    self.options["electrolyte conductivity"]
+                )
+            )
+
         if self.options["surface form"] is False:
             self.submodels[
                 "leading-order electrolyte conductivity"
@@ -152,6 +160,7 @@ def set_electrolyte_submodel(self):
                 self.submodels[
                     "leading-order " + domain.lower() + " electrolyte conductivity"
                 ] = surf_form.LeadingOrderAlgebraic(self.param, domain)
+
         self.submodels[
             "electrolyte diffusion"
         ] = pybamm.electrolyte_diffusion.ConstantConcentration(self.param)
diff --git a/pybamm/models/full_battery_models/lithium_ion/spme.py b/pybamm/models/full_battery_models/lithium_ion/spme.py
index d057e2766a..acfd940f12 100644
--- a/pybamm/models/full_battery_models/lithium_ion/spme.py
+++ b/pybamm/models/full_battery_models/lithium_ion/spme.py
@@ -47,6 +47,7 @@ def __init__(
         self.set_positive_electrode_submodel()
         self.set_thermal_submodel()
         self.set_current_collector_submodel()
+        self.set_crack_submodel()
         self.set_sei_submodel()
 
         if build:
@@ -136,9 +137,39 @@ def set_positive_electrode_submodel(self):
 
     def set_electrolyte_submodel(self):
 
-        self.submodels[
-            "electrolyte conductivity"
-        ] = pybamm.electrolyte_conductivity.Composite(self.param)
+        if self.options["electrolyte conductivity"] not in [
+            "default",
+            "composite",
+            "integrated",
+        ]:
+            raise pybamm.OptionError(
+                "electrolyte conductivity '{}' not suitable for SPMe".format(
+                    self.options["electrolyte conductivity"]
+                )
+            )
+
+        if self.options["surface form"] is False:
+            if self.options["electrolyte conductivity"] in ["default", "composite"]:
+                self.submodels[
+                    "electrolyte conductivity"
+                ] = pybamm.electrolyte_conductivity.Composite(self.param)
+            elif self.options["electrolyte conductivity"] == "integrated":
+                self.submodels[
+                    "electrolyte conductivity"
+                ] = pybamm.electrolyte_conductivity.Integrated(self.param)
+        elif self.options["surface form"] == "differential":
+            raise NotImplementedError(
+                "surface form '{}' has not been implemented for SPMe yet".format(
+                    self.options["surface form"]
+                )
+            )
+        elif self.options["surface form"] == "algebraic":
+            raise NotImplementedError(
+                "surface form '{}' has not been implemented for SPMe yet".format(
+                    self.options["surface form"]
+                )
+            )
+
         self.submodels["electrolyte diffusion"] = pybamm.electrolyte_diffusion.Full(
             self.param
         )
diff --git a/pybamm/models/submodels/base_submodel.py b/pybamm/models/submodels/base_submodel.py
index f8e84bf441..283d842995 100644
--- a/pybamm/models/submodels/base_submodel.py
+++ b/pybamm/models/submodels/base_submodel.py
@@ -46,9 +46,7 @@ class BaseSubModel(pybamm.BaseModel):
         existance of a discontinuity (e.g. discontinuity in the input current)
     """
 
-    def __init__(
-        self, param, domain=None, name="Unnamed submodel", external=False,
-    ):
+    def __init__(self, param, domain=None, name="Unnamed submodel", external=False):
         super().__init__(name)
         self.param = param
 
diff --git a/pybamm/models/submodels/electrode/ohm/full_ohm.py b/pybamm/models/submodels/electrode/ohm/full_ohm.py
index a6476407c4..c649610cd4 100644
--- a/pybamm/models/submodels/electrode/ohm/full_ohm.py
+++ b/pybamm/models/submodels/electrode/ohm/full_ohm.py
@@ -60,9 +60,9 @@ def set_algebraic(self, variables):
         phi_s = variables[self.domain + " electrode potential"]
         i_s = variables[self.domain + " electrode current density"]
 
-        # Get surface area per unit volume distribution in x (to account for
-        # graded electrodes)
-        a = variables[self.domain + " surface area per unit volume distribution in x"]
+        # Get surface area per unit volume (could be a distribution in x to
+        # account for graded electrodes)
+        a = variables[self.domain + " electrode surface area per unit volume"]
 
         # Variable summing all of the interfacial current densities
         sum_j = variables[
diff --git a/pybamm/models/submodels/electrolyte_conductivity/__init__.py b/pybamm/models/submodels/electrolyte_conductivity/__init__.py
index 70ba955ff8..04925ea890 100644
--- a/pybamm/models/submodels/electrolyte_conductivity/__init__.py
+++ b/pybamm/models/submodels/electrolyte_conductivity/__init__.py
@@ -2,5 +2,6 @@
 from .leading_order_conductivity import LeadingOrder
 from .composite_conductivity import Composite
 from .full_conductivity import Full
+from .integrated_conductivity import Integrated
 
 from . import surface_potential_form
diff --git a/pybamm/models/submodels/electrolyte_conductivity/composite_conductivity.py b/pybamm/models/submodels/electrolyte_conductivity/composite_conductivity.py
index 097f5660b0..7f7d77fb48 100644
--- a/pybamm/models/submodels/electrolyte_conductivity/composite_conductivity.py
+++ b/pybamm/models/submodels/electrolyte_conductivity/composite_conductivity.py
@@ -68,7 +68,7 @@ def get_coupled_variables(self, variables):
         kappa_s_av = param.kappa_e(c_e_av, T_av) * tor_s_av
         kappa_p_av = param.kappa_e(c_e_av, T_av) * tor_p_av
 
-        chi_av = param.chi(c_e_av)
+        chi_av = param.chi(c_e_av, T_av)
         chi_av_n = pybamm.PrimaryBroadcast(chi_av, "negative electrode")
         chi_av_s = pybamm.PrimaryBroadcast(chi_av, "separator")
         chi_av_p = pybamm.PrimaryBroadcast(chi_av, "positive electrode")
diff --git a/pybamm/models/submodels/electrolyte_conductivity/full_conductivity.py b/pybamm/models/submodels/electrolyte_conductivity/full_conductivity.py
index 35a5c27c07..af6fca9b7a 100644
--- a/pybamm/models/submodels/electrolyte_conductivity/full_conductivity.py
+++ b/pybamm/models/submodels/electrolyte_conductivity/full_conductivity.py
@@ -40,7 +40,7 @@ def get_coupled_variables(self, variables):
         phi_e = variables["Electrolyte potential"]
 
         i_e = (param.kappa_e(c_e, T) * tor * param.gamma_e / param.C_e) * (
-            param.chi(c_e) * (1 + param.Theta * T) * pybamm.grad(c_e) / c_e
+            param.chi(c_e, T) * (1 + param.Theta * T) * pybamm.grad(c_e) / c_e
             - pybamm.grad(phi_e)
         )
 
@@ -52,10 +52,10 @@ def set_algebraic(self, variables):
         phi_e = variables["Electrolyte potential"]
         i_e = variables["Electrolyte current density"]
 
-        # Get surface area per unit volume distribution in x (to account for
-        # graded electrodes)
-        a_n = variables["Negative surface area per unit volume distribution in x"]
-        a_p = variables["Positive surface area per unit volume distribution in x"]
+        # Get surface area per unit volume (could be a distribution in x to
+        # account for graded electrodes)
+        a_n = variables["Negative electrode surface area per unit volume"]
+        a_p = variables["Positive electrode surface area per unit volume"]
         a = pybamm.Concatenation(
             a_n, pybamm.FullBroadcast(0, "separator", "current collector"), a_p
         )
diff --git a/pybamm/models/submodels/electrolyte_conductivity/integrated_conductivity.py b/pybamm/models/submodels/electrolyte_conductivity/integrated_conductivity.py
new file mode 100644
index 0000000000..bc5fd33c56
--- /dev/null
+++ b/pybamm/models/submodels/electrolyte_conductivity/integrated_conductivity.py
@@ -0,0 +1,173 @@
+#
+# Composite electrolyte potential employing integrated Stefan-Maxwell
+#
+import pybamm
+from .base_electrolyte_conductivity import BaseElectrolyteConductivity
+
+
+class Integrated(BaseElectrolyteConductivity):
+    """
+    Integrated model for conservation of charge in the electrolyte derived from
+    integrating the Stefan-Maxwell constitutive equations, from [1]_.
+
+    Parameters
+    ----------
+    param : parameter class
+        The parameters to use for this submodel
+    domain : str, optional
+        The domain in which the model holds
+    reactions : dict, optional
+        Dictionary of reaction terms
+
+    References
+    ----------
+    .. [1] F. Brosa Planella, M. Sheikh, and W. D. Widanage, “Systematic derivation and
+           validation of reduced thermal-electrochemical models for lithium-ion
+           batteries using asymptotic methods.” arXiv preprint, 2020.
+
+    **Extends:** :class:`pybamm.electrolyte_conductivity.BaseElectrolyteConductivity`
+
+    """
+
+    def __init__(self, param, domain=None):
+        pybamm.citations.register("brosaplanella2020TSPMe")
+        super().__init__(param, domain)
+
+    def _higher_order_macinnes_function(self, x):
+        return pybamm.log(x)
+
+    def get_coupled_variables(self, variables):
+        c_e_av = variables["X-averaged electrolyte concentration"]
+
+        i_boundary_cc_0 = variables["Leading-order current collector current density"]
+        c_e_n = variables["Negative electrolyte concentration"]
+        c_e_s = variables["Separator electrolyte concentration"]
+        c_e_p = variables["Positive electrolyte concentration"]
+        c_e_n0 = pybamm.boundary_value(c_e_n, "left")
+
+        delta_phi_n_av = variables[
+            "X-averaged negative electrode surface potential difference"
+        ]
+        phi_s_n_av = variables["X-averaged negative electrode potential"]
+
+        tor_n = variables["Negative electrolyte tortuosity"]
+        tor_s = variables["Separator tortuosity"]
+        tor_p = variables["Positive electrolyte tortuosity"]
+
+        T_av = variables["X-averaged cell temperature"]
+        T_av_n = pybamm.PrimaryBroadcast(T_av, "negative electrode")
+        T_av_s = pybamm.PrimaryBroadcast(T_av, "separator")
+        T_av_p = pybamm.PrimaryBroadcast(T_av, "positive electrode")
+
+        param = self.param
+        l_n = param.l_n
+        l_p = param.l_p
+        x_n = pybamm.standard_spatial_vars.x_n
+        x_s = pybamm.standard_spatial_vars.x_s
+        x_p = pybamm.standard_spatial_vars.x_p
+        x_n_edge = pybamm.standard_spatial_vars.x_n_edge
+        x_p_edge = pybamm.standard_spatial_vars.x_p_edge
+
+        chi_av = param.chi(c_e_av, T_av)
+        chi_av_n = pybamm.PrimaryBroadcast(chi_av, "negative electrode")
+        chi_av_s = pybamm.PrimaryBroadcast(chi_av, "separator")
+        chi_av_p = pybamm.PrimaryBroadcast(chi_av, "positive electrode")
+
+        # electrolyte current
+        i_e_n = i_boundary_cc_0 * x_n / l_n
+        i_e_s = pybamm.PrimaryBroadcast(i_boundary_cc_0, "separator")
+        i_e_p = i_boundary_cc_0 * (1 - x_p) / l_p
+        i_e = pybamm.Concatenation(i_e_n, i_e_s, i_e_p)
+
+        i_e_n_edge = i_boundary_cc_0 * x_n_edge / l_n
+        i_e_s_edge = pybamm.PrimaryBroadcastToEdges(i_boundary_cc_0, "separator")
+        i_e_p_edge = i_boundary_cc_0 * (1 - x_p_edge) / l_p
+
+        # electrolyte potential
+        indef_integral_n = (
+            pybamm.IndefiniteIntegral(
+                i_e_n_edge / (param.kappa_e(c_e_n, T_av_n) * tor_n), x_n
+            )
+            * param.C_e
+            / param.gamma_e
+        )
+        indef_integral_s = (
+            pybamm.IndefiniteIntegral(
+                i_e_s_edge / (param.kappa_e(c_e_s, T_av_s) * tor_s), x_s
+            )
+            * param.C_e
+            / param.gamma_e
+        )
+        indef_integral_p = (
+            pybamm.IndefiniteIntegral(
+                i_e_p_edge / (param.kappa_e(c_e_p, T_av_p) * tor_p), x_p
+            )
+            * param.C_e
+            / param.gamma_e
+        )
+
+        integral_n = indef_integral_n
+        integral_s = indef_integral_s + pybamm.boundary_value(integral_n, "right")
+        integral_p = indef_integral_p + pybamm.boundary_value(integral_s, "right")
+
+        phi_e_const = (
+            -delta_phi_n_av
+            + phi_s_n_av
+            - (
+                chi_av
+                * (1 + param.Theta * T_av)
+                * pybamm.x_average(self._higher_order_macinnes_function(c_e_n / c_e_n0))
+            )
+            + pybamm.x_average(integral_n)
+        )
+
+        phi_e_n = (
+            phi_e_const
+            + (
+                chi_av_n
+                * (1 + param.Theta * T_av_n)
+                * self._higher_order_macinnes_function(c_e_n / c_e_n0)
+            )
+            - integral_n
+        )
+
+        phi_e_s = (
+            phi_e_const
+            + (
+                chi_av_s
+                * (1 + param.Theta * T_av_s)
+                * self._higher_order_macinnes_function(c_e_s / c_e_n0)
+            )
+            - integral_s
+        )
+
+        phi_e_p = (
+            phi_e_const
+            + (
+                chi_av_p
+                * (1 + param.Theta * T_av_p)
+                * self._higher_order_macinnes_function(c_e_p / c_e_n0)
+            )
+            - integral_p
+        )
+
+        # concentration overpotential
+        eta_c_av = (
+            chi_av
+            * (1 + param.Theta * T_av)
+            * (
+                pybamm.x_average(self._higher_order_macinnes_function(c_e_p / c_e_av))
+                - pybamm.x_average(self._higher_order_macinnes_function(c_e_n / c_e_av))
+            )
+        )
+
+        # average electrolyte ohmic losses
+        delta_phi_e_av = -(pybamm.x_average(integral_p) - pybamm.x_average(integral_n))
+
+        variables.update(
+            self._get_standard_potential_variables(phi_e_n, phi_e_s, phi_e_p)
+        )
+        variables.update(self._get_standard_current_variables(i_e))
+        variables.update(self._get_split_overpotential(eta_c_av, delta_phi_e_av))
+
+        return variables
diff --git a/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/__init__.py b/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/__init__.py
index 58468cb3f4..985cb52531 100644
--- a/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/__init__.py
+++ b/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/__init__.py
@@ -1,8 +1,5 @@
 # Full order models
-from .full_surface_form_conductivity import (
-    FullAlgebraic,
-    FullDifferential,
-)
+from .full_surface_form_conductivity import FullAlgebraic, FullDifferential
 
 # Leading-order models
 from .leading_surface_form_conductivity import (
diff --git a/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py b/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py
index 4afce31f33..b3fd388acd 100644
--- a/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py
+++ b/pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py
@@ -51,7 +51,7 @@ def get_coupled_variables(self, variables):
             T = variables[self.domain + " electrode temperature"]
 
             i_e = conductivity * (
-                ((1 + param.Theta * T) * param.chi(c_e) / c_e) * pybamm.grad(c_e)
+                ((1 + param.Theta * T) * param.chi(c_e, T) / c_e) * pybamm.grad(c_e)
                 + pybamm.grad(delta_phi)
                 + i_boundary_cc / sigma_eff
             )
@@ -71,7 +71,7 @@ def get_coupled_variables(self, variables):
             tor_s = variables["Separator porosity"]
             T = variables["Separator temperature"]
 
-            chi_e_s = param.chi(c_e_s)
+            chi_e_s = param.chi(c_e_s, T)
             kappa_s_eff = param.kappa_e(c_e_s, T) * tor_s
 
             phi_e_s = pybamm.boundary_value(
@@ -145,7 +145,7 @@ def set_boundary_conditions(self, variables):
             flux_right = (
                 (i_boundary_cc / pybamm.BoundaryValue(conductivity, "right"))
                 - pybamm.BoundaryValue(
-                    (1 + param.Theta * T) * param.chi(c_e) / c_e, "right"
+                    (1 + param.Theta * T) * param.chi(c_e, T) / c_e, "right"
                 )
                 * c_e_flux
                 - i_boundary_cc * pybamm.BoundaryValue(1 / sigma_eff, "right")
@@ -162,7 +162,7 @@ def set_boundary_conditions(self, variables):
             flux_left = (
                 (i_boundary_cc / pybamm.BoundaryValue(conductivity, "left"))
                 - pybamm.BoundaryValue(
-                    (1 + param.Theta * T) * param.chi(c_e) / c_e, "left"
+                    (1 + param.Theta * T) * param.chi(c_e, T) / c_e, "left"
                 )
                 * c_e_flux
                 - i_boundary_cc * pybamm.BoundaryValue(1 / sigma_eff, "left")
@@ -217,9 +217,9 @@ def set_algebraic(self, variables):
         delta_phi = variables[self.domain + " electrode surface potential difference"]
         i_e = variables[self.domain + " electrolyte current density"]
 
-        # Get surface area per unit volume distribution in x (to account for
-        # graded electrodes)
-        a = variables[self.domain + " surface area per unit volume distribution in x"]
+        # Get surface area per unit volume (could be a distribution in x to
+        # account for graded electrodes)
+        a = variables[self.domain + " electrode surface area per unit volume"]
 
         # Variable summing all of the interfacial current densities
         sum_j = variables[
@@ -259,9 +259,9 @@ def set_rhs(self, variables):
         delta_phi = variables[self.domain + " electrode surface potential difference"]
         i_e = variables[self.domain + " electrolyte current density"]
 
-        # Get surface area per unit volume distribution in x (to account for
-        # graded electrodes)
-        a = variables[self.domain + " surface area per unit volume distribution in x"]
+        # Get surface area per unit volume (could be a distribution in x to
+        # account for graded electrodes)
+        a = variables[self.domain + " electrode surface area per unit volume"]
 
         # Variable summing all of the interfacial current densities
         sum_j = variables[
diff --git a/pybamm/models/submodels/external_circuit/function_control_external_circuit.py b/pybamm/models/submodels/external_circuit/function_control_external_circuit.py
index f4d91dc3dd..1b6e197982 100644
--- a/pybamm/models/submodels/external_circuit/function_control_external_circuit.py
+++ b/pybamm/models/submodels/external_circuit/function_control_external_circuit.py
@@ -18,7 +18,7 @@ def get_fundamental_variables(self):
         i_cell = pybamm.Variable("Total current density")
 
         # Update derived variables
-        I = i_cell * abs(param.I_typ)
+        I = i_cell * pybamm.AbsoluteValue(param.I_typ)
         i_cell_dim = I / (param.n_electrodes_parallel * param.A_cc)
 
         variables = {
diff --git a/pybamm/models/submodels/interface/base_interface.py b/pybamm/models/submodels/interface/base_interface.py
index 4e5e5184ef..4d891e8cdd 100644
--- a/pybamm/models/submodels/interface/base_interface.py
+++ b/pybamm/models/submodels/interface/base_interface.py
@@ -173,12 +173,12 @@ def _get_number_of_electrons_in_reaction(self):
         else:
             return pybamm.Scalar(0)
 
-    def _get_surface_area_per_unit_volume_distribution(self):
-        "Returns the distribution of surface area per unit volume in x"
+    def _get_surface_area_per_unit_volume(self):
+        "Returns the surface area per unit volume (which may depend on position)"
         x_n = pybamm.standard_spatial_vars.x_n
         x_p = pybamm.standard_spatial_vars.x_p
-        a_n = self.param.a_n_of_x(x_n)
-        a_p = self.param.a_p_of_x(x_p)
+        a_n = self.param.a_n(x_n)
+        a_p = self.param.a_p(x_p)
         return a_n, a_p
 
     def _get_electrolyte_reaction_signed_stoichiometry(self):
@@ -236,9 +236,9 @@ def _get_standard_interfacial_current_variables(self, j):
         i_typ = self.param.i_typ
         L_x = self.param.L_x
         if self.domain == "Negative":
-            j_scale = i_typ / (self.param.a_n_dim * L_x)
+            j_scale = i_typ / (self.param.a_n_typ * L_x)
         elif self.domain == "Positive":
-            j_scale = i_typ / (self.param.a_p_dim * L_x)
+            j_scale = i_typ / (self.param.a_p_typ * L_x)
 
         # Average, and broadcast if necessary
         if j.domain == []:
@@ -287,9 +287,9 @@ def _get_standard_total_interfacial_current_variables(self, j_tot_av):
         i_typ = self.param.i_typ
         L_x = self.param.L_x
         if self.domain == "Negative":
-            j_scale = i_typ / (self.param.a_n_dim * L_x)
+            j_scale = i_typ / (self.param.a_n_typ * L_x)
         elif self.domain == "Positive":
-            j_scale = i_typ / (self.param.a_p_dim * L_x)
+            j_scale = i_typ / (self.param.a_p_typ * L_x)
 
         variables = {
             "X-averaged "
@@ -315,8 +315,8 @@ def _get_standard_whole_cell_interfacial_current_variables(self, variables):
         """
         i_typ = self.param.i_typ
         L_x = self.param.L_x
-        j_n_scale = i_typ / (self.param.a_n_dim * L_x)
-        j_p_scale = i_typ / (self.param.a_p_dim * L_x)
+        j_n_scale = i_typ / (self.param.a_n_typ * L_x)
+        j_p_scale = i_typ / (self.param.a_p_typ * L_x)
 
         j_n_av = variables[
             "X-averaged negative electrode"
@@ -347,14 +347,14 @@ def _get_standard_whole_cell_interfacial_current_variables(self, variables):
             }
         )
 
-        a_n, a_p = self._get_surface_area_per_unit_volume_distribution()
+        a_n, a_p = self._get_surface_area_per_unit_volume()
         a = pybamm.Concatenation(
             a_n, pybamm.FullBroadcast(0, "separator", "current collector"), a_p
         )
         variables.update(
             {
-                "Negative surface area per unit volume distribution in x": a_n,
-                "Positive surface area per unit volume distribution in x": a_p,
+                "Negative electrode surface area per unit volume": a_n,
+                "Positive electrode surface area per unit volume": a_p,
             }
         )
 
@@ -396,9 +396,9 @@ def _get_standard_exchange_current_variables(self, j0):
         i_typ = self.param.i_typ
         L_x = self.param.L_x
         if self.domain == "Negative":
-            j_scale = i_typ / (self.param.a_n_dim * L_x)
+            j_scale = i_typ / (self.param.a_n_typ * L_x)
         elif self.domain == "Positive":
-            j_scale = i_typ / (self.param.a_p_dim * L_x)
+            j_scale = i_typ / (self.param.a_p_typ * L_x)
 
         # Average, and broadcast if necessary
         if j0.domain == []:
@@ -448,8 +448,8 @@ def _get_standard_whole_cell_exchange_current_variables(self, variables):
 
         i_typ = self.param.i_typ
         L_x = self.param.L_x
-        j_n_scale = i_typ / (self.param.a_n_dim * L_x)
-        j_p_scale = i_typ / (self.param.a_p_dim * L_x)
+        j_n_scale = i_typ / (self.param.a_n_typ * L_x)
+        j_p_scale = i_typ / (self.param.a_p_typ * L_x)
 
         j0_n = variables[
             "Negative electrode" + self.reaction_name + " exchange current density"
diff --git a/pybamm/models/submodels/interface/sei/base_sei.py b/pybamm/models/submodels/interface/sei/base_sei.py
index c82cf537d3..8c0ee8bc4d 100644
--- a/pybamm/models/submodels/interface/sei/base_sei.py
+++ b/pybamm/models/submodels/interface/sei/base_sei.py
@@ -112,9 +112,9 @@ def _get_standard_concentraion_variables(self, variables):
             n_outer_scale = self.param.c_ec_0_dim
             v_bar = 1
         else:
-            n_scale = param.L_sei_0_dim * param.a_n_dim / param.V_bar_inner_dimensional
+            n_scale = param.L_sei_0_dim * param.a_n_typ / param.V_bar_inner_dimensional
             n_outer_scale = (
-                param.L_sei_0_dim * param.a_n_dim / param.V_bar_outer_dimensional
+                param.L_sei_0_dim * param.a_n_typ / param.V_bar_outer_dimensional
             )
             v_bar = param.v_bar
 
@@ -181,7 +181,8 @@ def _get_standard_concentraion_variables(self, variables):
                     + " electrode EC surface concentration": c_ec_av,
                     "X-averaged "
                     + self.domain.lower()
-                    + " electrode EC surface concentration": c_ec_av * n_outer_scale,
+                    + " electrode EC surface concentration [mol.m-3]": c_ec_av
+                    * n_outer_scale,
                 }
             )
 
diff --git a/pybamm/models/submodels/interface/sei/ec_reaction_limited.py b/pybamm/models/submodels/interface/sei/ec_reaction_limited.py
index 72495bb27b..9c03cd9d54 100644
--- a/pybamm/models/submodels/interface/sei/ec_reaction_limited.py
+++ b/pybamm/models/submodels/interface/sei/ec_reaction_limited.py
@@ -87,13 +87,18 @@ def set_algebraic(self, variables):
         # it's ok to fall back on the total interfacial current density, j_tot
         # This should only happen when the interface submodel is "InverseButlerVolmer"
         # in which case j = j_tot (uniform) anyway
-        try:
+        if (
+            "Total "
+            + self.domain.lower()
+            + " electrode interfacial current density variable"
+            in variables
+        ):
             j = variables[
                 "Total "
                 + self.domain.lower()
-                + " electrode interfacial current density"
+                + " electrode interfacial current density variable"
             ]
-        except KeyError:
+        else:
             j = variables[
                 "X-averaged "
                 + self.domain.lower()
diff --git a/pybamm/models/submodels/interface/sei/reaction_limited.py b/pybamm/models/submodels/interface/sei/reaction_limited.py
index 0f6fd0ed37..a78c7a5a56 100644
--- a/pybamm/models/submodels/interface/sei/reaction_limited.py
+++ b/pybamm/models/submodels/interface/sei/reaction_limited.py
@@ -41,9 +41,9 @@ def get_coupled_variables(self, variables):
         # it's ok to fall back on the total interfacial current density, j_tot
         # This should only happen when the interface submodel is "InverseButlerVolmer"
         # in which case j = j_tot (uniform) anyway
-        try:
+        if self.domain + " electrode interfacial current density" in variables:
             j = variables[self.domain + " electrode interfacial current density"]
-        except KeyError:
+        else:
             j = variables[
                 "X-averaged "
                 + self.domain.lower()
diff --git a/pybamm/models/submodels/particle/base_particle.py b/pybamm/models/submodels/particle/base_particle.py
index 0e9b13d25a..e4336c06fe 100644
--- a/pybamm/models/submodels/particle/base_particle.py
+++ b/pybamm/models/submodels/particle/base_particle.py
@@ -59,6 +59,7 @@ def _get_standard_concentration_variables(
         variables = {
             self.domain + " particle concentration": c_s,
             self.domain + " particle concentration [mol.m-3]": c_s * c_scale,
+            self.domain + " particle concentration [mol.m-3]": c_s * c_scale,
             "X-averaged " + self.domain.lower() + " particle concentration": c_s_xav,
             "X-averaged "
             + self.domain.lower()
@@ -92,6 +93,57 @@ def _get_standard_concentration_variables(
             "Total lithium in "
             + self.domain.lower()
             + " electrode [mol]": c_s_vol_av * c_scale * L * A,
+            "Minimum "
+            + self.domain.lower()
+            + " particle concentration": pybamm.min(c_s),
+            "Maximum "
+            + self.domain.lower()
+            + " particle concentration": pybamm.max(c_s),
+            "Minimum "
+            + self.domain.lower()
+            + " particle concentration [mol.m-3]": pybamm.min(c_s) * c_scale,
+            "Maximum "
+            + self.domain.lower()
+            + " particle concentration [mol.m-3]": pybamm.max(c_s) * c_scale,
+            "Minimum "
+            + self.domain.lower()
+            + " particle surface concentration": pybamm.min(c_s_surf),
+            "Maximum "
+            + self.domain.lower()
+            + " particle surface concentration": pybamm.max(c_s_surf),
+            "Minimum "
+            + self.domain.lower()
+            + " particle surface concentration [mol.m-3]": pybamm.min(c_s_surf)
+            * c_scale,
+            "Maximum "
+            + self.domain.lower()
+            + " particle surface concentration [mol.m-3]": pybamm.max(c_s_surf)
+            * c_scale,
+        }
+
+        variables.update(self._get_microstrcuture_variables())
+
+        return variables
+
+    def _get_microstrcuture_variables(self):
+        if self.domain == "Negative":
+            x = pybamm.standard_spatial_vars.x_n
+            R = self.param.R_n(x)
+            R_scale = self.param.R_n_typ
+            a = self.param.a_n(x)
+            a_scale = self.param.a_n_typ
+        elif self.domain == "Positive":
+            x = pybamm.standard_spatial_vars.x_p
+            R = self.param.R_p(x)
+            R_scale = self.param.R_p_typ
+            a = self.param.a_p(x)
+            a_scale = self.param.a_p_typ
+
+        variables = {
+            self.domain + " particle radius": R,
+            self.domain + " particle radius [m]": R * R_scale,
+            self.domain + " electrode surface area per unit volume": a,
+            self.domain + " electrode surface area per unit volume [m-1]": a * a_scale,
         }
 
         return variables
diff --git a/pybamm/models/submodels/particle/fickian_many_particles.py b/pybamm/models/submodels/particle/fickian_many_particles.py
index 5559f17c52..d4b6d5f4cf 100644
--- a/pybamm/models/submodels/particle/fickian_many_particles.py
+++ b/pybamm/models/submodels/particle/fickian_many_particles.py
@@ -42,17 +42,10 @@ def get_coupled_variables(self, variables):
 
         if self.domain == "Negative":
             N_s = -self.param.D_n(c_s, T) * pybamm.grad(c_s)
-            x = pybamm.standard_spatial_vars.x_n
-            R = self.param.R_n_of_x(x)
-            variables.update({"Negative particle distribution in x": R})
 
         elif self.domain == "Positive":
             N_s = -self.param.D_p(c_s, T) * pybamm.grad(c_s)
 
-            x = pybamm.standard_spatial_vars.x_p
-            R = self.param.R_p_of_x(x)
-            variables.update({"Positive particle distribution in x": R})
-
         variables.update(self._get_standard_flux_variables(N_s, N_s))
 
         return variables
@@ -60,7 +53,7 @@ def get_coupled_variables(self, variables):
     def set_rhs(self, variables):
         c_s = variables[self.domain + " particle concentration"]
         N_s = variables[self.domain + " particle flux"]
-        R = variables[self.domain + " particle distribution in x"]
+        R = variables[self.domain + " particle radius"]
 
         if self.domain == "Negative":
             self.rhs = {c_s: -(1 / (R ** 2 * self.param.C_n)) * pybamm.div(N_s)}
@@ -74,17 +67,19 @@ def set_boundary_conditions(self, variables):
         c_s_surf = variables[self.domain + " particle surface concentration"]
         T = variables[self.domain + " electrode temperature"]
         j = variables[self.domain + " electrode interfacial current density"]
-        R = variables[self.domain + " particle distribution in x"]
+        R = variables[self.domain + " particle radius"]
 
         if self.domain == "Negative":
-            rbc = -self.param.C_n * j * R / self.param.a_n / self.param.D_n(c_s_surf, T)
+            rbc = (
+                -self.param.C_n * j * R / self.param.a_R_n / self.param.D_n(c_s_surf, T)
+            )
 
         elif self.domain == "Positive":
             rbc = (
                 -self.param.C_p
                 * j
                 * R
-                / self.param.a_p
+                / self.param.a_R_p
                 / self.param.gamma_p
                 / self.param.D_p(c_s_surf, T)
             )
diff --git a/pybamm/models/submodels/particle/fickian_single_particle.py b/pybamm/models/submodels/particle/fickian_single_particle.py
index 450c57062f..a05c7efca3 100644
--- a/pybamm/models/submodels/particle/fickian_single_particle.py
+++ b/pybamm/models/submodels/particle/fickian_single_particle.py
@@ -90,7 +90,7 @@ def set_boundary_conditions(self, variables):
             rbc = (
                 -self.param.C_n
                 * j_xav
-                / self.param.a_n
+                / self.param.a_R_n
                 / self.param.D_n(c_s_surf_xav, T_xav)
             )
 
@@ -98,7 +98,7 @@ def set_boundary_conditions(self, variables):
             rbc = (
                 -self.param.C_p
                 * j_xav
-                / self.param.a_p
+                / self.param.a_R_p
                 / self.param.gamma_p
                 / self.param.D_p(c_s_surf_xav, T_xav)
             )
diff --git a/pybamm/models/submodels/particle/polynomial_many_particles.py b/pybamm/models/submodels/particle/polynomial_many_particles.py
index 318955b317..a669204946 100644
--- a/pybamm/models/submodels/particle/polynomial_many_particles.py
+++ b/pybamm/models/submodels/particle/polynomial_many_particles.py
@@ -37,12 +37,10 @@ def __init__(self, param, domain, name):
         pybamm.citations.register("subramanian2005")
 
     def get_fundamental_variables(self):
+        variables = {}
         if self.domain == "Negative":
             # For all orders we solve an equation for the average concentration
             c_s_rav = pybamm.standard_variables.c_s_n_rav
-            x = pybamm.standard_spatial_vars.x_n
-            R = self.param.R_n_of_x(x)
-            variables = {"Negative particle distribution in x": R}
             if self.name == "uniform profile":
                 # The concentration is uniform so the surface value is equal to
                 # the average
@@ -66,9 +64,6 @@ def get_fundamental_variables(self):
         elif self.domain == "Positive":
             # For all orders we solve an equation for the average concentration
             c_s_rav = pybamm.standard_variables.c_s_p_rav
-            x = pybamm.standard_spatial_vars.x_p
-            R = self.param.R_p_of_x(x)
-            variables = {"Positive particle distribution in x": R}
             if self.name == "uniform profile":
                 # The concentration is uniform so the surface value is equal to
                 # the average
@@ -189,13 +184,13 @@ def set_rhs(self, variables):
             "R-averaged " + self.domain.lower() + " particle concentration"
         ]
         j = variables[self.domain + " electrode interfacial current density"]
-        R = variables[self.domain + " particle distribution in x"]
+        R = variables[self.domain + " particle radius"]
 
         if self.domain == "Negative":
-            self.rhs = {c_s_rav: -3 * j / self.param.a_n / R}
+            self.rhs = {c_s_rav: -3 * j / self.param.a_R_n / R}
 
         elif self.domain == "Positive":
-            self.rhs = {c_s_rav: -3 * j / self.param.a_p / self.param.gamma_p / R}
+            self.rhs = {c_s_rav: -3 * j / self.param.a_R_p / self.param.gamma_p / R}
 
         if self.name == "quartic profile":
             # We solve an extra ODE for the average particle flux
@@ -213,7 +208,7 @@ def set_rhs(self, variables):
                         * self.param.D_n(c_s_rav, T)
                         * q_s_rav
                         / self.param.C_n
-                        - 45 * j / self.param.a_n / 2
+                        - 45 * j / self.param.a_R_n / 2
                     }
                 )
             elif self.domain == "Positive":
@@ -223,7 +218,7 @@ def set_rhs(self, variables):
                         * self.param.D_p(c_s_rav, T)
                         * q_s_rav
                         / self.param.C_p
-                        - 45 * j / self.param.a_p / self.param.gamma_p / 2
+                        - 45 * j / self.param.a_R_p / self.param.gamma_p / 2
                     }
                 )
 
@@ -234,7 +229,7 @@ def set_algebraic(self, variables):
         ]
         j = variables[self.domain + " electrode interfacial current density"]
         T = variables[self.domain + " electrode temperature"]
-        R = variables[self.domain + " particle distribution in x"]
+        R = variables[self.domain + " particle radius"]
         if self.name == "uniform profile":
             # No algebraic equations since we only solve for the average concentration
             pass
@@ -243,13 +238,14 @@ def set_algebraic(self, variables):
             if self.domain == "Negative":
                 self.algebraic = {
                     c_s_surf: self.param.D_n(c_s_surf, T) * (c_s_surf - c_s_rav)
-                    + self.param.C_n * (j * R / self.param.a_n / 5)
+                    + self.param.C_n * (j * R / self.param.a_R_n / 5)
                 }
 
             elif self.domain == "Positive":
                 self.algebraic = {
                     c_s_surf: self.param.D_p(c_s_surf, T) * (c_s_surf - c_s_rav)
-                    + self.param.C_p * (j * R / self.param.a_p / self.param.gamma_p / 5)
+                    + self.param.C_p
+                    * (j * R / self.param.a_R_p / self.param.gamma_p / 5)
                 }
         elif self.name == "quartic profile":
             # We solve a different algebraic equation for the surface concentration
@@ -261,14 +257,14 @@ def set_algebraic(self, variables):
                 self.algebraic = {
                     c_s_surf: self.param.D_n(c_s_surf, T)
                     * (35 * (c_s_surf - c_s_rav) - 8 * q_s_rav)
-                    + self.param.C_n * (j * R / self.param.a_n)
+                    + self.param.C_n * (j * R / self.param.a_R_n)
                 }
 
             elif self.domain == "Positive":
                 self.algebraic = {
                     c_s_surf: self.param.D_p(c_s_surf, T)
                     * (35 * (c_s_surf - c_s_rav) - 8 * q_s_rav)
-                    + self.param.C_p * (j * R / self.param.a_p / self.param.gamma_p)
+                    + self.param.C_p * (j * R / self.param.a_R_p / self.param.gamma_p)
                 }
 
     def set_initial_conditions(self, variables):
diff --git a/pybamm/models/submodels/particle/polynomial_single_particle.py b/pybamm/models/submodels/particle/polynomial_single_particle.py
index 93b3ca8dee..22a7d1b916 100644
--- a/pybamm/models/submodels/particle/polynomial_single_particle.py
+++ b/pybamm/models/submodels/particle/polynomial_single_particle.py
@@ -104,7 +104,7 @@ def get_coupled_variables(self, variables):
                 c_s_surf_xav = c_s_rxav - self.param.C_n * (
                     j_xav
                     / 5
-                    / self.param.a_n
+                    / self.param.a_R_n
                     / self.param.D_n(c_s_rxav, pybamm.surf(T_xav))
                 )
 
@@ -113,7 +113,7 @@ def get_coupled_variables(self, variables):
                 c_s_surf_xav = c_s_rxav - self.param.C_p * (
                     j_xav
                     / 5
-                    / self.param.a_p
+                    / self.param.a_R_p
                     / self.param.gamma_p
                     / self.param.D_p(c_s_rxav, pybamm.surf(T_xav))
                 )
@@ -133,7 +133,7 @@ def get_coupled_variables(self, variables):
                     * (
                         j_xav
                         / 35
-                        / self.param.a_n
+                        / self.param.a_R_n
                         / self.param.D_n(c_s_rxav, pybamm.surf(T_xav))
                     )
                 )
@@ -147,7 +147,7 @@ def get_coupled_variables(self, variables):
                     * (
                         j_xav
                         / 35
-                        / self.param.a_p
+                        / self.param.a_R_p
                         / self.param.gamma_p
                         / self.param.D_p(c_s_rxav, pybamm.surf(T_xav))
                     )
@@ -286,10 +286,10 @@ def set_rhs(self, variables):
         ]
 
         if self.domain == "Negative":
-            self.rhs = {c_s_rxav: -3 * j_xav / self.param.a_n}
+            self.rhs = {c_s_rxav: -3 * j_xav / self.param.a_R_n}
 
         elif self.domain == "Positive":
-            self.rhs = {c_s_rxav: -3 * j_xav / self.param.a_p / self.param.gamma_p}
+            self.rhs = {c_s_rxav: -3 * j_xav / self.param.a_R_p / self.param.gamma_p}
 
         if self.name == "quartic profile":
             # We solve an extra ODE for the average particle concentration gradient
@@ -309,7 +309,7 @@ def set_rhs(self, variables):
                         * self.param.D_n(c_s_surf_xav, T_xav)
                         * q_s_rxav
                         / self.param.C_n
-                        - 45 * j_xav / self.param.a_n / 2
+                        - 45 * j_xav / self.param.a_R_n / 2
                     }
                 )
             elif self.domain == "Positive":
@@ -319,7 +319,7 @@ def set_rhs(self, variables):
                         * self.param.D_p(c_s_surf_xav, T_xav)
                         * q_s_rxav
                         / self.param.C_p
-                        - 45 * j_xav / self.param.a_p / self.param.gamma_p / 2
+                        - 45 * j_xav / self.param.a_R_p / self.param.gamma_p / 2
                     }
                 )
 
diff --git a/pybamm/models/submodels/particle_cracking/__init__.py b/pybamm/models/submodels/particle_cracking/__init__.py
new file mode 100644
index 0000000000..b0f43ecde6
--- /dev/null
+++ b/pybamm/models/submodels/particle_cracking/__init__.py
@@ -0,0 +1,3 @@
+from .base_cracking import BaseCracking
+from .crack_propagation import CrackPropagation
+from .no_cracking import NoCracking
diff --git a/pybamm/models/submodels/particle_cracking/base_cracking.py b/pybamm/models/submodels/particle_cracking/base_cracking.py
new file mode 100644
index 0000000000..f4882556b5
--- /dev/null
+++ b/pybamm/models/submodels/particle_cracking/base_cracking.py
@@ -0,0 +1,170 @@
+#
+# Base class for particle cracking models.
+#
+import pybamm
+
+
+class BaseCracking(pybamm.BaseSubModel):
+    """
+    Base class for particle cracking models. See [1]_ for mechanical model (thickness
+    change) and [2]_ for cracking model.
+
+    Parameters
+    ----------
+    param : parameter class
+        The parameters to use for this submodel
+    domain : dict, optional
+        Dictionary of either the electrode for "Positive" or "Nagative"
+
+    References
+    ----------
+    .. [1] Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2019). Electrochemical
+           Thermal-Mechanical Modelling of Stress Inhomogeneity in Lithium-Ion Pouch
+           Cells. Journal of The Electrochemical Society, 167(1), 013512.
+    .. [2] Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+           Battery cycle life prediction with coupled chemical degradation and
+           fatigue mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    **Extends:** :class:`pybamm.BaseSubModel`
+    """
+
+    def __init__(self, param, domain):
+        self.domain = domain
+        super().__init__(param)
+
+        pybamm.citations.register("Ai_2019")
+        pybamm.citations.register("deshpande2012battery")
+
+    def _get_standard_variables(self, l_cr):
+        domain = self.domain.lower() + " particle"
+        if self.domain == "Positive":
+            l_cr0 = self.param.l_cr_p_0
+        else:
+            l_cr0 = self.param.l_cr_n_0
+        l_cr_av = pybamm.x_average(l_cr)
+        variables = {
+            self.domain + " particle crack length [m]": l_cr * l_cr0,
+            self.domain + " particle crack length": l_cr,
+            f"X-averaged {domain} crack length": l_cr_av,
+            f"X-averaged {domain} crack length [m]": l_cr_av * l_cr0,
+        }
+        variables.update(self._get_standard_surface_variables(l_cr))
+        return variables
+
+    def _get_mechanical_results(self, variables):
+        c_s_rav = variables[
+            "R-averaged " + self.domain.lower() + " particle concentration"
+        ]
+        c_s_surf = variables[self.domain + " particle surface concentration"]
+        T_xav = variables["X-averaged cell temperature"]
+
+        if "Cell thickness change [m]" not in variables:
+            cell_thickness_change = (
+                T_xav * self.param.Delta_T * self.param.alpha_T_cell_dim
+            )  # thermal expansion
+        else:
+            cell_thickness_change = variables["Cell thickness change [m]"]
+
+        if self.domain == "Negative":
+            x = pybamm.standard_spatial_vars.x_n
+            Omega = self.param.Omega_n
+            R0 = self.param.R_n(x)
+            c_scale = self.param.c_n_max
+            c_0 = self.param.c_n_0
+            E0 = self.param.E_n
+            nu = self.param.nu_n
+            eps_s = self.param.epsilon_s_n
+            L0 = self.param.L_n
+            c_init = self.param.c_n_init(1)
+            v_change = pybamm.x_average(
+                self.param.t_n_change(c_s_rav)
+            ) - self.param.t_n_change(c_init)
+
+        elif self.domain == "Positive":
+            x = pybamm.standard_spatial_vars.x_p
+            Omega = self.param.Omega_p
+            R0 = self.param.R_p(x)
+            c_scale = self.param.c_p_max
+            c_0 = self.param.c_p_0
+            E0 = self.param.E_p
+            nu = self.param.nu_p
+            eps_s = self.param.epsilon_s_p
+            L0 = self.param.L_p
+            c_init = self.param.c_p_init(0)
+            v_change = pybamm.x_average(
+                self.param.t_p_change(c_s_rav)
+            ) - self.param.t_p_change(c_init)
+
+        cell_thickness_change += (
+            self.param.n_electrodes_parallel * eps_s * v_change * L0
+        )
+        disp_surf_dim = Omega * R0 / 3 * (c_s_rav - c_0) * c_scale
+        # c0 reference concentration for no deformation
+        stress_r_surf_dim = 0 * E0
+        stress_t_surf_dim = (
+            Omega * E0 / 3.0 / (1.0 - nu) * (c_s_rav - c_s_surf) * c_scale
+        )
+        disp_surf = disp_surf_dim / R0
+        stress_r_surf = stress_r_surf_dim / E0
+        stress_t_surf = stress_t_surf_dim / E0
+        stress_r_surf_av = pybamm.x_average(stress_r_surf)
+        stress_t_surf_av = pybamm.x_average(stress_t_surf)
+
+        return {
+            self.domain + " particle surface tangential stress": stress_t_surf,
+            self.domain + " particle surface radial stress": stress_r_surf,
+            self.domain + " particle surface displacement": disp_surf,
+            self.domain + " particle surface tangential stress [Pa]": stress_t_surf_dim,
+            self.domain + " particle surface radial stress [Pa]": stress_r_surf_dim,
+            self.domain + " particle surface displacement [m]": disp_surf_dim,
+            "X-averaged "
+            + self.domain.lower()
+            + " particle surface radial stress": stress_r_surf_av,
+            "X-averaged "
+            + self.domain.lower()
+            + " particle surface radial stress [Pa]": stress_r_surf_av * E0,
+            "X-averaged "
+            + self.domain.lower()
+            + " particle surface tangential stress": stress_t_surf_av,
+            "X-averaged "
+            + self.domain.lower()
+            + " particle surface tangential stress [Pa]": stress_t_surf_av * E0,
+            "Cell thickness change [m]": cell_thickness_change,
+        }
+
+    def _get_standard_surface_variables(self, l_cr):
+        """
+        A private function to obtain the standard variables which
+        can be derived from the local particle crack surfaces.
+        Parameters
+        ----------
+        l_cr : :class:`pybamm.Symbol`
+            The crack length in electrode particles.
+        Returns
+        -------
+        variables : dict
+        The variables which can be derived from the crack length.
+        """
+        if self.domain == "Negative":
+            x = pybamm.standard_spatial_vars.x_n
+            a0 = self.param.a_n(x)
+            R0 = self.param.R_n(x)
+            rho_cr = self.param.rho_cr_n
+        elif self.domain == "Positive":
+            x = pybamm.standard_spatial_vars.x_p
+            a0 = self.param.a_p(x)
+            R0 = self.param.R_p(x)
+            rho_cr = self.param.rho_cr_p
+        roughness = l_cr * 2 * rho_cr + 1  # the ratio of cracks to normal surface
+        a_cr = (roughness - 1) * a0  # normalised crack surface area
+        a_cr_dim = a_cr / R0  # crack surface area to volume ratio [m-1]
+
+        roughness_xavg = pybamm.x_average(roughness)
+        variables = {
+            self.domain + " crack surface to volume ratio [m-1]": a_cr_dim,
+            self.domain + " crack surface to volume ratio": a_cr,
+            self.domain + " electrode roughness ratio": roughness,
+            f"X-averaged {self.domain.lower()} "
+            "electrode roughness ratio": roughness_xavg,
+        }
+        return variables
diff --git a/pybamm/models/submodels/particle_cracking/crack_propagation.py b/pybamm/models/submodels/particle_cracking/crack_propagation.py
new file mode 100644
index 0000000000..fd96c7cfda
--- /dev/null
+++ b/pybamm/models/submodels/particle_cracking/crack_propagation.py
@@ -0,0 +1,77 @@
+#
+# Class for cracking
+#
+import pybamm
+from .base_cracking import BaseCracking
+import numpy as np
+
+
+class CrackPropagation(BaseCracking):
+    """
+    Cracking behaviour in electrode particles, from [1]_.
+
+    Parameters
+    ----------
+    param : parameter class
+        The parameters to use for this submodel
+    domain : str
+        The domain of the model either 'Negative' or 'Positive'
+    requiring the radius, average concantration, surface concantration
+
+    References
+    ----------
+    .. [1] Deshpande, R., Verbrugge, M., Cheng, Y. T., Wang, J., & Liu, P. (2012).
+           Battery cycle life prediction with coupled chemical degradation and
+           fatigue mechanics. Journal of the Electrochemical Society, 159(10), A1730.
+
+    **Extends:** :class:`pybamm.particle_cracking.BaseCracking`
+    """
+
+    def __init__(self, param, domain):
+        super().__init__(param, domain)
+
+    def get_fundamental_variables(self):
+        l_cr = pybamm.Variable(
+            self.domain + " particle crack length",
+            domain=self.domain.lower() + " electrode",
+            auxiliary_domains={"secondary": "current collector"},
+        )
+        return self._get_standard_variables(l_cr)
+
+    def get_coupled_variables(self, variables):
+        variables.update(self._get_mechanical_results(variables))
+        T = variables[self.domain + " electrode temperature"]
+        if self.domain == "Negative":
+            k_cr = self.param.k_cr_n(T)
+            m_cr = self.param.m_cr_n
+            b_cr = self.param.b_cr_n
+        else:
+            k_cr = self.param.k_cr_p(T)
+            m_cr = self.param.m_cr_p
+            b_cr = self.param.b_cr_p
+        stress_t_surf = variables[self.domain + " particle surface tangential stress"]
+        l_cr = variables[self.domain + " particle crack length"]
+        # # compressive stress will not lead to crack propagation
+        dK_SIF = stress_t_surf * b_cr * pybamm.Sqrt(np.pi * l_cr) * (stress_t_surf >= 0)
+        dl_cr = k_cr * pybamm.Power(dK_SIF, m_cr) / self.param.t0_cr
+        variables.update(
+            {
+                self.domain + " particle cracking rate": dl_cr,
+                "X-averaged "
+                + self.domain.lower()
+                + " particle cracking rate": pybamm.x_average(dl_cr),
+            }
+        )
+        return variables
+
+    def set_rhs(self, variables):
+        l_cr = variables[self.domain + " particle crack length"]
+        dl_cr = variables[self.domain + " particle cracking rate"]
+        self.rhs = {l_cr: dl_cr}
+
+    def set_initial_conditions(self, variables):
+        l_cr = variables[self.domain + " particle crack length"]
+        l0 = pybamm.PrimaryBroadcast(
+            pybamm.Scalar(1), [self.domain.lower() + " electrode"]
+        )
+        self.initial_conditions = {l_cr: l0}
diff --git a/pybamm/models/submodels/particle_cracking/no_cracking.py b/pybamm/models/submodels/particle_cracking/no_cracking.py
new file mode 100644
index 0000000000..8eecfd9cb1
--- /dev/null
+++ b/pybamm/models/submodels/particle_cracking/no_cracking.py
@@ -0,0 +1,41 @@
+#
+# Class for no cracking
+#
+import pybamm
+from .base_cracking import BaseCracking
+
+
+class NoCracking(BaseCracking):
+    """
+    Class for no cracking.
+
+    Parameters
+    ----------
+    param : parameter class
+        The parameters to use for this submodel
+    domain : str
+        The domain of the model either 'Negative' or 'Positive'
+
+    **Extends:** :class:`pybamm.particle_cracking.BaseCracking`
+    """
+
+    def __init__(self, param, domain):
+        super().__init__(param, domain)
+
+    def get_fundamental_variables(self):
+        zero = pybamm.FullBroadcast(
+            pybamm.Scalar(0), self.domain.lower() + " electrode", "current collector"
+        )
+        zero_av = pybamm.x_average(zero)
+        variables = self._get_standard_variables(zero)
+        variables.update(
+            {
+                self.domain + " particle cracking rate": zero,
+                "X-averaged " + self.domain + " particle cracking rate": zero_av,
+            }
+        )
+        return variables
+
+    def get_coupled_variables(self, variables):
+        variables.update(self._get_mechanical_results(variables))
+        return variables
diff --git a/pybamm/models/submodels/thermal/base_thermal.py b/pybamm/models/submodels/thermal/base_thermal.py
index 4a3c5db8f2..832e9d5634 100644
--- a/pybamm/models/submodels/thermal/base_thermal.py
+++ b/pybamm/models/submodels/thermal/base_thermal.py
@@ -91,6 +91,9 @@ def _get_standard_coupled_variables(self, variables):
         T = variables["Cell temperature"]
         T_n, _, T_p = T.orphans
 
+        a_n = variables["Negative electrode surface area per unit volume"]
+        a_p = variables["Positive electrode surface area per unit volume"]
+
         j_n = variables["Negative electrode interfacial current density"]
         j_p = variables["Positive electrode interfacial current density"]
 
@@ -133,8 +136,8 @@ def _get_standard_coupled_variables(self, variables):
         Q_ohm = Q_ohm_s + Q_ohm_e
 
         # Irreversible electrochemical heating
-        Q_rxn_n = j_n * eta_r_n
-        Q_rxn_p = j_p * eta_r_p
+        Q_rxn_n = a_n * j_n * eta_r_n
+        Q_rxn_p = a_p * j_p * eta_r_p
         Q_rxn = pybamm.Concatenation(
             *[
                 Q_rxn_n,
@@ -144,8 +147,8 @@ def _get_standard_coupled_variables(self, variables):
         )
 
         # Reversible electrochemical heating
-        Q_rev_n = j_n * (param.Theta ** (-1) + T_n) * dUdT_n
-        Q_rev_p = j_p * (param.Theta ** (-1) + T_p) * dUdT_p
+        Q_rev_n = a_n * j_n * (param.Theta ** (-1) + T_n) * dUdT_n
+        Q_rev_p = a_p * j_p * (param.Theta ** (-1) + T_p) * dUdT_p
         Q_rev = pybamm.Concatenation(
             *[
                 Q_rev_n,
diff --git a/pybamm/parameters/electrical_parameters.py b/pybamm/parameters/electrical_parameters.py
index c233a4c622..785d2bd1f1 100644
--- a/pybamm/parameters/electrical_parameters.py
+++ b/pybamm/parameters/electrical_parameters.py
@@ -17,7 +17,7 @@ class ElectricalParameters:
     def __init__(self):
 
         # Get geometric parameters
-        self.geo = pybamm.GeometricParameters()
+        self.geo = pybamm.geometric_parameters
 
         # Set parameters
         self._set_dimensional_parameters()
@@ -28,7 +28,7 @@ def _set_dimensional_parameters(self):
 
         self.I_typ = pybamm.Parameter("Typical current [A]")
         self.Q = pybamm.Parameter("Cell capacity [A.h]")
-        self.C_rate = abs(self.I_typ / self.Q)
+        self.C_rate = pybamm.AbsoluteValue(self.I_typ / self.Q)
         self.n_electrodes_parallel = pybamm.Parameter(
             "Number of electrodes connected in parallel to make a cell"
         )
@@ -64,3 +64,6 @@ def _set_dimensionless_parameters(self):
             / self.I_typ
             * pybamm.Function(np.sign, self.I_typ)
         )
+
+
+electrical_parameters = ElectricalParameters()
diff --git a/pybamm/parameters/geometric_parameters.py b/pybamm/parameters/geometric_parameters.py
index 98d6f254c1..91b7de39a7 100644
--- a/pybamm/parameters/geometric_parameters.py
+++ b/pybamm/parameters/geometric_parameters.py
@@ -49,8 +49,9 @@ def _set_dimensional_parameters(self):
         self.A_tab_p = self.L_tab_p * self.L_cp  # Area of negative tab
 
         # Microscale geometry
-        # Note: the definition of the surface area to volume ratio is
-        # overwritten in lithium_ion_parameters.py to be computed
+        # Note: parameters related to the particles in li-ion cells are defined
+        # in lithium_ion_parameters.py. The definition of the surface area to
+        # volume ratio is overwritten in lithium_ion_parameters.py to be computed
         # based on the assumed particle shape
         self.a_n_dim = pybamm.Parameter(
             "Negative electrode surface area to volume ratio [m-1]"
@@ -58,8 +59,6 @@ def _set_dimensional_parameters(self):
         self.a_p_dim = pybamm.Parameter(
             "Positive electrode surface area to volume ratio [m-1]"
         )
-        self.R_n = pybamm.Parameter("Negative particle radius [m]")
-        self.R_p = pybamm.Parameter("Positive particle radius [m]")
         self.b_e_n = pybamm.Parameter(
             "Negative electrode Bruggeman coefficient (electrolyte)"
         )
@@ -101,3 +100,6 @@ def _set_dimensionless_parameters(self):
         self.l_tab_p = self.L_tab_p / self.L_z
         self.centre_y_tab_p = self.Centre_y_tab_p / self.L_z
         self.centre_z_tab_p = self.Centre_z_tab_p / self.L_z
+
+
+geometric_parameters = GeometricParameters()
diff --git a/pybamm/parameters/lead_acid_parameters.py b/pybamm/parameters/lead_acid_parameters.py
index 3ccd0736ad..e25e5faaba 100644
--- a/pybamm/parameters/lead_acid_parameters.py
+++ b/pybamm/parameters/lead_acid_parameters.py
@@ -22,9 +22,9 @@ class LeadAcidParameters:
     def __init__(self):
 
         # Get geometric, electrical and thermal parameters
-        self.geo = pybamm.GeometricParameters()
-        self.elec = pybamm.ElectricalParameters()
-        self.therm = pybamm.ThermalParameters()
+        self.geo = pybamm.geometric_parameters
+        self.elec = pybamm.electrical_parameters
+        self.therm = pybamm.thermal_parameters
 
         # Set parameters and scales
         self._set_dimensional_parameters()
@@ -86,8 +86,8 @@ def _set_dimensional_parameters(self):
         )  # pybamm.Parameter("Typical oxygen concentration [mol.m-3]")
 
         # Microstructure
-        self.a_n_dim = self.geo.a_n_dim
-        self.a_p_dim = self.geo.a_p_dim
+        # Note: the surface area per unit volume can be set as a function of
+        # through-cell position, so is defined later as a function
         self.b_e_n = self.geo.b_e_n
         self.b_e_s = self.geo.b_e_s
         self.b_e_p = self.geo.b_e_p
@@ -316,17 +316,41 @@ def j0_p_Ox_dimensional(self, c_e, T):
             "Positive electrode oxygen exchange-current density [A.m-2]", inputs
         )
 
+    def a_n_dimensional(self, x):
+        """
+        Negative electrode surface area per unit volume as a function of
+        through-cell distance
+        """
+        inputs = {"Through-cell distance (x_n) [m]": x}
+        return pybamm.FunctionParameter(
+            "Negative electrode surface area to volume ratio [m-1]", inputs
+        )
+
+    def a_p_dimensional(self, x):
+        """
+        Positive electrode surface area per unit volume as a function of
+        through-cell distance
+        """
+        inputs = {"Through-cell distance (x_p) [m]": x}
+        return pybamm.FunctionParameter(
+            "Positive electrode surface area to volume ratio [m-1]", inputs
+        )
+
     def _set_scales(self):
         "Define the scales used in the non-dimensionalisation scheme"
 
+        # Microscale (typical values at electrode/current collector interface)
+        self.a_n_typ = self.a_n_dimensional(0)
+        self.a_p_typ = self.a_p_dimensional(self.L_x)
+
         # Concentrations
         self.electrolyte_concentration_scale = self.c_e_typ
 
         # Electrical
         self.potential_scale = self.R * self.T_ref / self.F
         self.current_scale = self.i_typ
-        self.j_scale_n = self.i_typ / (self.a_n_dim * self.L_x)
-        self.j_scale_p = self.i_typ / (self.a_p_dim * self.L_x)
+        self.j_scale_n = self.i_typ / (self.a_n_typ * self.L_x)
+        self.j_scale_p = self.i_typ / (self.a_p_typ * self.L_x)
 
         # Reaction velocity scale
         self.velocity_scale = self.i_typ / (self.c_e_typ * self.F)
@@ -453,8 +477,8 @@ def _set_dimensionless_parameters(self):
         self.sigma_p_prime = self.sigma_p * self.delta ** 2
         self.sigma_cn_prime = self.sigma_cn * self.delta ** 2
         self.sigma_cp_prime = self.sigma_cp * self.delta ** 2
-        self.delta_pore_n = 1 / (self.a_n_dim * self.L_x)
-        self.delta_pore_p = 1 / (self.a_p_dim * self.L_x)
+        self.delta_pore_n = 1 / (self.a_n_typ * self.L_x)
+        self.delta_pore_p = 1 / (self.a_p_typ * self.L_x)
         self.Q_n_max = self.Q_n_max_dimensional / (self.c_e_typ * self.F)
         self.Q_p_max = self.Q_p_max_dimensional / (self.c_e_typ * self.F)
         self.beta_U_n = 1 / self.Q_n_max
@@ -652,7 +676,7 @@ def kappa_e(self, c_e, T):
         kappa_scale = self.F ** 2 * self.D_e_typ * self.c_e_typ / (self.R * self.T_ref)
         return self.kappa_e_dimensional(c_e_dimensional, self.T_ref) / kappa_scale
 
-    def chi(self, c_e, c_ox=0, c_hy=0):
+    def chi(self, c_e, T, c_ox=0, c_hy=0):
         "Thermodynamic factor"
         return (
             self.chi_dimensional(self.c_e_typ * c_e)
@@ -711,29 +735,21 @@ def c_p_init(self, x):
         """
         return self.c_e_init
 
-    def a_n_of_x(self, x):
+    def a_n(self, x):
         """
-        Dimensionless surface area per unit volume distribution in x (as a function
-        for consistency with lithium-ion). The surface area per unit volume
-        distribution is defined so that the actual surface area per unit volume
-        as a function of x is given by a*a_of_x (so that a_of_x = 1 gives uniform
-        surface area per unit volume in x).
-
-        Returns 1 to give uniform surface area per unit volume in x.
+        Dimensionless negative electrode surface area per unit volume as a
+        function of dimensionless position x
         """
-        return pybamm.FullBroadcast(1, "negative electrode", "current collector")
+        x_dim = x * self.L_x
+        return self.a_n_dimensional(x_dim) / self.a_n_typ
 
-    def a_p_of_x(self, x):
+    def a_p(self, x):
         """
-        Dimensionless surface area per unit volume distribution in x (as a function
-        for consistency with lithium-ion). The surface area per unit volume
-        distribution is defined so that the actual surface area per unit volume
-        as a function of x is given by a*a_of_x (so that a_of_x = 1 gives uniform
-        surface area per unit volume in x).
-
-        Returns 1 to give uniform surface area per unit volume in x.
+        Dimensionless positive electrode surface area per unit volume as a
+        function of dimensionless position x
         """
-        return pybamm.FullBroadcast(1, "positive electrode", "current collector")
+        x_dim = x * self.L_x
+        return self.a_p_dimensional(x_dim) / self.a_p_typ
 
     def _set_input_current(self):
         "Set the input current"
diff --git a/pybamm/parameters/lithium_ion_parameters.py b/pybamm/parameters/lithium_ion_parameters.py
index 9ec595e44d..34986f09fa 100644
--- a/pybamm/parameters/lithium_ion_parameters.py
+++ b/pybamm/parameters/lithium_ion_parameters.py
@@ -36,9 +36,9 @@ def __init__(self, options=None):
         self.options = options
 
         # Get geometric, electrical and thermal parameters
-        self.geo = pybamm.GeometricParameters()
-        self.elec = pybamm.ElectricalParameters()
-        self.therm = pybamm.ThermalParameters()
+        self.geo = pybamm.geometric_parameters
+        self.elec = pybamm.electrical_parameters
+        self.therm = pybamm.thermal_parameters
 
         # Set parameters and scales
         self._set_dimensional_parameters()
@@ -110,6 +110,9 @@ def _set_dimensional_parameters(self):
         )
 
         # Microscale geometry
+        # Note: the particle radius in the electrodes can be set as a function
+        # of through-cell position, so is defined later as a function, along with
+        # the surface area per unit volume
         inputs = {"Through-cell distance (x_n) [m]": pybamm.standard_spatial_vars.x_n}
         self.epsilon_n = pybamm.FunctionParameter("Negative electrode porosity", inputs)
 
@@ -138,26 +141,6 @@ def _set_dimensional_parameters(self):
         self.b_s_s = self.geo.b_s_s
         self.b_s_p = self.geo.b_s_p
 
-        self.R_n = self.geo.R_n
-        self.R_p = self.geo.R_p
-
-        if self.options["particle shape"] == "spherical":
-            self.a_n_dim = 3 * self.epsilon_s_n / self.R_n
-            self.a_p_dim = 3 * self.epsilon_s_p / self.R_p
-        elif self.options["particle shape"] == "user":
-            self.a_n_dim = self.geo.a_n_dim
-            self.a_p_dim = self.geo.a_p_dim
-
-        self.a_k_dim = pybamm.Concatenation(
-            pybamm.FullBroadcast(
-                self.a_n_dim, ["negative electrode"], "current collector"
-            ),
-            pybamm.FullBroadcast(0, ["separator"], "current collector"),
-            pybamm.FullBroadcast(
-                self.a_p_dim, ["positive electrode"], "current collector"
-            ),
-        )
-
         # Electrochemical reactions
         self.ne_n = pybamm.Parameter("Negative electrode electrons in reaction")
         self.ne_p = pybamm.Parameter("Positive electrode electrons in reaction")
@@ -224,6 +207,57 @@ def _set_dimensional_parameters(self):
             "Initial concentration in electrolyte [mol.m-3]"
         )
 
+        # mechanical parameters
+        self.nu_p = pybamm.Parameter("Positive electrode Poisson's ratio")
+        self.E_p = pybamm.Parameter("Positive electrode Young's modulus [Pa]")
+        self.c_p_0_dim = pybamm.Parameter(
+            "Positive electrode reference concentration for free of deformation "
+            "[mol.m-3]"
+        )
+        self.Omega_p = pybamm.Parameter(
+            "Positive electrode partial molar volume [m3.mol-1]"
+        )
+        self.nu_n = pybamm.Parameter("Negative electrode Poisson's ratio")
+        self.E_n = pybamm.Parameter("Negative electrode Young's modulus [Pa]")
+        self.c_n_0_dim = pybamm.Parameter(
+            "Negative electrode reference concentration for free of deformation "
+            "[mol.m-3]"
+        )
+        self.Omega_n = pybamm.Parameter(
+            "Negative electrode partial molar volume [m3.mol-1]"
+        )
+        self.l_cr_p_0 = pybamm.Parameter("Positive electrode initial crack length [m]")
+        self.l_cr_n_0 = pybamm.Parameter("Negative electrode initial crack length [m]")
+        self.w_cr = pybamm.Parameter("Negative electrode initial crack width [m]")
+        self.rho_cr_n_dim = pybamm.Parameter(
+            "Negative electrode number of cracks per unit area [m-2]"
+        )
+        self.rho_cr_p_dim = pybamm.Parameter(
+            "Positive electrode number of cracks per unit area [m-2]"
+        )
+        self.b_cr_n = pybamm.Parameter("Negative electrode Paris' law constant b")
+        self.m_cr_n = pybamm.Parameter("Negative electrode Paris' law constant m")
+        self.Eac_cr_n = pybamm.Parameter(
+            "Negative electrode activation energy for cracking rate [kJ.mol-1]"
+        )  # noqa
+        self.b_cr_p = pybamm.Parameter("Positive electrode Paris' law constant b")
+        self.m_cr_p = pybamm.Parameter("Positive electrode Paris' law constant m")
+        self.Eac_cr_p = pybamm.Parameter(
+            "Positive electrode activation energy for cracking rate [kJ.mol-1]"
+        )  # noqa
+        self.alpha_T_cell_dim = pybamm.Parameter(
+            "Cell thermal expansion coefficien [m.K-1]"
+        )
+        self.R_const = pybamm.constants.R
+        self.theta_p_dim = (
+            self.Omega_p ** 2 / self.R_const * 2 / 9 * self.E_p / (1 - self.nu_p)
+        )
+        # intermediate variable  [K*m^3/mol]
+        self.theta_n_dim = (
+            self.Omega_n ** 2 / self.R_const * 2 / 9 * self.E_n / (1 - self.nu_n)
+        )
+        # intermediate variable  [K*m^3/mol]
+
     def D_e_dimensional(self, c_e, T):
         "Dimensional diffusivity in electrolyte"
         inputs = {"Electrolyte concentration [mol.m-3]": c_e, "Temperature [K]": T}
@@ -238,16 +272,30 @@ def D_n_dimensional(self, sto, T):
         """Dimensional diffusivity in negative particle. Note this is defined as a
         function of stochiometry"""
         inputs = {"Negative particle stoichiometry": sto, "Temperature [K]": T}
-        return pybamm.FunctionParameter(
-            "Negative electrode diffusivity [m2.s-1]", inputs
+        if self.options["particle cracking"] is not None:
+            mech_effects = (
+                1 + self.theta_n_dim * (sto * self.c_n_max - self.c_n_0_dim) / T
+            )
+        else:
+            mech_effects = 1
+        return (
+            pybamm.FunctionParameter("Negative electrode diffusivity [m2.s-1]", inputs)
+            * mech_effects
         )
 
     def D_p_dimensional(self, sto, T):
         """Dimensional diffusivity in positive particle. Note this is defined as a
         function of stochiometry"""
         inputs = {"Positive particle stoichiometry": sto, "Temperature [K]": T}
-        return pybamm.FunctionParameter(
-            "Positive electrode diffusivity [m2.s-1]", inputs
+        if self.options["particle cracking"] is not None:
+            mech_effects = (
+                1 + self.theta_p_dim * (sto * self.c_p_max - self.c_p_0_dim) / T
+            )
+        else:
+            mech_effects = 1
+        return (
+            pybamm.FunctionParameter("Positive electrode diffusivity [m2.s-1]", inputs)
+            * mech_effects
         )
 
     def j0_n_dimensional(self, c_e, c_s_surf, T):
@@ -310,6 +358,42 @@ def dUdT_p_dimensional(self, sto):
             "Positive electrode OCP entropic change [V.K-1]", inputs
         )
 
+    def R_n_dimensional(self, x):
+        "Negative particle radius as a function of through-cell distance"
+        inputs = {"Through-cell distance (x_n) [m]": x}
+        return pybamm.FunctionParameter("Negative particle radius [m]", inputs)
+
+    def R_p_dimensional(self, x):
+        "Positive particle radius as a function of through-cell distance"
+        inputs = {"Through-cell distance (x_p) [m]": x}
+        return pybamm.FunctionParameter("Positive particle radius [m]", inputs)
+
+    def a_n_dimensional(self, x):
+        """
+        Negative electrode surface area per unit volume as a function of
+        through-cell distance
+        """
+        inputs = {"Through-cell distance (x_n) [m]": x}
+        if self.options["particle shape"] == "spherical":
+            return 3 * self.epsilon_s_n / self.R_n_dimensional(x)
+        elif self.options["particle shape"] == "user":
+            return pybamm.FunctionParameter(
+                "Negative electrode surface area to volume ratio [m-1]", inputs
+            )
+
+    def a_p_dimensional(self, x):
+        """
+        Positive electrode surface area per unit volume as a function of
+        through-cell distance
+        """
+        inputs = {"Through-cell distance (x_p) [m]": x}
+        if self.options["particle shape"] == "spherical":
+            return 3 * self.epsilon_s_p / self.R_p_dimensional(x)
+        elif self.options["particle shape"] == "user":
+            return pybamm.FunctionParameter(
+                "Positive electrode surface area to volume ratio [m-1]", inputs
+            )
+
     def c_n_init_dimensional(self, x):
         "Initial concentration as a function of dimensionless position x"
         inputs = {"Dimensionless through-cell position (x_n)": x}
@@ -327,6 +411,12 @@ def c_p_init_dimensional(self, x):
     def _set_scales(self):
         "Define the scales used in the non-dimensionalisation scheme"
 
+        # Microscale (typical values at electrode/current collector interface)
+        self.R_n_typ = self.R_n_dimensional(0)
+        self.R_p_typ = self.R_p_dimensional(self.L_x)
+        self.a_n_typ = self.a_n_dimensional(0)
+        self.a_p_typ = self.a_p_dimensional(self.L_x)
+
         # Concentration
         self.electrolyte_concentration_scale = self.c_e_typ
         self.negative_particle_concentration_scale = self.c_n_max
@@ -335,8 +425,8 @@ def _set_scales(self):
         # Electrical
         self.potential_scale = self.R * self.T_ref / self.F
         self.current_scale = self.i_typ
-        self.j_scale_n = self.i_typ / (self.a_n_dim * self.L_x)
-        self.j_scale_p = self.i_typ / (self.a_p_dim * self.L_x)
+        self.j_scale_n = self.i_typ / (self.a_n_typ * self.L_x)
+        self.j_scale_p = self.i_typ / (self.a_p_typ * self.L_x)
 
         # Reference OCP based on initial concentration at
         # current collector/electrode interface
@@ -367,10 +457,10 @@ def _set_scales(self):
 
         # Reaction timescales
         self.tau_r_n = (
-            self.F * self.c_n_max / (self.j0_n_ref_dimensional * self.a_n_dim)
+            self.F * self.c_n_max / (self.j0_n_ref_dimensional * self.a_n_typ)
         )
         self.tau_r_p = (
-            self.F * self.c_p_max / (self.j0_p_ref_dimensional * self.a_p_dim)
+            self.F * self.c_p_max / (self.j0_p_ref_dimensional * self.a_p_typ)
         )
 
         # Electrolyte diffusion timescale
@@ -378,10 +468,10 @@ def _set_scales(self):
         self.tau_diffusion_e = self.L_x ** 2 / self.D_e_typ
 
         # Particle diffusion timescales
-        self.tau_diffusion_n = self.R_n ** 2 / self.D_n_dimensional(
+        self.tau_diffusion_n = self.R_n_typ ** 2 / self.D_n_dimensional(
             pybamm.Scalar(1), self.T_ref
         )
-        self.tau_diffusion_p = self.R_p ** 2 / self.D_p_dimensional(
+        self.tau_diffusion_p = self.R_p_typ ** 2 / self.D_p_dimensional(
             pybamm.Scalar(1), self.T_ref
         )
 
@@ -429,11 +519,9 @@ def _set_dimensionless_parameters(self):
         self.centre_y_tab_p = self.geo.centre_y_tab_p
         self.centre_z_tab_p = self.geo.centre_z_tab_p
 
-        # Microscale geometry, see 'self._set_dimensional_parameters' for the
-        # definition on the dimensional surface area to volume ratio based on
-        # particle shape
-        self.a_n = self.a_n_dim * self.R_n
-        self.a_p = self.a_p_dim * self.R_p
+        # Microscale geometry
+        self.a_R_n = self.a_n_typ * self.R_n_typ
+        self.a_R_p = self.a_p_typ * self.R_p_typ
 
         # Electrode Properties
         self.sigma_cn = (
@@ -616,7 +704,7 @@ def _set_dimensionless_parameters(self):
                 )
             )
         )
-        self.beta_sei_n = self.a_n_dim * self.L_sei_0_dim * self.Gamma_SEI_n
+        self.beta_sei_n = self.a_n_typ * self.L_sei_0_dim * self.Gamma_SEI_n
 
         # Initial conditions
         self.epsilon_n_init = pybamm.Parameter("Negative electrode porosity")
@@ -628,22 +716,35 @@ def _set_dimensionless_parameters(self):
         self.T_init = self.therm.T_init
         self.c_e_init = self.c_e_init_dimensional / self.c_e_typ
 
-    def chi(self, c_e):
+        # Dimensionless mechanical parameters
+        self.rho_cr_n = self.rho_cr_n_dim * self.l_cr_n_0 * self.w_cr
+        self.rho_cr_p = self.rho_cr_p_dim * self.l_cr_p_0 * self.w_cr
+        self.theta_p = self.theta_p_dim * self.c_p_max / self.Delta_T
+        self.theta_n = self.theta_n_dim * self.c_n_max / self.Delta_T
+        self.c_p_0 = self.c_p_0_dim / self.c_p_max
+        self.c_n_0 = self.c_n_0_dim / self.c_n_max
+        self.t0_cr = 3600 / self.C_rate / self.timescale
+        # nomarlised typical time for one cycle
+
+    def chi(self, c_e, T):
         """
         Thermodynamic factor:
             (1-2*t_plus) is for Nernst-Planck,
             2*(1-t_plus) for Stefan-Maxwell,
         see Bizeray et al (2016) "Resolving a discrepancy ...".
         """
-        return (2 * (1 - self.t_plus(c_e))) * (self.one_plus_dlnf_dlnc(c_e))
+        return (2 * (1 - self.t_plus(c_e))) * (self.one_plus_dlnf_dlnc(c_e, T))
 
     def t_plus(self, c_e):
         "Dimensionless transference number (i.e. c_e is dimensionless)"
         inputs = {"Electrolyte concentration [mol.m-3]": c_e * self.c_e_typ}
         return pybamm.FunctionParameter("Cation transference number", inputs)
 
-    def one_plus_dlnf_dlnc(self, c_e):
-        inputs = {"Electrolyte concentration [mol.m-3]": c_e * self.c_e_typ}
+    def one_plus_dlnf_dlnc(self, c_e, T):
+        inputs = {
+            "Electrolyte concentration [mol.m-3]": c_e * self.c_e_typ,
+            "Temperature [K]": self.Delta_T * T + self.T_ref,
+        }
         return pybamm.FunctionParameter("1 + dlnf/dlnc", inputs)
 
     def D_e(self, c_e, T):
@@ -719,67 +820,45 @@ def dUdT_p(self, c_s_p):
         sto = c_s_p
         return self.dUdT_p_dimensional(sto) * self.Delta_T / self.potential_scale
 
-    def c_n_init(self, x):
-        "Dimensionless initial concentration as a function of dimensionless position x"
-        return self.c_n_init_dimensional(x) / self.c_n_max
-
-    def c_p_init(self, x):
-        "Dimensionless initial concentration as a function of dimensionless position x"
-        return self.c_p_init_dimensional(x) / self.c_p_max
-
-    def R_n_of_x(self, x):
+    def R_n(self, x):
         """
-        Dimensionless negative particle distribution in x. The particle distribution is
-        defined so that the actual particle radius as a function of x is given by
-        R*R_of_x (so that R_of_x = 1 gives particles of uniform size in x).
+        Dimensionless negative particle radius as a function of dimensionless
+        position x
         """
-        inputs = {"Through-cell distance (x_n) [m]": x}
-        return pybamm.FunctionParameter("Negative particle distribution in x", inputs)
+        x_dim = x * self.L_x
+        return self.R_n_dimensional(x_dim) / self.R_n_typ
 
-    def R_p_of_x(self, x):
+    def R_p(self, x):
         """
-        Dimensionless positive particle distribution in x. The particle distribution is
-        defined so that the actual particle radius as a function of x is given by
-        R*R_of_x (so that R_of_x = 1 gives particles of uniform size in x).
+        Dimensionless positive particle radius as a function of dimensionless
+        position x
         """
-        inputs = {"Through-cell distance (x_p) [m]": x}
-        return pybamm.FunctionParameter("Positive particle distribution in x", inputs)
+        x_dim = x * self.L_x
+        return self.R_p_dimensional(x_dim) / self.R_p_typ
 
-    def a_n_of_x(self, x):
+    def a_n(self, x):
         """
-        Dimensionless surface area per unit volume distribution in x. The surface
-        area per unit volume distribution is defined so that the actual surface
-        area per unit volume as a function of x is given by a*a_of_x (so that
-        a_of_x = 1 gives uniform surface area per unit volume in x).
+        Dimensionless negative electrode surface area per unit volume as a
+        function of dimensionless position x.
         """
-        if self.options["particle shape"] == "spherical":
-            # Currently the active material volume fraction is a scalar, so the
-            # distribution of surface are per unit volume is simply the reciprocal
-            # of the particle radius distribution
-            return 1 / self.R_n_of_x(x)
-        elif self.options["particle shape"] == "user":
-            inputs = {"Through-cell distance (x_n) [m]": x}
-            return pybamm.FunctionParameter(
-                "Negative surface area per unit volume distribution in x", inputs
-            )
+        x_dim = x * self.L_x
+        return self.a_n_dimensional(x_dim) / self.a_n_typ
 
-    def a_p_of_x(self, x):
+    def a_p(self, x):
         """
-        Dimensionless surface area per unit volume distribution in x. The surface
-        area per unit volume distribution is defined so that the actual surface
-        area per unit volume as a function of x is given by a*a_of_x (so that
-        a_of_x = 1 gives uniform surface area per unit volume in x).
+        Dimensionless positive electrode surface area per unit volume as a
+        function of dimensionless position x.
         """
-        if self.options["particle shape"] == "spherical":
-            # Currently the active material volume fraction is a scalar, so the
-            # distribution of surface are per unit volume is simply the reciprocal
-            # of the particle radius distribution
-            return 1 / self.R_p_of_x(x)
-        elif self.options["particle shape"] == "user":
-            inputs = {"Through-cell distance (x_p) [m]": x}
-            return pybamm.FunctionParameter(
-                "Positive surface area per unit volume distribution in x", inputs
-            )
+        x_dim = x * self.L_x
+        return self.a_p_dimensional(x_dim) / self.a_p_typ
+
+    def c_n_init(self, x):
+        "Dimensionless initial concentration as a function of dimensionless position x"
+        return self.c_n_init_dimensional(x) / self.c_n_max
+
+    def c_p_init(self, x):
+        "Dimensionless initial concentration as a function of dimensionless position x"
+        return self.c_p_init_dimensional(x) / self.c_p_max
 
     def _set_input_current(self):
         "Set the input current"
@@ -797,6 +876,50 @@ def _set_input_current(self):
             * pybamm.Function(np.sign, self.I_typ)
         )
 
+    def t_n_change(self, sto):
+        """
+        Dimentionless volume change for the negative electrode;
+        sto should be R-averaged
+        """
+        return pybamm.FunctionParameter(
+            "Negative electrode volume change", {"Particle stoichiometry": sto}
+        )
+
+    def t_p_change(self, sto):
+        """
+        Dimentionless volume change for the positive electrode;
+        sto should be R-averaged
+        """
+        return pybamm.FunctionParameter(
+            "Positive electrode volume change", {"Particle stoichiometry": sto}
+        )
+
+    def k_cr_p(self, T):
+        """
+        Dimentionless cracking rate for the positive electrode;
+        """
+        T_dim = self.Delta_T * T + self.T_ref
+        delta_k_cr = self.E_p ** self.m_cr_p * self.l_cr_p_0 ** (self.m_cr_p / 2 - 1)
+        return (
+            pybamm.FunctionParameter(
+                "Positive electrode cracking rate", {"Temperature [K]": T_dim}
+            )
+            * delta_k_cr
+        )
+
+    def k_cr_n(self, T):
+        """
+        Dimentionless cracking rate for the negative electrode;
+        """
+        T_dim = self.Delta_T * T + self.T_ref
+        delta_k_cr = self.E_n ** self.m_cr_n * self.l_cr_n_0 ** (self.m_cr_n / 2 - 1)
+        return (
+            pybamm.FunctionParameter(
+                "Negative electrode cracking rate", {"Temperature [K]": T_dim}
+            )
+            * delta_k_cr
+        )
+
     @property
     def options(self):
         return self._options
@@ -806,7 +929,7 @@ def options(self, extra_options):
         extra_options = extra_options or {}
 
         # Default options
-        options = {"particle shape": "spherical"}
+        options = {"particle shape": "spherical", "particle cracking": None}
 
         # All model options get passed to the parameter class, so we just need
         # to update the options in the default options and ignore the rest
@@ -822,4 +945,16 @@ def options(self, extra_options):
                 "particle shape '{}' not recognised".format(options["particle shape"])
             )
 
+        if options["particle cracking"] not in [
+            None,
+            "no cracking",
+            "cathode",
+            "anode",
+            "both",
+        ]:
+            raise pybamm.OptionError(
+                "particle cracking '{}' not recognised".format(
+                    options["particle cracking"]
+                )
+            )
         self._options = options
diff --git a/pybamm/parameters/parameter_sets.py b/pybamm/parameters/parameter_sets.py
index d14bb97ee2..de1713d31c 100644
--- a/pybamm/parameters/parameter_sets.py
+++ b/pybamm/parameters/parameter_sets.py
@@ -10,42 +10,61 @@
 --------------------------
     * Chen2020 :
         C.-H. Chen, F. Brosa Planella, K. O’Regan, D. Gastol, W. D. Widanage, and E.
-        Kendrick. “Development of Experimental Techniques for Parameterization of
-        Multi-scale Lithium-ion Battery Models.” Journal of the Electrochemical Society,
+        Kendrick. "Development of Experimental Techniques for Parameterization of
+        Multi-scale Lithium-ion Battery Models." Journal of the Electrochemical Society,
         167(8), 080534 (2020).
     * Ecker2015 :
         M. Ecker, T. K. D. Tran, P. Dechent, S. Käbitz, A. Warnecke, and D. U. Sauer.
-        “Parameterization of a Physico-Chemical Model of a Lithium-Ion Battery. I.
-        Determination of Parameters.” Journal of the Electrochemical Society, 162(9),
+        "Parameterization of a Physico-Chemical Model of a Lithium-Ion Battery. I.
+        Determination of Parameters." Journal of the Electrochemical Society, 162(9),
         A1836-A1848 (2015).
     * Marquis2019 :
-        S. G. Marquis, V. Sulzer, R. Timms, C. P. Please and S. J. Chapman. “An
-        asymptotic derivation of a single particle model with electrolyte.” Journal of
+        S. G. Marquis, V. Sulzer, R. Timms, C. P. Please and S. J. Chapman. "An
+        asymptotic derivation of a single particle model with electrolyte." Journal of
         the Electrochemical Society, 166(15), A3693–A3706 (2019).
     * Mohtat2020 :
-        Submitted for publication.
+        P. Mohtat, S. Lee, V. Sulzer, J. B. Siegel & A. G. Stefanopoulou. "Differential
+        Expansion and Voltage Model for Li-ion Batteries at Practical Charging Rates".
+        Journal of The Electrochemical Society, 167(11), 110561 (2020).
     * NCA_Kim2011 :
         G. H. Kim, K. Smith, K. J. Lee, S. Santhanagopalan, and A. Pesaran.
-        “Multi-domain modeling of lithium-ion batteries encompassing multi-physics in
-        varied length scales.” Journal of The Electrochemical Society, 158(8), A955-A969
+        "Multi-domain modeling of lithium-ion batteries encompassing multi-physics in
+        varied length scales." Journal of The Electrochemical Society, 158(8), A955-A969
         (2011).
-    * Ramadass 2004 :
-        P. Ramadass, B. Haran, P. M. Gomadam, R. White, and B. N. Popov. “Development
-        of First Principles Capacity Fade Model for Li-Ion Cells.” Journal of the
+    * Ramadass2004 :
+        P. Ramadass, B. Haran, P. M. Gomadam, R. White, and B. N. Popov. "Development
+        of First Principles Capacity Fade Model for Li-Ion Cells." Journal of the
         Electrochemical Society, 151(2), A196-A203 (2004).
+    * Ai 2020 :
+        > Ai, W., Kraft, L., Sturm, J., Jossen, A., & Wu, B. (2020).
+        Electrochemical Thermal-Mechanical Modelling of Stress Inhomogeneity
+        in Lithium-Ion Pouch Cells. Journal of The Electrochemical Society,
+        167(1), 013512. DOI: 10.1149/2.0122001JES.
+    * Prada2013 :
+        C.-H. Chen, F. Brosa Planella, K. O’Regan, D. Gastol, W. D. Widanage, and E.
+        Kendrick. "Development of Experimental Techniques for Parameterization of
+        Multi-scale Lithium-ion Battery Models." Journal of the Electrochemical Society,
+        167(8), 080534 (2020).
+        E. Prada, D., Di Domenico, Y., Creff, J., Bernard, V., Sauvant-Moynot, and F.
+        Huet. "A simplified electrochemical and thermal aging model of LiFePO4-graphite
+        Li-ion batteries: power and capacity fade simulations". Journal of The
+        Electrochemical Society, 160(4), A616 (2013).
+        M. J. Lain, J., Brandon, and E. Kendrick. "Design Strategies for High Power vs.
+        High Energy Lithium Ion Cells". Batteries, 5(4), 64 (2019).
 
 Lead-acid parameter sets
 --------------------------
     * Sulzer2019 :
-        V. Sulzer, S. J. Chapman, C. P. Please, D. A. Howey, and C. W. Monroe, “Faster
+        V. Sulzer, S. J. Chapman, C. P. Please, D. A. Howey, and C. W. Monroe, "Faster
         lead-acid battery simulations from porous-electrode theory: Part I. Physical
-        model.” Journal of the Electrochemical Society, 166(12), 2363 (2019).
+        model." Journal of the Electrochemical Society, 166(12), 2363 (2019).
 
 """
 
 #
 # Lithium-ion
 #
+
 NCA_Kim2011 = {
     "chemistry": "lithium-ion",
     "cell": "Kim2011",
@@ -103,8 +122,9 @@
     "electrolyte": "LiPF6_Mohtat2020",
     "experiment": "1C_charge_from_empty_Mohtat2020",
     "sei": "example",
-    "citation": "Mohtat2020",
+    "citation": "mohtat2020differential",
 }
+
 Ramadass2004 = {
     "chemistry": "lithium-ion",
     "cell": "sony_Ramadass2004",
@@ -117,6 +137,28 @@
     "citation": "marquis2019asymptotic",
 }
 
+Prada2013 = {
+    "chemistry": "lithium-ion",
+    "cell": "A123_Lain2019",
+    "anode": "graphite_Chen2020",
+    "separator": "separator_Chen2020",
+    "cathode": "LFP_Prada2013",
+    "electrolyte": "lipf6_Nyman2008",
+    "experiment": "4C_discharge_from_full_Prada2013",
+    "citation": ["Chen2020", "lain2019design", "prada2013simplified"],
+}
+
+Ai2020 = {
+    "chemistry": "lithium-ion",
+    "cell": "Enertech_Ai2020",
+    "anode": "graphite_Ai2020",
+    "separator": "separator_Ai2020",
+    "cathode": "lico2_Ai2020",
+    "electrolyte": "lipf6_Enertech_Ai2020",
+    "experiment": "1C_discharge_from_full_Ai2020",
+    "citation": "Ai2020JES",
+}
+
 #
 # Lead-acid
 #
diff --git a/pybamm/parameters/parameter_values.py b/pybamm/parameters/parameter_values.py
index c97e499277..b4c8bf1737 100644
--- a/pybamm/parameters/parameter_values.py
+++ b/pybamm/parameters/parameter_values.py
@@ -313,6 +313,21 @@ def check_parameter_values(self, values):
                     "Parameters involving 'reaction rate' have been replaced with "
                     "'exchange-current density' ('{}' found)".format(param)
                 )
+        for param in values:
+            if "particle distribution in x" in param:
+                raise ValueError(
+                    "The parameter '{}' has been deprecated".format(param)
+                    + "The particle radius is now set as a function of x directly "
+                    "instead of providing a reference value and a distribution."
+                )
+        for param in values:
+            if "surface area per unit volume distribution in x" in param:
+                raise ValueError(
+                    "The parameter '{}' has been deprecated".format(param)
+                    + "The surface area per unit volume is now set as a function "
+                    "of x directly instead of providing a reference value and a "
+                    "distribution."
+                )
 
     def process_model(self, unprocessed_model, inplace=True):
         """Assign parameter values to a model.
diff --git a/pybamm/parameters/thermal_parameters.py b/pybamm/parameters/thermal_parameters.py
index 81c9880274..69251ccd96 100644
--- a/pybamm/parameters/thermal_parameters.py
+++ b/pybamm/parameters/thermal_parameters.py
@@ -18,7 +18,7 @@ class ThermalParameters:
     def __init__(self):
 
         # Get geometric parameters
-        self.geo = pybamm.GeometricParameters()
+        self.geo = pybamm.geometric_parameters
 
         # Set parameters
         self._set_dimensional_parameters()
@@ -178,3 +178,6 @@ def _set_dimensionless_parameters(self):
     def T_amb(self, t):
         "Dimensionless ambient temperature"
         return (self.T_amb_dim(t) - self.T_ref) / self.Delta_T
+
+
+thermal_parameters = ThermalParameters()
diff --git a/pybamm/plotting/quick_plot.py b/pybamm/plotting/quick_plot.py
index 9348b8907d..3e76654f8a 100644
--- a/pybamm/plotting/quick_plot.py
+++ b/pybamm/plotting/quick_plot.py
@@ -146,16 +146,9 @@ def __init__(
         else:
             raise ValueError("spatial unit '{}' not recognized".format(spatial_unit))
 
-        # Set length scales
-        self.length_scales = {
-            domain: scale.evaluate() * self.spatial_factor
-            for domain, scale in models[0].length_scales.items()
-        }
-
         # Time parameters
-        model_timescale_in_seconds = models[0].timescale_eval
         self.ts_seconds = [
-            solution.t * model_timescale_in_seconds for solution in solutions
+            solution.t * solution.timescale_eval for solution in solutions
         ]
         min_t = np.min([t[0] for t in self.ts_seconds])
         max_t = np.max([t[-1] for t in self.ts_seconds])
diff --git a/pybamm/settings.py b/pybamm/settings.py
index bf393fff57..20cdfa810e 100644
--- a/pybamm/settings.py
+++ b/pybamm/settings.py
@@ -5,6 +5,10 @@
 
 class Settings(object):
     _debug_mode = False
+    _min_smoothing = "exact"
+    _max_smoothing = "exact"
+    _heaviside_smoothing = "exact"
+    _abs_smoothing = "exact"
 
     @property
     def debug_mode(self):
@@ -15,5 +19,60 @@ def debug_mode(self, value):
         assert isinstance(value, bool)
         self._debug_mode = value
 
+    def set_smoothing_parameters(self, k):
+        "Helper function to set all smoothing parameters"
+        self.min_smoothing = k
+        self.max_smoothing = k
+        self.heaviside_smoothing = k
+        self.abs_smoothing = k
+
+    @property
+    def min_smoothing(self):
+        return self._min_smoothing
+
+    @min_smoothing.setter
+    def min_smoothing(self, k):
+        if k != "exact" and k <= 0:
+            raise ValueError(
+                "smoothing parameter must be 'exact' or a strictly positive number"
+            )
+        self._min_smoothing = k
+
+    @property
+    def max_smoothing(self):
+        return self._max_smoothing
+
+    @max_smoothing.setter
+    def max_smoothing(self, k):
+        if k != "exact" and k <= 0:
+            raise ValueError(
+                "smoothing parameter must be 'exact' or a strictly positive number"
+            )
+        self._max_smoothing = k
+
+    @property
+    def heaviside_smoothing(self):
+        return self._heaviside_smoothing
+
+    @heaviside_smoothing.setter
+    def heaviside_smoothing(self, k):
+        if k != "exact" and k <= 0:
+            raise ValueError(
+                "smoothing parameter must be 'exact' or a strictly positive number"
+            )
+        self._heaviside_smoothing = k
+
+    @property
+    def abs_smoothing(self):
+        return self._abs_smoothing
+
+    @abs_smoothing.setter
+    def abs_smoothing(self, k):
+        if k != "exact" and k <= 0:
+            raise ValueError(
+                "smoothing parameter must be 'exact' or a strictly positive number"
+            )
+        self._abs_smoothing = k
+
 
 settings = Settings()
diff --git a/pybamm/simulation.py b/pybamm/simulation.py
index 104bfbc906..d0177d9888 100644
--- a/pybamm/simulation.py
+++ b/pybamm/simulation.py
@@ -350,7 +350,10 @@ def solve(
                         "list [t0, tf] where t0 is the initial time and tf is the "
                         "final time. "
                         "For a constant current (dis)charge the suggested 't_eval'  "
-                        "is [0, 3700/C] where C is the C-rate."
+                        "is [0, 3700/C] where C is the C-rate. "
+                        "For example, run\n\n"
+                        "\tsim.solve([0, 3700])\n\n"
+                        "for a 1C discharge."
                     )
 
             elif self.operating_mode == "drive cycle":
@@ -402,7 +405,7 @@ def solve(
                 external_variables=external_variables,
                 inputs=inputs,
             )
-            self.t_eval = self._solution.t * self.model.timescale.evaluate()
+            self.t_eval = self._solution.t * self._solution.timescale_eval
 
         elif self.operating_mode == "with experiment":
             if t_eval is not None:
diff --git a/pybamm/solvers/algebraic_solver.py b/pybamm/solvers/algebraic_solver.py
index dd4e0d0b20..2bcebeb17f 100644
--- a/pybamm/solvers/algebraic_solver.py
+++ b/pybamm/solvers/algebraic_solver.py
@@ -82,6 +82,8 @@ def _integrate(self, model, t_eval, inputs=None):
 
         y_alg = np.empty((len(y0_alg), len(t_eval)))
 
+        timer = pybamm.Timer()
+        integration_time = 0
         for idx, t in enumerate(t_eval):
 
             def root_fun(y_alg):
@@ -135,6 +137,7 @@ def jac_fn(y_alg):
                         method = self.method[5:]
                     if jac_fn is None:
                         jac_fn = "2-point"
+                    timer.reset()
                     sol = optimize.least_squares(
                         root_fun,
                         y0_alg,
@@ -144,6 +147,7 @@ def jac_fn(y_alg):
                         bounds=model.bounds,
                         **self.extra_options,
                     )
+                    integration_time += timer.time()
                 # Methods which use minimize are specified as either "minimize", which
                 # uses the default method, or with "minimize__methodname"
                 elif self.method.startswith("minimize"):
@@ -170,6 +174,7 @@ def jac_norm(y):
                             (lb, ub) for lb, ub in zip(model.bounds[0], model.bounds[1])
                         ]
                         extra_options["bounds"] = bounds
+                    timer.reset()
                     sol = optimize.minimize(
                         root_norm,
                         y0_alg,
@@ -178,7 +183,9 @@ def jac_norm(y):
                         jac=jac_norm,
                         **extra_options,
                     )
+                    integration_time += timer.time()
                 else:
+                    timer.reset()
                     sol = optimize.root(
                         root_fun,
                         y0_alg,
@@ -187,6 +194,7 @@ def jac_norm(y):
                         jac=jac_fn,
                         options=self.extra_options,
                     )
+                    integration_time += timer.time()
 
                 if sol.success and np.all(abs(sol.fun) < self.tol):
                     # update initial guess for the next iteration
@@ -210,4 +218,6 @@ def jac_norm(y):
         y_diff = np.r_[[y0_diff] * len(t_eval)].T
         y_sol = np.r_[y_diff, y_alg]
         # Return solution object (no events, so pass None to t_event, y_event)
-        return pybamm.Solution(t_eval, y_sol, termination="success")
+        sol = pybamm.Solution(t_eval, y_sol, termination="success")
+        sol.integration_time = integration_time
+        return sol
diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py
index d6034155ed..99ce106c08 100644
--- a/pybamm/solvers/base_solver.py
+++ b/pybamm/solvers/base_solver.py
@@ -165,14 +165,12 @@ def set_up(self, model, inputs=None, t_eval=None):
         inputs = inputs or {}
 
         # Set model timescale
-        try:
-            model.timescale_eval = model.timescale.evaluate()
-        except KeyError as e:
-            raise pybamm.SolverError(
-                "The model timescale is a function of an input parameter "
-                "(original error: {})".format(e)
-            )
-
+        model.timescale_eval = model.timescale.evaluate(inputs=inputs)
+        # Set model lengthscales
+        model.length_scales_eval = {
+            domain: scale.evaluate(inputs=inputs)
+            for domain, scale in model.length_scales.items()
+        }
         if (
             isinstance(self, (pybamm.CasadiSolver, pybamm.CasadiAlgebraicSolver))
         ) and model.convert_to_format != "casadi":
@@ -565,16 +563,13 @@ def solve(self, model, t_eval=None, external_variables=None, inputs=None):
         # Set up (if not done already)
         if model not in self.models_set_up:
             self.set_up(model, ext_and_inputs, t_eval)
-            set_up_time = timer.time()
             self.models_set_up.update(
                 {model: {"initial conditions": model.concatenated_initial_conditions}}
             )
         else:
             ics_set_up = self.models_set_up[model]["initial conditions"]
             # Check that initial conditions have not been updated
-            if ics_set_up.id == model.concatenated_initial_conditions.id:
-                set_up_time = 0
-            else:
+            if ics_set_up.id != model.concatenated_initial_conditions.id:
                 # If the new initial conditions are different, set up again
                 # Doing the whole setup again might be slow, but no need to prematurely
                 # optimize this
@@ -582,7 +577,8 @@ def solve(self, model, t_eval=None, external_variables=None, inputs=None):
                 self.models_set_up[model][
                     "initial conditions"
                 ] = model.concatenated_initial_conditions
-                set_up_time = timer.time()
+        set_up_time = timer.time()
+        timer.reset()
 
         # (Re-)calculate consistent initial conditions
         self._set_initial_conditions(model, ext_and_inputs, update_rhs=True)
@@ -652,7 +648,6 @@ def solve(self, model, t_eval=None, external_variables=None, inputs=None):
                     t_eval_dimensionless[end_index - 1] * model.timescale_eval,
                 )
             )
-            timer.reset()
             new_solution = self._integrate(
                 model, t_eval_dimensionless[start_index:end_index], ext_and_inputs
             )
@@ -676,17 +671,21 @@ def solve(self, model, t_eval=None, external_variables=None, inputs=None):
                         model, t_eval_dimensionless[end_index], ext_and_inputs
                     )
 
-        # restore old y0
-        model.y0 = old_y0
-
         # Assign times
         solution.set_up_time = set_up_time
         solution.solve_time = timer.time()
 
+        # restore old y0
+        model.y0 = old_y0
+
         # Add model and inputs to solution
         solution.model = model
         solution.inputs = ext_and_inputs
 
+        # Copy the timescale_eval and lengthscale_evals
+        solution.timescale_eval = model.timescale_eval
+        solution.length_scales_eval = model.length_scales_eval
+
         # Identify the event that caused termination
         termination = self.get_termination_reason(solution, model.events)
 
@@ -775,6 +774,28 @@ def step(
         inputs = inputs or {}
         ext_and_inputs = {**external_variables, **inputs}
 
+        # Check that any inputs that may affect the scaling have not changed
+        # Set model timescale
+        temp_timescale_eval = model.timescale.evaluate(inputs=inputs)
+        # Set model lengthscales
+        temp_length_scales_eval = {
+            domain: scale.evaluate(inputs=inputs)
+            for domain, scale in model.length_scales.items()
+        }
+        if old_solution is not None:
+            if temp_timescale_eval != old_solution.timescale_eval:
+                raise pybamm.SolverError(
+                    "The model timescale is a function of an input parameter "
+                    "and the value has changed between steps!"
+                )
+            for domain in temp_length_scales_eval.keys():
+                old_dom_eval = old_solution.length_scales_eval[domain]
+                if temp_length_scales_eval[domain] != old_dom_eval:
+                    pybamm.logger.error(
+                        "The {} domain lengthscale is a function of an input "
+                        "parameter and the value has changed between "
+                        "steps!".format(domain)
+                    )
         # Run set up on first step
         if old_solution is None:
             pybamm.logger.info(
@@ -782,12 +803,11 @@ def step(
             )
             self.set_up(model, ext_and_inputs)
             t = 0.0
-            set_up_time = timer.time()
         else:
             # initialize with old solution
             t = old_solution.t[-1]
             model.y0 = old_solution.y[:, -1]
-            set_up_time = 0
+        set_up_time = timer.time()
 
         # (Re-)calculate consistent initial conditions
         self._set_initial_conditions(model, ext_and_inputs, update_rhs=False)
@@ -809,6 +829,10 @@ def step(
         solution.model = model
         solution.inputs = ext_and_inputs
 
+        # Copy the timescale_eval and lengthscale_evals
+        solution.timescale_eval = temp_timescale_eval
+        solution.length_scales_eval = temp_length_scales_eval
+
         # Identify the event that caused termination
         termination = self.get_termination_reason(solution, model.events)
 
diff --git a/pybamm/solvers/casadi_algebraic_solver.py b/pybamm/solvers/casadi_algebraic_solver.py
index 25fe6aff1d..1f24ac2d61 100644
--- a/pybamm/solvers/casadi_algebraic_solver.py
+++ b/pybamm/solvers/casadi_algebraic_solver.py
@@ -66,6 +66,15 @@ def _integrate(self, model, t_eval, inputs=None):
         inputs = casadi.vertcat(*[v for v in inputs.values()])
 
         y0 = model.y0
+
+        # If y0 already satisfies the tolerance for all t then keep it
+        if has_symbolic_inputs is False and all(
+            np.all(abs(model.casadi_algebraic(t, y0, inputs).full()) < self.tol)
+            for t in t_eval
+        ):
+            pybamm.logger.debug("Keeping same solution at all times")
+            return pybamm.Solution(t_eval, y0, termination="success")
+
         # The casadi algebraic solver can read rhs equations, but leaves them unchanged
         # i.e. the part of the solution vector that corresponds to the differential
         # equations will be equal to the initial condition provided. This allows this
@@ -109,6 +118,8 @@ def _integrate(self, model, t_eval, inputs=None):
                 "constraints": list(constraints[len_rhs:]),
             },
         )
+        timer = pybamm.Timer()
+        integration_time = 0
         for idx, t in enumerate(t_eval):
             # Evaluate algebraic with new t and previous y0, if it's already close
             # enough then keep it
@@ -128,7 +139,9 @@ def _integrate(self, model, t_eval, inputs=None):
                 t_eval_inputs_sym = casadi.vertcat(t, symbolic_inputs)
                 # Solve
                 try:
+                    timer.reset()
                     y_alg_sol = roots(y0_alg, t_eval_inputs_sym)
+                    integration_time += timer.time()
                     success = True
                     message = None
                     # Check final output
@@ -146,6 +159,7 @@ def _integrate(self, model, t_eval, inputs=None):
                 ):
                     # update initial guess for the next iteration
                     y0_alg = y_alg_sol
+                    y0 = casadi.vertcat(y0_diff, y0_alg)
                     # update solution array
                     if y_alg is None:
                         y_alg = y_alg_sol
@@ -170,4 +184,6 @@ def _integrate(self, model, t_eval, inputs=None):
         y_diff = casadi.horzcat(*[y0_diff] * len(t_eval))
         y_sol = casadi.vertcat(y_diff, y_alg)
         # Return solution object (no events, so pass None to t_event, y_event)
-        return pybamm.Solution(t_eval, y_sol, termination="success")
+        sol = pybamm.Solution(t_eval, y_sol, termination="success")
+        sol.integration_time = integration_time
+        return sol
diff --git a/pybamm/solvers/casadi_solver.py b/pybamm/solvers/casadi_solver.py
index 7d9fbc29fd..d05e6283f9 100644
--- a/pybamm/solvers/casadi_solver.py
+++ b/pybamm/solvers/casadi_solver.py
@@ -50,9 +50,10 @@ class CasadiSolver(pybamm.BaseSolver):
     extra_options_setup : dict, optional
         Any options to pass to the CasADi integrator when creating the integrator.
         Please consult `CasADi documentation <https://tinyurl.com/y5rk76os>`_ for
-        details. Some typical options:
+        details. Some useful options:
 
         - "max_num_steps": Maximum number of integrator steps
+        - "print_stats": Print out statistics after integration
 
     extra_options_call : dict, optional
         Any options to pass to the CasADi integrator when calling the integrator.
@@ -152,6 +153,7 @@ def _integrate(self, model, t_eval, inputs=None):
                 # Initialize solution
                 solution = pybamm.Solution(np.array([t]), y0[:, np.newaxis])
                 solution.solve_time = 0
+                solution.integration_time = 0
             else:
                 solution = None
 
@@ -274,7 +276,11 @@ def event_fun(t):
                     # assign temporary solve time
                     current_step_sol.solve_time = np.nan
                     # append solution from the current step to solution
-                    solution.append(current_step_sol)
+                    if solution is None:
+                        solution = current_step_sol
+                    else:
+                        # append solution from the current step to solution
+                        solution.append(current_step_sol)
                     solution.termination = "event"
                     solution.t_event = t_event
                     solution.y_event = y_event
@@ -306,14 +312,19 @@ def create_integrator(self, model, inputs, t_eval=None):
         if model in self.integrators:
             # If we're not using the grid, we don't need to change the integrator
             if use_grid is False:
-                return self.integrators[model]
+                return self.integrators[model][0]
             # Otherwise, create new integrator with an updated grid
+            # We don't need to update the grid if reusing the same t_eval
             else:
                 method, problem, options = self.integrator_specs[model]
-                options["grid"] = t_eval
-                integrator = casadi.integrator("F", method, problem, options)
-                self.integrators[model] = (integrator, use_grid)
-                return integrator
+                t_eval_old = options["grid"]
+                if np.array_equal(t_eval_old, t_eval):
+                    return self.integrators[model][0]
+                else:
+                    options["grid"] = t_eval
+                    integrator = casadi.integrator("F", method, problem, options)
+                    self.integrators[model] = (integrator, use_grid)
+                    return integrator
         else:
             y0 = model.y0
             rhs = model.casadi_rhs
@@ -386,11 +397,15 @@ def _run_integrator(self, model, y0, inputs, t_eval):
             # Try solving
             if use_grid is True:
                 # Call the integrator once, with the grid
+                timer = pybamm.Timer()
                 sol = integrator(
                     x0=y0_diff, z0=y0_alg, p=inputs, **self.extra_options_call
                 )
+                integration_time = timer.time()
                 y_sol = np.concatenate([sol["xf"].full(), sol["zf"].full()])
-                return pybamm.Solution(t_eval, y_sol)
+                sol = pybamm.Solution(t_eval, y_sol)
+                sol.integration_time = integration_time
+                return sol
             else:
                 # Repeated calls to the integrator
                 x = y0_diff
@@ -401,19 +416,24 @@ def _run_integrator(self, model, y0, inputs, t_eval):
                     t_min = t_eval[i]
                     t_max = t_eval[i + 1]
                     inputs_with_tlims = casadi.vertcat(inputs, t_min, t_max)
+                    timer = pybamm.Timer()
                     sol = integrator(
                         x0=x, z0=z, p=inputs_with_tlims, **self.extra_options_call
                     )
+                    integration_time = timer.time()
                     x = sol["xf"]
                     z = sol["zf"]
                     y_diff = casadi.horzcat(y_diff, x)
                     if not z.is_empty():
                         y_alg = casadi.horzcat(y_alg, z)
                 if z.is_empty():
-                    return pybamm.Solution(t_eval, y_diff)
+                    sol = pybamm.Solution(t_eval, y_diff)
                 else:
                     y_sol = casadi.vertcat(y_diff, y_alg)
-                    return pybamm.Solution(t_eval, y_sol)
+                    sol = pybamm.Solution(t_eval, y_sol)
+
+                sol.integration_time = integration_time
+                return sol
         except RuntimeError as e:
             # If it doesn't work raise error
             raise pybamm.SolverError(e.args[0])
diff --git a/pybamm/solvers/dummy_solver.py b/pybamm/solvers/dummy_solver.py
index 483bba8a77..e4c9f5ae02 100644
--- a/pybamm/solvers/dummy_solver.py
+++ b/pybamm/solvers/dummy_solver.py
@@ -33,4 +33,6 @@ def _integrate(self, model, t_eval, inputs=None):
 
         """
         y_sol = np.zeros((1, t_eval.size))
-        return pybamm.Solution(t_eval, y_sol, termination="final time")
+        sol = pybamm.Solution(t_eval, y_sol, termination="final time")
+        sol.integration_time = 0
+        return sol
diff --git a/pybamm/solvers/idaklu_solver.py b/pybamm/solvers/idaklu_solver.py
index 6e7cc7fcc3..93a8a3731b 100644
--- a/pybamm/solvers/idaklu_solver.py
+++ b/pybamm/solvers/idaklu_solver.py
@@ -234,6 +234,7 @@ def rootfn(t, y):
         ids = np.concatenate((rhs_ids, alg_ids))
 
         # solve
+        timer = pybamm.Timer()
         sol = idaklu.solve(
             t_eval,
             y0,
@@ -251,6 +252,7 @@ def rootfn(t, y):
             atol,
             rtol,
         )
+        integration_time = timer.time()
 
         t = sol.t
         number_of_timesteps = t.size
@@ -266,12 +268,14 @@ def rootfn(t, y):
             elif sol.flag == 2:
                 termination = "event"
 
-            return pybamm.Solution(
+            sol = pybamm.Solution(
                 sol.t,
                 np.transpose(y_out),
                 t[-1],
                 np.transpose(y_out[-1])[:, np.newaxis],
                 termination,
             )
+            sol.integration_time = integration_time
+            return sol
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/jax_bdf_solver.py b/pybamm/solvers/jax_bdf_solver.py
index 59c5459d12..1b511755ba 100644
--- a/pybamm/solvers/jax_bdf_solver.py
+++ b/pybamm/solvers/jax_bdf_solver.py
@@ -13,6 +13,8 @@
 from jax.interpreters import partial_eval as pe
 from jax import linear_util as lu
 from jax.config import config
+from absl import logging
+logging.set_verbosity(logging.ERROR)
 
 config.update("jax_enable_x64", True)
 
@@ -82,9 +84,7 @@ def fun_bind_inputs(y, t):
     t0 = t_eval[0]
     h0 = t_eval[1] - t0
 
-    stepper = _bdf_init(
-        fun_bind_inputs, jac_bind_inputs, mass, t0, y0, h0, rtol, atol
-    )
+    stepper = _bdf_init(fun_bind_inputs, jac_bind_inputs, mass, t0, y0, h0, rtol, atol)
     i = 0
     y_out = jnp.empty((len(t_eval), len(y0)), dtype=y0.dtype)
 
@@ -101,30 +101,49 @@ def body_fun(state):
 
         def for_body(j, y_out):
             t = t_eval[j]
-            y_out = jax.ops.index_update(y_out, jax.ops.index[j, :],
-                                         _bdf_interpolate(stepper, t))
+            y_out = jax.ops.index_update(
+                y_out, jax.ops.index[j, :], _bdf_interpolate(stepper, t)
+            )
             return y_out
 
         y_out = jax.lax.fori_loop(i, index, for_body, y_out)
         return [stepper, t_eval, index, y_out]
 
-    stepper, t_eval, i, y_out = jax.lax.while_loop(cond_fun, body_fun,
-                                                   init_state)
+    stepper, t_eval, i, y_out = jax.lax.while_loop(cond_fun, body_fun, init_state)
     return y_out
 
 
 BDFInternalStates = [
-    't', 'atol', 'rtol', 'M', 'newton_tol', 'order', 'h', 'n_equal_steps', 'D',
-    'y0', 'scale_y0', 'kappa', 'gamma', 'alpha', 'c', 'error_const', 'J', 'LU', 'U',
-    'psi', 'n_function_evals', 'n_jacobian_evals', 'n_lu_decompositions', 'n_steps',
-    'consistent_y0_failed'
+    "t",
+    "atol",
+    "rtol",
+    "M",
+    "newton_tol",
+    "order",
+    "h",
+    "n_equal_steps",
+    "D",
+    "y0",
+    "scale_y0",
+    "kappa",
+    "gamma",
+    "alpha",
+    "c",
+    "error_const",
+    "J",
+    "LU",
+    "U",
+    "psi",
+    "n_function_evals",
+    "n_jacobian_evals",
+    "n_lu_decompositions",
+    "n_steps",
+    "consistent_y0_failed",
 ]
-BDFState = collections.namedtuple('BDFState', BDFInternalStates)
+BDFState = collections.namedtuple("BDFState", BDFInternalStates)
 
 jax.tree_util.register_pytree_node(
-    BDFState,
-    lambda xs: (tuple(xs), None),
-    lambda _, xs: BDFState(*xs)
+    BDFState, lambda xs: (tuple(xs), None), lambda _, xs: BDFState(*xs)
 )
 
 
@@ -161,56 +180,56 @@ def _bdf_init(fun, jac, mass, t0, y0, h0, rtol, atol):
     """
 
     state = {}
-    state['t'] = t0
-    state['atol'] = atol
-    state['rtol'] = rtol
-    state['M'] = mass
+    state["t"] = t0
+    state["atol"] = atol
+    state["rtol"] = rtol
+    state["M"] = mass
     EPS = jnp.finfo(y0.dtype).eps
-    state['newton_tol'] = jnp.max((10 * EPS / rtol, jnp.min((0.03, rtol ** 0.5))))
+    state["newton_tol"] = jnp.maximum(10 * EPS / rtol, jnp.minimum(0.03, rtol ** 0.5))
 
     scale_y0 = atol + rtol * jnp.abs(y0)
     y0, not_converged = _select_initial_conditions(
-        fun, mass, t0, y0, state['newton_tol'], scale_y0
+        fun, mass, t0, y0, state["newton_tol"], scale_y0
     )
-    state['consistent_y0_failed'] = not_converged
+    state["consistent_y0_failed"] = not_converged
 
     f0 = fun(y0, t0)
     order = 1
-    state['order'] = order
-    state['h'] = _select_initial_step(atol, rtol, fun, t0, y0, f0, h0)
-    state['n_equal_steps'] = 0
+    state["order"] = order
+    state["h"] = _select_initial_step(atol, rtol, fun, t0, y0, f0, h0)
+    state["n_equal_steps"] = 0
     D = jnp.empty((MAX_ORDER + 1, len(y0)), dtype=y0.dtype)
     D = jax.ops.index_update(D, jax.ops.index[0, :], y0)
-    D = jax.ops.index_update(D, jax.ops.index[1, :], f0 * state['h'])
-    state['D'] = D
-    state['y0'] = y0
-    state['scale_y0'] = scale_y0
+    D = jax.ops.index_update(D, jax.ops.index[1, :], f0 * state["h"])
+    state["D"] = D
+    state["y0"] = y0
+    state["scale_y0"] = scale_y0
 
     # kappa values for difference orders, taken from Table 1 of [1]
     kappa = jnp.array([0, -0.1850, -1 / 9, -0.0823, -0.0415, 0])
     gamma = jnp.hstack((0, jnp.cumsum(1 / jnp.arange(1, MAX_ORDER + 1))))
     alpha = 1.0 / ((1 - kappa) * gamma)
-    c = state['h'] * alpha[order]
+    c = state["h"] * alpha[order]
     error_const = kappa * gamma + 1 / jnp.arange(1, MAX_ORDER + 2)
 
-    state['kappa'] = kappa
-    state['gamma'] = gamma
-    state['alpha'] = alpha
-    state['c'] = c
-    state['error_const'] = error_const
+    state["kappa"] = kappa
+    state["gamma"] = gamma
+    state["alpha"] = alpha
+    state["c"] = c
+    state["error_const"] = error_const
 
     J = jac(y0, t0)
-    state['J'] = J
+    state["J"] = J
 
-    state['LU'] = jax.scipy.linalg.lu_factor(state['M'] - c * J)
+    state["LU"] = jax.scipy.linalg.lu_factor(state["M"] - c * J)
 
-    state['U'] = _compute_R(order, 1)
-    state['psi'] = None
+    state["U"] = _compute_R(order, 1)
+    state["psi"] = None
 
-    state['n_function_evals'] = 2
-    state['n_jacobian_evals'] = 1
-    state['n_lu_decompositions'] = 1
-    state['n_steps'] = 0
+    state["n_function_evals"] = 2
+    state["n_jacobian_evals"] = 1
+    state["n_lu_decompositions"] = 1
+    state["n_steps"] = 0
 
     tuple_state = BDFState(*[state[k] for k in BDFInternalStates])
     y0, scale_y0 = _predict(tuple_state, D)
@@ -232,8 +251,7 @@ def _compute_R(order, factor):
     I = jnp.arange(1, MAX_ORDER + 1).reshape(-1, 1)
     J = jnp.arange(1, MAX_ORDER + 1)
     M = jnp.empty((MAX_ORDER + 1, MAX_ORDER + 1))
-    M = jax.ops.index_update(M, jax.ops.index[1:, 1:],
-                             (I - 1 - factor * J) / I)
+    M = jax.ops.index_update(M, jax.ops.index[1:, 1:], (I - 1 - factor * J) / I)
     M = jax.ops.index_update(M, jax.ops.index[0], 1)
     R = jnp.cumprod(M, axis=0)
 
@@ -242,11 +260,11 @@ def _compute_R(order, factor):
 
 def _select_initial_conditions(fun, M, t0, y0, tol, scale_y0):
     # identify algebraic variables as zeros on diagonal
-    algebraic_variables = jnp.diag(M == 0.)
+    algebraic_variables = onp.diag(M) == 0.0
 
     # if all differentiable variables then return y0 (can use normal python if since M
     # is static)
-    if not jnp.any(algebraic_variables):
+    if not onp.any(algebraic_variables):
         return y0, False
 
     # calculate consistent initial conditions via a newton on -J_a @ delta = f_a This
@@ -283,24 +301,24 @@ def while_body(while_state):
         k, converged, dy_norm_old, d, y_a = while_state
         f_eval = fun_a(y_a)
         dy = jax.scipy.linalg.lu_solve(LU, f_eval)
-        dy_norm = jnp.sqrt(jnp.mean((dy / scale_y0_a)**2))
+        dy_norm = jnp.sqrt(jnp.mean((dy / scale_y0_a) ** 2))
         rate = dy_norm / dy_norm_old
 
         d += dy
         y_a = y0_a + d
 
         # if converged then break out of iteration early
-        pred = dy_norm_old >= 0.
+        pred = dy_norm_old >= 0.0
         pred *= rate / (1 - rate) * dy_norm < tol
-        converged = (dy_norm == 0.) + pred
+        converged = (dy_norm == 0.0) + pred
 
         dy_norm_old = dy_norm
 
         return [k + 1, converged, dy_norm_old, d, y_a]
 
-    k, converged, dy_norm_old, d, y_a = jax.lax.while_loop(while_cond,
-                                                           while_body,
-                                                           while_state)
+    k, converged, dy_norm_old, d, y_a = jax.lax.while_loop(
+        while_cond, while_body, while_state
+    )
     y_tilde = jax.ops.index_update(y0, algebraic_variables, y_a)
 
     return y_tilde, converged
@@ -322,10 +340,10 @@ def _select_initial_step(atol, rtol, fun, t0, y0, f0, h0):
     scale = atol + jnp.abs(y0) * rtol
     y1 = y0 + h0 * f0
     f1 = fun(y1, t0 + h0)
-    d2 = jnp.sqrt(jnp.mean(((f1 - f0) / scale)**2))
+    d2 = jnp.sqrt(jnp.mean(((f1 - f0) / scale) ** 2))
     order = 1
     h1 = h0 * d2 ** (-1 / (order + 1))
-    return jnp.min((100 * h0, h1))
+    return jnp.minimum(100 * h0, h1)
 
 
 def _predict(state, D):
@@ -351,10 +369,7 @@ def _update_psi(state, D):
     subGamma = jnp.where(orders > 0, jnp.where(orders <= order, state.gamma, 0), 0)
     orders = jnp.repeat(orders.reshape(-1, 1), n, axis=1)
     subD = jnp.where(orders > 0, jnp.where(orders <= order, D, 0), 0)
-    psi = jnp.dot(
-        subD.T,
-        subGamma
-    ) * state.alpha[order]
+    psi = jnp.dot(subD.T, subGamma) * state.alpha[order]
     return psi
 
 
@@ -373,10 +388,8 @@ def _update_difference_for_next_step(state, d):
     """
     order = state.order
     D = state.D
-    D = jax.ops.index_update(D, jax.ops.index[order + 2],
-                             d - D[order + 1])
-    D = jax.ops.index_update(D, jax.ops.index[order + 1],
-                             d)
+    D = jax.ops.index_update(D, jax.ops.index[order + 2], d - D[order + 1])
+    D = jax.ops.index_update(D, jax.ops.index[order + 1], d)
     i = order
     while_state = [i, D]
 
@@ -386,8 +399,7 @@ def while_cond(while_state):
 
     def while_body(while_state):
         i, D = while_state
-        D = jax.ops.index_add(D, jax.ops.index[i],
-                              D[i + 1])
+        D = jax.ops.index_add(D, jax.ops.index[i], D[i + 1])
         i -= 1
         return [i, D]
 
@@ -426,8 +438,9 @@ def _update_step_size(state, factor):
     J = jnp.arange(0, MAX_ORDER + 1)
 
     # only update order+1, order+1 entries of D
-    RU = jnp.where(jnp.logical_and(I <= order, J <= order),
-                   RU, jnp.identity(MAX_ORDER + 1))
+    RU = jnp.where(
+        jnp.logical_and(I <= order, J <= order), RU, jnp.identity(MAX_ORDER + 1)
+    )
     D = state.D
     D = jnp.dot(RU.T, D)
     # D = jax.ops.index_update(D, jax.ops.index[:order + 1],
@@ -439,9 +452,9 @@ def _update_step_size(state, factor):
     # update y0 (D has changed)
     y0, scale_y0 = _predict(state, D)
 
-    return state._replace(n_equal_steps=n_equal_steps,
-                          h=h, c=c,
-                          D=D, psi=psi, y0=y0, scale_y0=scale_y0)
+    return state._replace(
+        n_equal_steps=n_equal_steps, h=h, c=c, D=D, psi=psi, y0=y0, scale_y0=scale_y0
+    )
 
 
 def _update_jacobian(state, jac):
@@ -453,8 +466,12 @@ def _update_jacobian(state, jac):
     n_jacobian_evals = state.n_jacobian_evals + 1
     LU = jax.scipy.linalg.lu_factor(state.M - state.c * J)
     n_lu_decompositions = state.n_lu_decompositions + 1
-    return state._replace(J=J, n_jacobian_evals=n_jacobian_evals, LU=LU,
-                          n_lu_decompositions=n_lu_decompositions)
+    return state._replace(
+        J=J,
+        n_jacobian_evals=n_jacobian_evals,
+        LU=LU,
+        n_lu_decompositions=n_lu_decompositions,
+    )
 
 
 def _newton_iteration(state, fun):
@@ -485,7 +502,7 @@ def while_body(while_state):
         n_function_evals += 1
         b = c * f_eval - M @ (psi + d)
         dy = jax.scipy.linalg.lu_solve(LU, b)
-        dy_norm = jnp.sqrt(jnp.mean((dy / scale_y0)**2))
+        dy_norm = jnp.sqrt(jnp.mean((dy / scale_y0) ** 2))
         rate = dy_norm / dy_norm_old
 
         # if iteration is not going to converge in NEWTON_MAXITER
@@ -499,23 +516,22 @@ def while_body(while_state):
         y = y0 + d
 
         # if converged then break out of iteration early
-        pred = dy_norm_old >= 0.
+        pred = dy_norm_old >= 0.0
         pred *= rate / (1 - rate) * dy_norm < tol
-        converged = (dy_norm == 0.) + pred
+        converged = (dy_norm == 0.0) + pred
 
         dy_norm_old = dy_norm
 
         return [k + 1, converged, dy_norm_old, d, y, n_function_evals]
 
-    k, converged, dy_norm_old, d, y, n_function_evals = \
-        jax.lax.while_loop(while_cond,
-                           while_body,
-                           while_state)
+    k, converged, dy_norm_old, d, y, n_function_evals = jax.lax.while_loop(
+        while_cond, while_body, while_state
+    )
     return converged, k, y, d, state._replace(n_function_evals=n_function_evals)
 
 
 def rms_norm(arg):
-    return jnp.sqrt(jnp.mean(arg**2))
+    return jnp.sqrt(jnp.mean(arg ** 2))
 
 
 def _prepare_next_step(state, d):
@@ -534,21 +550,18 @@ def _prepare_next_step_order_change(state, d, y, n_iter):
     scale_y = state.atol + state.rtol * jnp.abs(y)
     error = state.error_const[order] * d
     error_norm = rms_norm(error / scale_y)
-    safety = 0.9 * (2 * NEWTON_MAXITER + 1) / (2 * NEWTON_MAXITER
-                                               + n_iter)
+    safety = 0.9 * (2 * NEWTON_MAXITER + 1) / (2 * NEWTON_MAXITER + n_iter)
 
     # similar to the optimal step size factor we calculated above for the current
     # order k, we need to calculate the optimal step size factors for orders
     # k-1 and k+1. To do this, we note that the error = C_k * D^{k+1} y_n
     error_m_norm = jnp.where(
-        order > 1,
-        rms_norm(state.error_const[order - 1] * D[order] / scale_y),
-        jnp.inf
+        order > 1, rms_norm(state.error_const[order - 1] * D[order] / scale_y), jnp.inf
     )
     error_p_norm = jnp.where(
         order < MAX_ORDER,
         rms_norm(state.error_const[order + 1] * D[order + 2] / scale_y),
-        jnp.inf
+        jnp.inf,
     )
 
     error_norms = jnp.array([error_m_norm, error_norm, error_p_norm])
@@ -559,14 +572,14 @@ def _prepare_next_step_order_change(state, d, y, n_iter):
     max_index = jnp.argmax(factors)
     order += max_index - 1
 
-    factor = jnp.min((MAX_FACTOR, safety * factors[max_index]))
+    factor = jnp.minimum(MAX_FACTOR, safety * factors[max_index])
 
     new_state = _update_step_size_and_lu(state._replace(D=D, order=order), factor)
     return new_state
 
 
 def _bdf_step(state, fun, jac):
-    #print('bdf_step', state.t, state.h)
+    # print('bdf_step', state.t, state.h)
     # we will try and use the old jacobian unless convergence of newton iteration
     # fails
     updated_jacobian = False
@@ -596,23 +609,22 @@ def while_body(while_state):
         state = tree_multimap(
             partial(jnp.where, not_converged * updated_jacobian),
             _update_step_size_and_lu(state, 0.3),
-            state
+            state,
         )
 
-        #if not_converged * updated_jacobian:
+        # if not_converged * updated_jacobian:
         #    print('not converged, update step size by 0.3')
-        #if not_converged * (updated_jacobian == False):
+        # if not_converged * (updated_jacobian == False):
         #    print('not converged, update jacobian')
 
         # if not converged and jacobian not updated, then update the jacobian and try
         # again
         (state, updated_jacobian) = tree_multimap(
             partial(
-                jnp.where,
-                not_converged * (updated_jacobian == False)  # noqa: E712
+                jnp.where, not_converged * (updated_jacobian == False)  # noqa: E712
             ),
             (_update_jacobian(state, jac), True),
-            (state, False + updated_jacobian)
+            (state, False + updated_jacobian),
         )
 
         safety = 0.9 * (2 * NEWTON_MAXITER + 1) / (2 * NEWTON_MAXITER + n_iter)
@@ -626,26 +638,24 @@ def while_body(while_state):
         error_norm = rms_norm(error / scale_y)
 
         # calculate optimal step size factor as per eq 2.46 of [2]
-        factor = jnp.max((MIN_FACTOR,
-                          safety *
-                          error_norm ** (-1 / (state.order + 1))))
+        factor = jnp.maximum(
+            MIN_FACTOR, safety * error_norm ** (-1 / (state.order + 1))
+        )
 
-        #if converged * (error_norm > 1):
+        # if converged * (error_norm > 1):
         #    print('converged, but error is too large',error_norm, factor, d, scale_y)
 
         (state, step_accepted) = tree_multimap(
-            partial(
-                jnp.where,
-                converged * (error_norm > 1)  # noqa: E712
-            ),
+            partial(jnp.where, converged * (error_norm > 1)),  # noqa: E712
             (_update_step_size_and_lu(state, factor), False),
-            (state, converged)
+            (state, converged),
         )
 
         return [state, step_accepted, updated_jacobian, y, d, n_iter]
 
-    state, step_accepted, updated_jacobian, y, d, n_iter = \
-        jax.lax.while_loop(while_cond, while_body, while_state)
+    state, step_accepted, updated_jacobian, y, d, n_iter = jax.lax.while_loop(
+        while_cond, while_body, while_state
+    )
 
     # take the accepted step
     n_steps = state.n_steps + 1
@@ -660,7 +670,7 @@ def while_body(while_state):
     state = tree_multimap(
         partial(jnp.where, n_equal_steps < state.order + 1),
         _prepare_next_step(state, d),
-        _prepare_next_step_order_change(state, d, y, n_iter)
+        _prepare_next_step_order_change(state, d, y, n_iter),
     )
 
     return state
@@ -692,9 +702,9 @@ def while_body(while_state):
         j += 1
         return [j, time_factor, order_summation]
 
-    j, time_factor, order_summation = jax.lax.while_loop(while_cond,
-                                                         while_body,
-                                                         while_state)
+    j, time_factor, order_summation = jax.lax.while_loop(
+        while_cond, while_body, while_state
+    )
     return order_summation
 
 
@@ -703,12 +713,12 @@ def block_fun(i, j, Ai, Aj):
         if i == j:
             return Ai
         else:
-            return jnp.zeros(
+            return onp.zeros(
                 (
                     Ai.shape[0] if Ai.ndim > 1 else 1,
                     Aj.shape[1] if Aj.ndim > 1 else 1,
                 ),
-                dtype=Ai.dtype
+                dtype=Ai.dtype,
             )
 
     blocks = [
@@ -716,7 +726,8 @@ def block_fun(i, j, Ai, Aj):
         for i, Ai in enumerate(lst)
     ]
 
-    return jnp.block(blocks)
+    return onp.block(blocks)
+
 
 # NOTE: the code below (except the docstring on jax_bdf_integrate and other minor
 # edits), has been modified from the JAX library at https://github.com/google/jax.
@@ -785,10 +796,13 @@ def jax_bdf_integrate(func, y0, t_eval, *args, rtol=1e-6, atol=1e-6, mass=None):
            fundamental algorithms for scientific computing in Python.
            Nature methods, 17(3), 261-272.
     """
+
     def _check_arg(arg):
         if not isinstance(arg, core.Tracer) and not core.valid_jaxtype(arg):
-            msg = ("The contents of odeint *args must be arrays or scalars, but got "
-                   "\n{}.")
+            msg = (
+                "The contents of odeint *args must be arrays or scalars, but got "
+                "\n{}."
+            )
         raise TypeError(msg.format(arg))
 
     flat_args, in_tree = tree_flatten((y0, t_eval[0], *args))
@@ -871,10 +885,10 @@ def aug_dynamics(augmented_state, t, *args):
 
         return (-y_dot, y_bar_dot, *rest)
 
-    algebraic_variables = jnp.diag(mass) == 0.
+    algebraic_variables = onp.diag(mass) == 0.0
     differentiable_variables = algebraic_variables == False  # noqa: E712
-    mass_is_I = (mass == jnp.eye(mass.shape[0])).all()
-    is_dae = jnp.any(algebraic_variables)
+    mass_is_I = onp.array_equal(mass, onp.eye(mass.shape[0]))
+    is_dae = onp.any(algebraic_variables)
 
     if not mass_is_I:
         M_dd = mass[onp.ix_(differentiable_variables, differentiable_variables)]
@@ -894,9 +908,9 @@ def initialise(g0, y0, t0):
             g0_a = g0[algebraic_variables]
             invJ_aa = jax.scipy.linalg.lu_solve(LU, g0_a)
             y_bar = jax.ops.index_update(
-                g0, differentiable_variables,
-                jax.scipy.linalg.lu_solve(LU_invM_dd,
-                                          g0_a - J_ad @ invJ_aa)
+                g0,
+                differentiable_variables,
+                jax.scipy.linalg.lu_solve(LU_invM_dd, g0_a - J_ad @ invJ_aa),
             )
         else:
             y_bar = jax.scipy.linalg.lu_solve(LU_invM_dd, g0)
@@ -904,12 +918,19 @@ def initialise(g0, y0, t0):
 
     y_bar = initialise(g[-1], ys[-1], ts[-1])
     ts_bar = []
-    t0_bar = 0.
+    t0_bar = 0.0
 
     def arg_to_identity(arg):
         return onp.identity(arg.shape[0] if arg.ndim > 0 else 1, dtype=arg.dtype)
 
-    aug_mass = (mass, mass, jnp.array(1.), tree_map(arg_to_identity, args))
+    def arg_dicts_to_values(args):
+        """
+        Note: JAX puts in empty arrays into args for some reason, we remove them here
+        """
+        return sum((tuple(b.values()) for b in args if isinstance(b, dict)), ())
+
+    aug_mass = (mass, mass, onp.array(1.0)) + \
+        arg_dicts_to_values(tree_map(arg_to_identity, args))
 
     def scan_fun(carry, i):
         y_bar, t0_bar, args_bar = carry
@@ -918,10 +939,14 @@ def scan_fun(carry, i):
         t0_bar = t0_bar - t_bar
         # Run augmented system backwards to previous observation
         _, y_bar, t0_bar, args_bar = jax_bdf_integrate(
-            aug_dynamics, (ys[i], y_bar, t0_bar, args_bar),
+            aug_dynamics,
+            (ys[i], y_bar, t0_bar, args_bar),
             jnp.array([-ts[i], -ts[i - 1]]),
-            *args, mass=aug_mass,
-            rtol=rtol, atol=atol)
+            *args,
+            mass=aug_mass,
+            rtol=rtol,
+            atol=atol
+        )
         y_bar, t0_bar, args_bar = tree_map(op.itemgetter(1), (y_bar, t0_bar, args_bar))
         # Add gradient from current output
         y_bar = y_bar + initialise(g[i - 1], ys[i - 1], ts[i - 1])
@@ -929,7 +954,8 @@ def scan_fun(carry, i):
 
     init_carry = (y_bar, t0_bar, tree_map(jnp.zeros_like, args))
     (y_bar, t0_bar, args_bar), rev_ts_bar = jax.lax.scan(
-        scan_fun, init_carry, jnp.arange(len(ts) - 1, 0, -1))
+        scan_fun, init_carry, jnp.arange(len(ts) - 1, 0, -1)
+    )
     ts_bar = jnp.concatenate([jnp.array([t0_bar]), rev_ts_bar[::-1]])
     return (y_bar, ts_bar, *args_bar)
 
@@ -939,21 +965,24 @@ def scan_fun(carry, i):
 
 @cache()
 def closure_convert(fun, in_tree, in_avals):
-    in_pvals = [pe.PartialVal.unknown(aval) for aval in in_avals]
-    wrapped_fun, out_tree = flatten_fun_nokwargs(lu.wrap_init(fun), in_tree)
-    with core.initial_style_staging():
-        jaxpr, _, consts = pe.trace_to_jaxpr(
-            wrapped_fun, in_pvals, instantiate=True, stage_out=False
-        )
+    if config.omnistaging_enabled:
+        wrapped_fun, out_tree = flatten_fun_nokwargs(lu.wrap_init(fun), in_tree)
+        jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(wrapped_fun, in_avals)
+    else:
+        in_pvals = [pe.PartialVal.unknown(aval) for aval in in_avals]
+        wrapped_fun, out_tree = flatten_fun_nokwargs(lu.wrap_init(fun), in_tree)
+        with core.initial_style_staging():  # type: ignore
+            jaxpr, _, consts = pe.trace_to_jaxpr(
+                wrapped_fun, in_pvals, instantiate=True, stage_out=False
+            )  # type: ignore
     out_tree = out_tree()
 
     # We only want to closure convert for constants with respect to which we're
     # differentiating. As a proxy for that, we hoist consts with float dtype.
     # TODO(mattjj): revise this approach
-    (closure_consts, hoisted_consts), merge = partition_list(
-        lambda c: dtypes.issubdtype(dtypes.dtype(c), jnp.inexact),
-        consts
-    )
+    def is_float(c):
+        return dtypes.issubdtype(dtypes.dtype(c), jnp.inexact)
+    (closure_consts, hoisted_consts), merge = partition_list(is_float, consts)
     num_consts = len(hoisted_consts)
 
     def converted_fun(y, t, *hconsts_args):
@@ -973,6 +1002,7 @@ def partition_list(choice, lst):
     def merge(l1, l2):
         i1, i2 = iter(l1), iter(l2)
         return [next(i2 if snd else i1) for snd in which]
+
     return out, merge
 
 
diff --git a/pybamm/solvers/jax_solver.py b/pybamm/solvers/jax_solver.py
index db912d0da1..c597556e5b 100644
--- a/pybamm/solvers/jax_solver.py
+++ b/pybamm/solvers/jax_solver.py
@@ -45,16 +45,17 @@ class JaxSolver(pybamm.BaseSolver):
         for details.
     """
 
-    def __init__(self, method='RK45', root_method=None,
-                 rtol=1e-6, atol=1e-6, extra_options=None):
+    def __init__(
+        self, method="RK45", root_method=None, rtol=1e-6, atol=1e-6, extra_options=None
+    ):
         # note: bdf solver itself calculates consistent initial conditions so can set
         # root_method to none, allow user to override this behavior
         super().__init__(method, rtol, atol, root_method=root_method)
-        method_options = ['RK45', 'BDF']
+        method_options = ["RK45", "BDF"]
         if method not in method_options:
-            raise ValueError('method must be one of {}'.format(method_options))
+            raise ValueError("method must be one of {}".format(method_options))
         self.ode_solver = False
-        if method == 'RK45':
+        if method == "RK45":
             self.ode_solver = True
         self.extra_options = extra_options or {}
         self.name = "JAX solver ({})".format(method)
@@ -80,8 +81,9 @@ def get_solve(self, model, t_eval):
         """
         if model not in self._cached_solves:
             if model not in self.models_set_up:
-                raise RuntimeError("Model is not set up for solving, run"
-                                   "`solver.solve(model)` first")
+                raise RuntimeError(
+                    "Model is not set up for solving, run" "`solver.solve(model)` first"
+                )
 
             self._cached_solves[model] = self.create_solve(model, t_eval)
 
@@ -106,32 +108,35 @@ def create_solve(self, model, t_eval):
 
         """
         if model.convert_to_format != "jax":
-            raise RuntimeError("Model must be converted to JAX to use this solver"
-                               " (i.e. `model.convert_to_format = 'jax')")
+            raise RuntimeError(
+                "Model must be converted to JAX to use this solver"
+                " (i.e. `model.convert_to_format = 'jax')"
+            )
 
         if model.terminate_events_eval:
-            raise RuntimeError("Terminate events not supported for this solver."
-                               " Model has the following events:"
-                               " {}.\nYou can remove events using `model.events = []`."
-                               " It might be useful to first solve the model using a"
-                               " different solver to obtain the time of the event, then"
-                               " re-solve using no events and a fixed"
-                               " end-time".format(model.events))
+            raise RuntimeError(
+                "Terminate events not supported for this solver."
+                " Model has the following events:"
+                " {}.\nYou can remove events using `model.events = []`."
+                " It might be useful to first solve the model using a"
+                " different solver to obtain the time of the event, then"
+                " re-solve using no events and a fixed"
+                " end-time".format(model.events)
+            )
 
         # Initial conditions, make sure they are an 0D array
         y0 = jnp.array(model.y0).reshape(-1)
         mass = None
-        if self.method == 'BDF':
+        if self.method == "BDF":
             mass = model.mass_matrix.entries.toarray()
 
         def rhs_ode(y, t, inputs):
-            return model.rhs_eval(t, y, inputs),
+            return (model.rhs_eval(t, y, inputs),)
 
         def rhs_dae(y, t, inputs):
-            return jnp.concatenate([
-                model.rhs_eval(t, y, inputs),
-                model.algebraic_eval(t, y, inputs),
-            ])
+            return jnp.concatenate(
+                [model.rhs_eval(t, y, inputs), model.algebraic_eval(t, y, inputs)]
+            )
 
         def solve_model_rk45(inputs):
             y = odeint(
@@ -158,7 +163,7 @@ def solve_model_bdf(inputs):
             )
             return jnp.transpose(y)
 
-        if self.method == 'RK45':
+        if self.method == "RK45":
             return jax.jit(solve_model_rk45)
         else:
             return jax.jit(solve_model_bdf)
@@ -183,16 +188,19 @@ def _integrate(self, model, t_eval, inputs=None):
             various diagnostic messages.
 
         """
+        timer = pybamm.Timer()
         if model not in self._cached_solves:
             self._cached_solves[model] = self.create_solve(model, t_eval)
 
-        y = self._cached_solves[model](inputs)
+        y = self._cached_solves[model](inputs).block_until_ready()
+        integration_time = timer.time()
 
-        # note - the actual solve is not done until this line!
+        # convert to a normal numpy array
         y = onp.array(y)
 
         termination = "final time"
         t_event = None
         y_event = onp.array(None)
-        return pybamm.Solution(t_eval, y,
-                               t_event, y_event, termination)
+        sol = pybamm.Solution(t_eval, y, t_event, y_event, termination)
+        sol.integration_time = integration_time
+        return sol
diff --git a/pybamm/solvers/processed_variable.py b/pybamm/solvers/processed_variable.py
index 5dce767dd9..1a8a3f176f 100644
--- a/pybamm/solvers/processed_variable.py
+++ b/pybamm/solvers/processed_variable.py
@@ -60,15 +60,12 @@ def __init__(self, base_variable, solution, known_evals=None, warn=True):
         self.warn = warn
 
         # Set timescale
-        self.timescale = solution.model.timescale.evaluate()
+        self.timescale = solution.timescale_eval
         self.t_pts = self.t_sol * self.timescale
 
         # Store length scales
         if solution.model:
-            self.length_scales = {
-                domain: scale.evaluate()
-                for domain, scale in solution.model.length_scales.items()
-            }
+            self.length_scales = solution.length_scales_eval
 
         # Evaluate base variable at initial time
         if self.known_evals:
@@ -354,11 +351,15 @@ def initialise_2D(self):
             self.second_dimension = "x"
             self.r_sol = first_dim_pts
             self.x_sol = second_dim_pts
-        elif self.domain[0] in [
-            "negative electrode",
-            "separator",
-            "positive electrode",
-        ] and self.auxiliary_domains["secondary"] == ["current collector"]:
+        elif (
+            self.domain[0]
+            in [
+                "negative electrode",
+                "separator",
+                "positive electrode",
+            ]
+            and self.auxiliary_domains["secondary"] == ["current collector"]
+        ):
             self.first_dimension = "x"
             self.second_dimension = "z"
             self.x_sol = first_dim_pts
diff --git a/pybamm/solvers/scikits_dae_solver.py b/pybamm/solvers/scikits_dae_solver.py
index 6f3b56ec8f..df2272e14c 100644
--- a/pybamm/solvers/scikits_dae_solver.py
+++ b/pybamm/solvers/scikits_dae_solver.py
@@ -130,7 +130,9 @@ def jacfn(t, y, ydot, residuals, cj, J):
 
         # set up and solve
         dae_solver = scikits_odes.dae(self.method, eqsres, **extra_options)
+        timer = pybamm.Timer()
         sol = dae_solver.solve(t_eval, y0, ydot0)
+        integration_time = timer.time()
 
         # return solution, we need to tranpose y to match scipy's interface
         if sol.flag in [0, 2]:
@@ -144,12 +146,14 @@ def jacfn(t, y, ydot, residuals, cj, J):
                 t_root = None
             else:
                 t_root = sol.roots.t
-            return pybamm.Solution(
+            sol = pybamm.Solution(
                 sol.values.t,
                 np.transpose(sol.values.y),
                 t_root,
                 np.transpose(sol.roots.y),
                 termination,
             )
+            sol.integration_time = integration_time
+            return sol
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/scikits_ode_solver.py b/pybamm/solvers/scikits_ode_solver.py
index 457e5b520c..0c4d6b9cd4 100644
--- a/pybamm/solvers/scikits_ode_solver.py
+++ b/pybamm/solvers/scikits_ode_solver.py
@@ -147,7 +147,9 @@ def jac_times_setupfn(t, y, fy, userdata):
             extra_options.update({"rootfn": rootfn, "nr_rootfns": len(events)})
 
         ode_solver = scikits_odes.ode(self.method, eqsydot, **extra_options)
+        timer = pybamm.Timer()
         sol = ode_solver.solve(t_eval, y0)
+        integration_time = timer.time()
 
         # return solution, we need to tranpose y to match scipy's ivp interface
         if sol.flag in [0, 2]:
@@ -161,12 +163,14 @@ def jac_times_setupfn(t, y, fy, userdata):
                 t_root = None
             else:
                 t_root = sol.roots.t
-            return pybamm.Solution(
+            sol = pybamm.Solution(
                 sol.values.t,
                 np.transpose(sol.values.y),
                 t_root,
                 np.transpose(sol.roots.y),
                 termination,
             )
+            sol.integration_time = integration_time
+            return sol
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/scipy_solver.py b/pybamm/solvers/scipy_solver.py
index 613ae72a51..41eb69838a 100644
--- a/pybamm/solvers/scipy_solver.py
+++ b/pybamm/solvers/scipy_solver.py
@@ -83,6 +83,7 @@ def event_fn(t, y):
             events = [event_wrapper(event) for event in model.terminate_events_eval]
             extra_options.update({"events": events})
 
+        timer = pybamm.Timer()
         sol = it.solve_ivp(
             lambda t, y: model.rhs_eval(t, y, inputs),
             (t_eval[0], t_eval[-1]),
@@ -92,6 +93,7 @@ def event_fn(t, y):
             dense_output=True,
             **extra_options
         )
+        integration_time = timer.time()
 
         if sol.success:
             # Set the reason for termination
@@ -107,6 +109,8 @@ def event_fn(t, y):
                 termination = "final time"
                 t_event = None
                 y_event = np.array(None)
-            return pybamm.Solution(sol.t, sol.y, t_event, y_event, termination)
+            sol = pybamm.Solution(sol.t, sol.y, t_event, y_event, termination)
+            sol.integration_time = integration_time
+            return sol
         else:
             raise pybamm.SolverError(sol.message)
diff --git a/pybamm/solvers/solution.py b/pybamm/solvers/solution.py
index c94b03791d..3ddbf5514e 100644
--- a/pybamm/solvers/solution.py
+++ b/pybamm/solvers/solution.py
@@ -50,15 +50,17 @@ def __init__(
         if copy_this is None:
             # initialize empty inputs and model, to be populated later
             self._inputs = pybamm.FuzzyDict()
-            self._model = pybamm.BaseModel()
+            self.model = pybamm.BaseModel()
             self.set_up_time = None
             self.solve_time = None
+            self.integration_time = None
             self.has_symbolic_inputs = False
         else:
             self._inputs = copy.copy(copy_this.inputs)
-            self._model = copy_this.model
+            self.model = copy_this.model
             self.set_up_time = copy_this.set_up_time
             self.solve_time = copy_this.solve_time
+            self.integration_time = copy_this.integration_time
             self.has_symbolic_inputs = copy_this.has_symbolic_inputs
 
         # initiaize empty variables and data
@@ -86,10 +88,24 @@ def model(self):
         return self._model
 
     @model.setter
-    def model(self, value):
+    def model(self, model):
         "Updates the model"
-        assert isinstance(value, pybamm.BaseModel)
-        self._model = value
+        assert isinstance(model, pybamm.BaseModel)
+        self._model = model
+
+        # Copy the timescale_eval and lengthscale_evals if they exist
+        if hasattr(model, "timescale_eval"):
+            self.timescale_eval = model.timescale_eval
+        else:
+            self.timescale_eval = model.timescale.evaluate()
+        # self.timescale_eval = model.timescale_eval
+        if hasattr(model, "length_scales_eval"):
+            self.length_scales_eval = model.length_scales_eval
+        else:
+            self.length_scales_eval = {
+                domain: scale.evaluate()
+                for domain, scale in model.length_scales.items()
+            }
 
     @property
     def inputs(self):
@@ -201,6 +217,23 @@ def __getitem__(self, key):
             self.update(key)
             return self._variables[key]
 
+    def plot(self, output_variables=None, **kwargs):
+        """
+        A method to quickly plot the outputs of the solution. Creates a
+        :class:`pybamm.QuickPlot` object (with keyword arguments 'kwargs') and
+        then calls :meth:`pybamm.QuickPlot.dynamic_plot`.
+
+        Parameters
+        ----------
+        output_variables: list, optional
+            A list of the variables to plot.
+        **kwargs
+            Additional keyword arguments passed to
+            :meth:`pybamm.QuickPlot.dynamic_plot`.
+            For a list of all possible keyword arguments see :class:`pybamm.QuickPlot`.
+        """
+        return pybamm.dynamic_plot(self, output_variables=output_variables, **kwargs)
+
     def save(self, filename):
         """Save the whole solution using pickle"""
         # No warning here if len(self.data)==0 as solution can be loaded
@@ -208,7 +241,7 @@ def save(self, filename):
         with open(filename, "wb") as f:
             pickle.dump(self, f, pickle.HIGHEST_PROTOCOL)
 
-    def save_data(self, filename, variables=None, to_format="pickle"):
+    def save_data(self, filename, variables=None, to_format="pickle", short_names=None):
         """
         Save solution data only (raw arrays)
 
@@ -224,7 +257,12 @@ def save_data(self, filename, variables=None, to_format="pickle"):
 
             - 'pickle' (default): creates a pickle file with the data dictionary
             - 'matlab': creates a .mat file, for loading in matlab
-            - 'csv': creates a csv file (1D variables only)
+            - 'csv': creates a csv file (0D variables only)
+        short_names : dict, optional
+            Dictionary of shortened names to use when saving. This may be necessary when
+            saving to MATLAB, since no spaces or special characters are allowed in
+            MATLAB variable names. Note that not all the variables need to be given
+            a short name.
 
         """
         if variables is None:
@@ -243,20 +281,55 @@ def save_data(self, filename, variables=None, to_format="pickle"):
                 to save.
                 """
             )
+
+        # Use any short names if provided
+        data_short_names = {}
+        short_names = short_names or {}
+        for name, var in data.items():
+            # change to short name if it exists
+            if name in short_names:
+                data_short_names[short_names[name]] = var
+            else:
+                data_short_names[name] = var
+
         if to_format == "pickle":
             with open(filename, "wb") as f:
-                pickle.dump(data, f, pickle.HIGHEST_PROTOCOL)
+                pickle.dump(data_short_names, f, pickle.HIGHEST_PROTOCOL)
         elif to_format == "matlab":
-            savemat(filename, data)
+            # Check all the variable names only contain a-z, A-Z or _ or numbers
+            for name in data_short_names.keys():
+                # Check the string only contains the following ASCII:
+                # a-z (97-122)
+                # A-Z (65-90)
+                # _ (95)
+                # 0-9 (48-57) but not in the first position
+                for i, s in enumerate(name):
+                    if not (
+                        97 <= ord(s) <= 122
+                        or 65 <= ord(s) <= 90
+                        or ord(s) == 95
+                        or (i > 0 and 48 <= ord(s) <= 57)
+                    ):
+                        raise ValueError(
+                            "Invalid character '{}' found in '{}'. ".format(s, name)
+                            + "MATLAB variable names must only contain a-z, A-Z, _, "
+                            "or 0-9 (except the first position). "
+                            "Use the 'short_names' argument to pass an alternative "
+                            "variable name, e.g. \n\n"
+                            "\tsolution.save_data(filename, "
+                            "['Electrolyte concentration'], to_format='matlab, "
+                            "short_names={'Electrolyte concentration': 'c_e'})"
+                        )
+            savemat(filename, data_short_names)
         elif to_format == "csv":
-            for name, var in data.items():
+            for name, var in data_short_names.items():
                 if var.ndim >= 2:
                     raise ValueError(
                         "only 0D variables can be saved to csv, but '{}' is {}D".format(
                             name, var.ndim - 1
                         )
                     )
-            df = pd.DataFrame(data)
+            df = pd.DataFrame(data_short_names)
             df.to_csv(filename, index=False)
         else:
             raise ValueError("format '{}' not recognised".format(to_format))
@@ -325,6 +398,7 @@ def append(self, solution, start_index=1, create_sub_solutions=False):
             self.inputs[name] = np.c_[inp, solution_inp[:, start_index:]]
         # Update solution time
         self.solve_time += solution.solve_time
+        self.integration_time += solution.integration_time
         # Update termination
         self._termination = solution.termination
         self._t_event = solution._t_event
diff --git a/pybamm/spatial_methods/spectral_volume.py b/pybamm/spatial_methods/spectral_volume.py
index c8f8848d3f..36b6a13f05 100644
--- a/pybamm/spatial_methods/spectral_volume.py
+++ b/pybamm/spatial_methods/spectral_volume.py
@@ -2,15 +2,7 @@
 
 import numpy as np
 
-from scipy.sparse import (
-    diags,
-    eye,
-    kron,
-    csr_matrix,
-    lil_matrix,
-    coo_matrix,
-    vstack,
-)
+from scipy.sparse import diags, eye, kron, csr_matrix, lil_matrix, coo_matrix, vstack
 
 
 class SpectralVolume(pybamm.FiniteVolume):
@@ -75,13 +67,18 @@ def chebyshev_collocation_points(self, noe, a=-1.0, b=1.0):
         Chebyshev collocation points on [a,b].
         """
 
-        return a + 0.5 * (b - a) * (1 + np.sin(np.pi * np.array(
-            [(noe - 1 - 2 * i) / (2 * noe - 2) for i in range(noe)])))
+        return a + 0.5 * (b - a) * (
+            1
+            + np.sin(
+                np.pi
+                * np.array([(noe - 1 - 2 * i) / (2 * noe - 2) for i in range(noe)])
+            )
+        )
 
     def cv_boundary_reconstruction_sub_matrix(self):
         """
         Coefficients for reconstruction of a function through averages.
-        The resulting matrix is scale-invariant.
+        The resulting matrix is scale-invariant [2]_.
 
         Parameters
         ----------
@@ -101,8 +98,7 @@ def cv_boundary_reconstruction_sub_matrix(self):
         # While Spectral Volume in general may use any point
         # distribution for CVs, the Chebyshev nodes are the most stable.
         # The differentiation matrices are only implemented for those.
-        edges = np.flip(
-            self.chebyshev_collocation_points(self.order + 1))
+        edges = np.flip(self.chebyshev_collocation_points(self.order + 1))
 
         # Nomenclature in the reference:
         # c[j,l] are the coefficients from the reference.
@@ -118,23 +114,30 @@ def cv_boundary_reconstruction_sub_matrix(self):
         def d_omega_d_x(j):
             return np.prod(
                 edges[j] - edges,
-                where=[True] * j + [False] + [True] * (len(edges) - 1 - j)
+                where=[True] * j + [False] + [True] * (len(edges) - 1 - j),
             )
 
         for j in range(self.order + 1):
             for ell in range(self.order):
-                c[j, ell] = h[ell] * np.sum([
-                    1.0 / d_omega_d_x(r) * np.sum(
-                        [
-                            np.prod(edges[j] - edges,
-                                    where=[q != r and q != m
-                                           for q in range(self.order + 1)])
-                            for m in range(self.order + 1)
-                        ],
-                        where=[m != r for m in range(self.order + 1)]
-                    )
-                    for r in range(ell + 1, self.order + 1)
-                ])
+                c[j, ell] = h[ell] * np.sum(
+                    [
+                        1.0
+                        / d_omega_d_x(r)
+                        * np.sum(
+                            [
+                                np.prod(
+                                    edges[j] - edges,
+                                    where=[
+                                        q != r and q != m for q in range(self.order + 1)
+                                    ],
+                                )
+                                for m in range(self.order + 1)
+                            ],
+                            where=[m != r for m in range(self.order + 1)],
+                        )
+                        for r in range(ell + 1, self.order + 1)
+                    ]
+                )
 
         return c
 
@@ -171,8 +174,7 @@ def cv_boundary_reconstruction_matrix(self, domain, auxiliary_domains):
         sub_matrix = csr_matrix(kron(eye(n), recon_sub_matrix))
 
         # number of repeats
-        second_dim_repeats = self._get_auxiliary_domain_repeats(
-            auxiliary_domains)
+        second_dim_repeats = self._get_auxiliary_domain_repeats(auxiliary_domains)
 
         # generate full matrix from the submatrix
         # Convert to csr_matrix so that we can take the index
@@ -185,7 +187,7 @@ def cv_boundary_reconstruction_matrix(self, domain, auxiliary_domains):
 
     def chebyshev_differentiation_matrices(self, noe, dod):
         """
-        Chebyshev differentiation matrices.
+        Chebyshev differentiation matrices [1]_.
 
         Parameters
         ----------
@@ -212,31 +214,32 @@ def chebyshev_differentiation_matrices(self, noe, dod):
                Society for Industrial and Applied Mathematics,
                24(5):1465–1487, 2003
         """
-        if(dod >= noe):
+        if dod >= noe:
             raise ValueError(
                 "Too many degrees of differentiation. At most "
-                + str(noe - 1) + " are possible for " + str(noe) + " edges."
+                + str(noe - 1)
+                + " are possible for "
+                + str(noe)
+                + " edges."
             )
 
         edges = self.chebyshev_collocation_points(noe)
 
         # These matrices tend to be dense, thus numpy arrays are used.
-        prefactors = np.array([
-            [(i - j + 1) % 2 - (i - j) % 2
-             for j in range(noe)]
-            for i in range(noe)
-        ])
-        prefactors = (prefactors * np.array(
-            [2] + [1 for i in range(noe - 2)] + [2])).T
-        prefactors = prefactors * np.array(
-            [0.5] + [1 for i in range(noe - 2)] + [0.5])
-
-        inverse_difference = np.array([
-            [1.0 / (edges[i] - edges[j]) for j in range(i)]
-            + [0.0]
-            + [1.0 / (edges[i] - edges[j]) for j in range(i + 1, noe)]
-            for i in range(noe)
-        ])
+        prefactors = np.array(
+            [[(i - j + 1) % 2 - (i - j) % 2 for j in range(noe)] for i in range(noe)]
+        )
+        prefactors = (prefactors * np.array([2] + [1 for i in range(noe - 2)] + [2])).T
+        prefactors = prefactors * np.array([0.5] + [1 for i in range(noe - 2)] + [0.5])
+
+        inverse_difference = np.array(
+            [
+                [1.0 / (edges[i] - edges[j]) for j in range(i)]
+                + [0.0]
+                + [1.0 / (edges[i] - edges[j]) for j in range(i + 1, noe)]
+                for i in range(noe)
+            ]
+        )
 
         differentiation_matrices = []
         # This matrix changes in each of the following iterations.
@@ -264,8 +267,10 @@ def gradient(self, symbol, discretised_symbol, boundary_conditions):
         domain = symbol.domain
 
         # Reconstruct edge values from node values.
-        reconstructed_symbol = self.cv_boundary_reconstruction_matrix(
-            domain, symbol.auxiliary_domains) @ discretised_symbol
+        reconstructed_symbol = (
+            self.cv_boundary_reconstruction_matrix(domain, symbol.auxiliary_domains)
+            @ discretised_symbol
+        )
 
         # Add Dirichlet boundary conditions, if defined
         if symbol.id in boundary_conditions:
@@ -277,18 +282,13 @@ def gradient(self, symbol, discretised_symbol, boundary_conditions):
                 )
 
         # note in 1D spherical grad and normal grad are the same
-        gradient_matrix = self.gradient_matrix(
-            domain,
-            symbol.auxiliary_domains
-        )
-        penalty_matrix = self.penalty_matrix(
-            domain,
-            symbol.auxiliary_domains
-        )
+        gradient_matrix = self.gradient_matrix(domain, symbol.auxiliary_domains)
+        penalty_matrix = self.penalty_matrix(domain, symbol.auxiliary_domains)
 
         # Multiply by gradient matrix
-        out = (gradient_matrix @ reconstructed_symbol
-               + penalty_matrix @ discretised_symbol)
+        out = (
+            gradient_matrix @ reconstructed_symbol + penalty_matrix @ discretised_symbol
+        )
 
         # Add Neumann boundary conditions, if defined
         if symbol.id in boundary_conditions:
@@ -331,16 +331,21 @@ def gradient_matrix(self, domain, auxiliary_domains):
         # Obtain the Chebyshev differentiation matrix.
         # Flip it, since it is defined for the Chebyshev
         # collocation points in descending order.
-        chebdiff = np.flip(self.chebyshev_differentiation_matrices(
-            self.order + 1, 1)[0])
+        chebdiff = np.flip(
+            self.chebyshev_differentiation_matrices(self.order + 1, 1)[0]
+        )
 
         # Create 1D matrix using submesh
         # submesh.npts is the number of CVs and n the number of SVs
         n = submesh.npts // self.order
         d = self.order
         # Compute the lengths of the Spectral Volumes.
-        d_sv_edges = np.array([np.sum(submesh.d_edges[d * i:d * i + d])
-                               for i in range(len(submesh.d_edges) // d)])
+        d_sv_edges = np.array(
+            [
+                np.sum(submesh.d_edges[d * i : d * i + d])
+                for i in range(len(submesh.d_edges) // d)
+            ]
+        )
         # The 2 scales from [-1,1] (Chebyshev default) to [0,1].
         # e = 2 / submesh.d_sv_edges
         e = 2 / d_sv_edges
@@ -356,29 +361,27 @@ def gradient_matrix(self, domain, auxiliary_domains):
             sub_matrix = sub_matrix_raw
         else:
             sub_matrix = lil_matrix((n * d + 1, n * (d + 1)))
-            sub_matrix[:d, :d + 1] = sub_matrix_raw[:d, :d + 1]
-            sub_matrix[d, :d + 1] = f * sub_matrix_raw[d, :d + 1]
+            sub_matrix[:d, : d + 1] = sub_matrix_raw[:d, : d + 1]
+            sub_matrix[d, : d + 1] = f * sub_matrix_raw[d, : d + 1]
             # for loop of shame (optimisation potential via vectorisation)
             for i in range(1, n - 1):
-                sub_matrix[i * d, i * (d + 1):(i + 1) * (d + 1)] = (
-                    f * sub_matrix_raw[i * (d + 1),
-                                       i * (d + 1):(i + 1) * (d + 1)]
+                sub_matrix[i * d, i * (d + 1) : (i + 1) * (d + 1)] = (
+                    f * sub_matrix_raw[i * (d + 1), i * (d + 1) : (i + 1) * (d + 1)]
                 )
-                sub_matrix[i * d + 1:(i + 1) * d,
-                           i * (d + 1):(i + 1) * (d + 1)] = (
-                    sub_matrix_raw[i * (d + 1) + 1:(i + 1) * (d + 1) - 1,
-                                   i * (d + 1):(i + 1) * (d + 1)]
+                sub_matrix[
+                    i * d + 1 : (i + 1) * d, i * (d + 1) : (i + 1) * (d + 1)
+                ] = sub_matrix_raw[
+                    i * (d + 1) + 1 : (i + 1) * (d + 1) - 1,
+                    i * (d + 1) : (i + 1) * (d + 1),
+                ]
+                sub_matrix[(i + 1) * d, i * (d + 1) : (i + 1) * (d + 1)] = (
+                    f * sub_matrix_raw[i * (d + 1) + d, i * (d + 1) : (i + 1) * (d + 1)]
                 )
-                sub_matrix[(i + 1) * d, i * (d + 1):(i + 1) * (d + 1)] = (
-                    f * sub_matrix_raw[i * (d + 1) + d,
-                                       i * (d + 1):(i + 1) * (d + 1)]
-                )
-            sub_matrix[-d - 1, -d - 1:] = f * sub_matrix_raw[-d - 1, -d - 1:]
-            sub_matrix[-d:, -d - 1:] = sub_matrix_raw[-d:, -d - 1:]
+            sub_matrix[-d - 1, -d - 1 :] = f * sub_matrix_raw[-d - 1, -d - 1 :]
+            sub_matrix[-d:, -d - 1 :] = sub_matrix_raw[-d:, -d - 1 :]
 
         # number of repeats
-        second_dim_repeats = self._get_auxiliary_domain_repeats(
-            auxiliary_domains)
+        second_dim_repeats = self._get_auxiliary_domain_repeats(auxiliary_domains)
 
         # generate full matrix from the submatrix
         # Convert to csr_matrix so that we can take the index
@@ -416,17 +419,13 @@ def penalty_matrix(self, domain, auxiliary_domains):
         n = submesh.npts
         d = self.order
         e = np.zeros(n - 1)
-        e[d - 1::d] = 1 / submesh.d_nodes[d - 1::d]
-        sub_matrix = vstack([
-            np.zeros(n),
-            diags([-e, e], [0, 1], shape=(n - 1, n)),
-            np.zeros(n),
-        ])
+        e[d - 1 :: d] = 1 / submesh.d_nodes[d - 1 :: d]
+        sub_matrix = vstack(
+            [np.zeros(n), diags([-e, e], [0, 1], shape=(n - 1, n)), np.zeros(n)]
+        )
 
         # number of repeats
-        second_dim_repeats = self._get_auxiliary_domain_repeats(
-            auxiliary_domains
-        )
+        second_dim_repeats = self._get_auxiliary_domain_repeats(auxiliary_domains)
 
         # generate full matrix from the submatrix
         # Convert to csr_matrix so that we can take the index
@@ -437,9 +436,9 @@ def penalty_matrix(self, domain, auxiliary_domains):
 
         return pybamm.Matrix(matrix)
 
-    #def spectral_volume_internal_neumann_condition(
+    # def spectral_volume_internal_neumann_condition(
     #    self, left_symbol_disc, right_symbol_disc, left_mesh, right_mesh
-    #):
+    # ):
     #    """
     #    A method to find the internal neumann conditions between two
     #    symbols on adjacent subdomains. This method is never called,
@@ -548,11 +547,9 @@ def replace_dirichlet_values(self, symbol, discretised_symbol, bcs):
         # write boundary values into vectors of according shape
         if lbc_type == "Dirichlet":
             lbc_sub_matrix = coo_matrix(([1], ([0], [0])), shape=(n, 1))
-            lbc_matrix = csr_matrix(kron(eye(second_dim_repeats),
-                                         lbc_sub_matrix))
+            lbc_matrix = csr_matrix(kron(eye(second_dim_repeats), lbc_sub_matrix))
             if lbc_value.evaluates_to_number():
-                left_bc = lbc_value * pybamm.Vector(
-                    np.ones(second_dim_repeats))
+                left_bc = lbc_value * pybamm.Vector(np.ones(second_dim_repeats))
             else:
                 left_bc = lbc_value
             lbc_vector = pybamm.Matrix(lbc_matrix) @ left_bc
@@ -566,11 +563,9 @@ def replace_dirichlet_values(self, symbol, discretised_symbol, bcs):
 
         if rbc_type == "Dirichlet":
             rbc_sub_matrix = coo_matrix(([1], ([n - 1], [0])), shape=(n, 1))
-            rbc_matrix = csr_matrix(kron(eye(second_dim_repeats),
-                                         rbc_sub_matrix))
+            rbc_matrix = csr_matrix(kron(eye(second_dim_repeats), rbc_sub_matrix))
             if rbc_value.evaluates_to_number():
-                right_bc = rbc_value * pybamm.Vector(
-                    np.ones(second_dim_repeats))
+                right_bc = rbc_value * pybamm.Vector(np.ones(second_dim_repeats))
             else:
                 right_bc = rbc_value
             rbc_vector = pybamm.Matrix(rbc_matrix) @ right_bc
@@ -592,9 +587,11 @@ def replace_dirichlet_values(self, symbol, discretised_symbol, bcs):
         # Make matrix which makes "gaps" at the boundaries into which
         # the known Dirichlet values will be added. If the boundary
         # condition is not Dirichlet, it acts as identity.
-        sub_matrix = diags([int(lbc_type != "Dirichlet")]
-                           + [1 for i in range(n - 2)]
-                           + [int(rbc_type != "Dirichlet")])
+        sub_matrix = diags(
+            [int(lbc_type != "Dirichlet")]
+            + [1 for i in range(n - 2)]
+            + [int(rbc_type != "Dirichlet")]
+        )
 
         # repeat matrix for secondary dimensions
         # Convert to csr_matrix so that we can take the index
@@ -644,12 +641,9 @@ def replace_neumann_values(self, symbol, discretised_gradient, bcs):
         # Add any values from Neumann boundary conditions to the bcs vector
         if lbc_type == "Neumann":
             lbc_sub_matrix = coo_matrix(([1], ([0], [0])), shape=(n, 1))
-            lbc_matrix = csr_matrix(kron(eye(second_dim_repeats),
-                                         lbc_sub_matrix))
+            lbc_matrix = csr_matrix(kron(eye(second_dim_repeats), lbc_sub_matrix))
             if lbc_value.evaluates_to_number():
-                left_bc = lbc_value * pybamm.Vector(
-                    np.ones(second_dim_repeats)
-                )
+                left_bc = lbc_value * pybamm.Vector(np.ones(second_dim_repeats))
             else:
                 left_bc = lbc_value
             lbc_vector = pybamm.Matrix(lbc_matrix) @ left_bc
@@ -663,11 +657,9 @@ def replace_neumann_values(self, symbol, discretised_gradient, bcs):
 
         if rbc_type == "Neumann":
             rbc_sub_matrix = coo_matrix(([1], ([n - 1], [0])), shape=(n, 1))
-            rbc_matrix = csr_matrix(kron(eye(second_dim_repeats),
-                                         rbc_sub_matrix))
+            rbc_matrix = csr_matrix(kron(eye(second_dim_repeats), rbc_sub_matrix))
             if rbc_value.evaluates_to_number():
-                right_bc = rbc_value * pybamm.Vector(
-                    np.ones(second_dim_repeats))
+                right_bc = rbc_value * pybamm.Vector(np.ones(second_dim_repeats))
             else:
                 right_bc = rbc_value
             rbc_vector = pybamm.Matrix(rbc_matrix) @ right_bc
@@ -689,9 +681,11 @@ def replace_neumann_values(self, symbol, discretised_gradient, bcs):
         # Make matrix which makes "gaps" at the boundaries into which
         # the known Neumann values will be added. If the boundary
         # condition is not Neumann, it acts as identity.
-        sub_matrix = diags([int(lbc_type != "Neumann")]
-                           + [1 for i in range(n - 2)]
-                           + [int(rbc_type != "Neumann")])
+        sub_matrix = diags(
+            [int(lbc_type != "Neumann")]
+            + [1 for i in range(n - 2)]
+            + [int(rbc_type != "Neumann")]
+        )
 
         # repeat matrix for secondary dimensions
         # Convert to csr_matrix so that we can take the index
@@ -700,7 +694,6 @@ def replace_neumann_values(self, symbol, discretised_gradient, bcs):
         # this should not be an issue.
         matrix = csr_matrix(kron(eye(second_dim_repeats), sub_matrix))
 
-        new_gradient = (pybamm.Matrix(matrix) @ discretised_gradient
-                        + bcs_vector)
+        new_gradient = pybamm.Matrix(matrix) @ discretised_gradient + bcs_vector
 
         return new_gradient
diff --git a/pybamm/util.py b/pybamm/util.py
index f58e04280f..46625e0d63 100644
--- a/pybamm/util.py
+++ b/pybamm/util.py
@@ -154,10 +154,14 @@ def format(self, time=None):
         """
         if time is None:
             time = self.time()
-        if time < 1e-2:
-            return str(time) + " seconds"
+        if time < 1e-6:
+            return "{:.3f} ns".format(time * 1e9)
+        if time < 1e-3:
+            return "{:.3f} us".format(time * 1e6)
+        if time < 1:
+            return "{:.3f} ms".format(time * 1e3)
         elif time < 60:
-            return str(round(time, 2)) + " seconds"
+            return "{:.3f} s".format(time)
         output = []
         time = int(round(time))
         units = [(604800, "week"), (86400, "day"), (3600, "hour"), (60, "minute")]
diff --git a/pybamm/version b/pybamm/version
index a050f8f285..da0481e75b 100644
--- a/pybamm/version
+++ b/pybamm/version
@@ -1 +1 @@
-0, 2, 4
+0, 3, 0
diff --git a/scripts/install_KLU_Sundials.py b/scripts/install_KLU_Sundials.py
index 539e41a268..92f3f27e5e 100755
--- a/scripts/install_KLU_Sundials.py
+++ b/scripts/install_KLU_Sundials.py
@@ -121,5 +121,3 @@ def download_extract_library(url, download_dir):
 print("-" * 10, "Building the sundials", "-" * 40)
 make_cmd = ["make", "install"]
 subprocess.run(make_cmd, cwd=build_dir)
-
-
diff --git a/setup.py b/setup.py
index f9a7a09c60..9f22d21343 100644
--- a/setup.py
+++ b/setup.py
@@ -161,18 +161,18 @@ def compile_KLU():
 jax_dependencies = []
 if system() != "Windows":
     jax_dependencies = [
-        "jax==0.1.75",
-        "jaxlib==0.1.52",
+        "jax==0.2.5",
+        "jaxlib==0.1.57",
     ]
 
 
 # Load text for description and license
-with open("README.md") as f:
+with open("README.md", encoding="utf-8") as f:
     readme = f.read()
 
 setup(
     name="pybamm",
-    version=load_version() + ".post3",
+    version=load_version() + "-beta",
     description="Python Battery Mathematical Modelling.",
     long_description=readme,
     long_description_content_type="text/markdown",
@@ -185,6 +185,8 @@ def compile_KLU():
         "install": CustomInstall,
     },
     package_data={"pybamm": pybamm_data},
+    # Python version
+    python_requires=">=3.6,<3.9",
     # List of dependencies
     install_requires=[
         "numpy>=1.16",
diff --git a/tests/integration/test_models/standard_model_tests.py b/tests/integration/test_models/standard_model_tests.py
index f1176493a5..48267a8bbf 100644
--- a/tests/integration/test_models/standard_model_tests.py
+++ b/tests/integration/test_models/standard_model_tests.py
@@ -128,8 +128,9 @@ def __init__(self, model, parameter_values=None, disc=None):
 
         self.model = model
 
-    def evaluate_model(self, simplify=False, use_known_evals=False,
-                       to_python=False, to_jax=False):
+    def evaluate_model(
+        self, simplify=False, use_known_evals=False, to_python=False, to_jax=False
+    ):
         result = np.empty((0, 1))
         for eqn in [self.model.concatenated_rhs, self.model.concatenated_algebraic]:
             if simplify:
diff --git a/tests/integration/test_models/standard_output_tests.py b/tests/integration/test_models/standard_output_tests.py
index d186fc4596..370c6cf4a0 100644
--- a/tests/integration/test_models/standard_output_tests.py
+++ b/tests/integration/test_models/standard_output_tests.py
@@ -67,7 +67,7 @@ def __init__(self, model, param, disc, solution, operating_condition):
 
         # Use dimensional time and space
         self.t = solution.t * model.timescale_eval
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
 
         L_x = param.evaluate(geo.L_x)
         self.x_n = disc.mesh["negative electrode"].nodes * L_x
@@ -81,8 +81,8 @@ def __init__(self, model, param, disc, solution, operating_condition):
         self.x_edge = disc.mesh.combine_submeshes(*whole_cell).edges * L_x
 
         if isinstance(self.model, pybamm.lithium_ion.BaseModel):
-            R_n = param.evaluate(geo.R_n)
-            R_p = param.evaluate(geo.R_p)
+            R_n = param.evaluate(model.param.R_n_typ)
+            R_p = param.evaluate(model.param.R_p_typ)
             self.r_n = disc.mesh["negative particle"].nodes * R_n
             self.r_p = disc.mesh["positive particle"].nodes * R_p
             self.r_n_edge = disc.mesh["negative particle"].edges * R_n
@@ -127,10 +127,10 @@ def __init__(self, model, param, disc, solution, operating_condition):
 
     def test_each_reaction_overpotential(self):
         """Testing that:
-            - discharge: eta_r_n > 0, eta_r_p < 0
-            - charge: eta_r_n < 0, eta_r_p > 0
-            - off: eta_r_n == 0, eta_r_p == 0
-            """
+        - discharge: eta_r_n > 0, eta_r_p < 0
+        - charge: eta_r_n < 0, eta_r_p > 0
+        - off: eta_r_n == 0, eta_r_p == 0
+        """
         tol = 0.01
         t, x_n, x_p = self.t, self.x_n, self.x_p
         if self.operating_condition == "discharge":
@@ -145,9 +145,9 @@ def test_each_reaction_overpotential(self):
 
     def test_overpotentials(self):
         """Testing that all are:
-            - discharge: . < 0
-            - charge: . > 0
-            - off: . == 0
+        - discharge: . < 0
+        - charge: . > 0
+        - off: . == 0
         """
         tol = 0.001
         if self.operating_condition == "discharge":
@@ -168,10 +168,10 @@ def test_overpotentials(self):
             )
 
     def test_ocps(self):
-        """ Testing that:
-            - discharge: ocp_n increases, ocp_p decreases
-            - charge: ocp_n decreases, ocp_p increases
-            - off: ocp_n, ocp_p constant
+        """Testing that:
+        - discharge: ocp_n increases, ocp_p decreases
+        - charge: ocp_n decreases, ocp_p increases
+        - off: ocp_n, ocp_p constant
         """
         neg_end_vs_start = self.ocp_n_av(self.t[-1]) - self.ocp_n_av(self.t[1])
         pos_end_vs_start = self.ocp_p_av(self.t[-1]) - self.ocp_p_av(self.t[1])
@@ -187,9 +187,9 @@ def test_ocps(self):
 
     def test_ocv(self):
         """Testing that:
-            - discharge: ocv decreases
-            - charge: ocv increases
-            - off: ocv constant
+        - discharge: ocv decreases
+        - charge: ocv increases
+        - off: ocv constant
         """
 
         end_vs_start = self.ocv_av(self.t[-1]) - self.ocv_av(self.t[1])
@@ -203,9 +203,9 @@ def test_ocv(self):
 
     def test_voltage(self):
         """Testing that:
-            - discharge: voltage decreases
-            - charge: voltage increases
-            - off: voltage constant
+        - discharge: voltage decreases
+        - charge: voltage increases
+        - off: voltage constant
         """
         end_vs_start = self.voltage(self.t[-1]) - self.voltage(self.t[1])
 
@@ -595,8 +595,8 @@ def __init__(self, model, param, disc, solution, operating_condition):
         self.i_s = solution["Electrode current density"]
         self.i_e = solution["Electrolyte current density"]
 
-        self.a_n = solution["Negative surface area per unit volume distribution in x"]
-        self.a_p = solution["Positive surface area per unit volume distribution in x"]
+        self.a_n = solution["Negative electrode surface area per unit volume"]
+        self.a_p = solution["Positive electrode surface area per unit volume"]
 
     def test_interfacial_current_average(self):
         """Test that average of the surface area density distribution (in x)
diff --git a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_compare_basic_models.py b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_compare_basic_models.py
index d8d9eaa120..efbd706ec5 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_compare_basic_models.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_compare_basic_models.py
@@ -19,7 +19,7 @@ def test_compare_full(self):
 
         # Solve basic Full mode
         basic_sim = pybamm.Simulation(
-            basic_full, solver=pybamm.CasadiSolver(), parameter_values=parameter_values,
+            basic_full, solver=pybamm.CasadiSolver(), parameter_values=parameter_values
         )
         t_eval = np.linspace(0, 400)
         basic_sim.solve(t_eval)
diff --git a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_composite.py b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_composite.py
index 53038800b4..6c0d5df552 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_composite.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_composite.py
@@ -49,13 +49,7 @@ def test_basic_processing_1plus1D(self):
         options = {"current collector": "potential pair", "dimensionality": 1}
         model = pybamm.lead_acid.Composite(options)
         var = pybamm.standard_spatial_vars
-        var_pts = {
-            var.x_n: 5,
-            var.x_s: 5,
-            var.x_p: 5,
-            var.y: 5,
-            var.z: 5,
-        }
+        var_pts = {var.x_n: 5, var.x_s: 5, var.x_p: 5, var.y: 5, var.z: 5}
         modeltest = tests.StandardModelTest(model, var_pts=var_pts)
         modeltest.test_all(skip_output_tests=True)
 
diff --git a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_full.py b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_full.py
index af34d8ee41..bc67a3617b 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_full.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_full.py
@@ -53,13 +53,7 @@ def test_basic_processing_1plus1D(self):
         options = {"current collector": "potential pair", "dimensionality": 1}
         model = pybamm.lead_acid.Full(options)
         var = pybamm.standard_spatial_vars
-        var_pts = {
-            var.x_n: 5,
-            var.x_s: 5,
-            var.x_p: 5,
-            var.y: 5,
-            var.z: 5,
-        }
+        var_pts = {var.x_n: 5, var.x_s: 5, var.x_p: 5, var.y: 5, var.z: 5}
         modeltest = tests.StandardModelTest(model, var_pts=var_pts)
         modeltest.test_all(skip_output_tests=True)
 
diff --git a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_loqs.py b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_loqs.py
index 1c4bebd105..1aa83c6315 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_loqs.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lead_acid/test_loqs.py
@@ -70,13 +70,7 @@ def test_basic_processing_1plus1D(self):
         options = {"current collector": "potential pair", "dimensionality": 1}
         model = pybamm.lead_acid.LOQS(options)
         var = pybamm.standard_spatial_vars
-        var_pts = {
-            var.x_n: 5,
-            var.x_s: 5,
-            var.x_p: 5,
-            var.y: 5,
-            var.z: 5,
-        }
+        var_pts = {var.x_n: 5, var.x_s: 5, var.x_p: 5, var.y: 5, var.z: 5}
         modeltest = tests.StandardModelTest(model, var_pts=var_pts)
         modeltest.test_all(skip_output_tests=True)
 
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
index fb338965c3..c188373e57 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_compare_outputs.py
@@ -15,7 +15,7 @@ def test_compare_outputs_surface_form(self):
         ]
         model_combos = [
             ([pybamm.lithium_ion.SPM(opt) for opt in options]),
-            ([pybamm.lithium_ion.SPMe(opt) for opt in options]),
+            # ([pybamm.lithium_ion.SPMe(opt) for opt in options]), # not implemented
             ([pybamm.lithium_ion.DFN(opt) for opt in options]),
         ]
 
@@ -137,8 +137,6 @@ def test_compare_particle_shape(self):
                         "Positive electrode surface area to volume ratio [m-1]": 3
                         * eps_s_p
                         / R_p,
-                        "Negative surface area per unit volume distribution in x": 1,
-                        "Positive surface area per unit volume distribution in x": 1,
                     },
                     check_already_exists=False,
                 )
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
index a9b85eb76c..da70b056db 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
@@ -122,15 +122,18 @@ def test_surface_form_algebraic(self):
     def test_particle_distribution_in_x(self):
         model = pybamm.lithium_ion.DFN()
         param = model.default_parameter_values
+        L_n = model.param.L_n
+        L_p = model.param.L_p
+        L = model.param.L_x
 
-        def negative_distribution(x):
-            return 1 + x
+        def negative_radius(x):
+            return (1 + x / L_n) * 1e-5
 
-        def positive_distribution(x):
-            return 1 + (x - (1 - model.param.l_p))
+        def positive_radius(x):
+            return (1 + (x - L_p) / (L - L_p)) * 1e-5
 
-        param["Negative particle distribution in x"] = negative_distribution
-        param["Positive particle distribution in x"] = positive_distribution
+        param["Negative particle radius [m]"] = negative_radius
+        param["Positive particle radius [m]"] = positive_radius
         modeltest = tests.StandardModelTest(model, parameter_values=param)
         modeltest.test_all()
 
@@ -179,6 +182,48 @@ def test_well_posed_ec_reaction_limited(self):
         modeltest.test_all()
 
 
+class TestDFNWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.DFN(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.DFN(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.DFN(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.DFN(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.DFN(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spm.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
index 2f3a42233f..78ead4bbab 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
@@ -165,6 +165,48 @@ def test_well_posed_ec_reaction_limited(self):
         modeltest.test_all()
 
 
+class TestSPMWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.SPM(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.SPM(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.SPM(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.SPM(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.SPM(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spme.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
index 1b76aca7e7..4261851106 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
@@ -112,14 +112,20 @@ def test_particle_quartic(self):
         modeltest = tests.StandardModelTest(model)
         modeltest.test_all()
 
-    def test_surface_form_differential(self):
-        options = {"surface form": "differential"}
-        model = pybamm.lithium_ion.SPMe(options)
-        modeltest = tests.StandardModelTest(model)
-        modeltest.test_all()
+    # def test_surface_form_differential(self):
+    #     options = {"surface form": "differential"}
+    #     model = pybamm.lithium_ion.SPMe(options)
+    #     modeltest = tests.StandardModelTest(model)
+    #     modeltest.test_all()
 
-    def test_surface_form_algebraic(self):
-        options = {"surface form": "algebraic"}
+    # def test_surface_form_algebraic(self):
+    #     options = {"surface form": "algebraic"}
+    #     model = pybamm.lithium_ion.SPMe(options)
+    #     modeltest = tests.StandardModelTest(model)
+    #     modeltest.test_all()
+
+    def test_integrated_conductivity(self):
+        options = {"electrolyte conductivity": "integrated"}
         model = pybamm.lithium_ion.SPMe(options)
         modeltest = tests.StandardModelTest(model)
         modeltest.test_all()
@@ -157,6 +163,48 @@ def test_well_posed_ec_reaction_limited(self):
         modeltest.test_all()
 
 
+class TestSPMeWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.SPMe(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.SPMe(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.SPMe(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.SPMe(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.SPMe(options)
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        modeltest = tests.StandardModelTest(model, parameter_values=parameter_values)
+        modeltest.test_all()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py
index 22d9ce6d6b..ca39a2c36c 100644
--- a/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py
+++ b/tests/integration/test_models/test_full_battery_models/test_lithium_ion/test_thermal_models.py
@@ -13,9 +13,7 @@ def test_consistent_cooling(self):
         # much larger realistic temperature rises
         # so that errors can be more easily observed
         C_rate = 5
-        options = {
-            "thermal": "x-lumped",
-        }
+        options = {"thermal": "x-lumped"}
         spme_1D = pybamm.lithium_ion.SPMe(options=options)
 
         options = {
diff --git a/tests/integration/test_solvers/test_external_variables.py b/tests/integration/test_solvers/test_external_variables.py
index 06a4197af2..29ef229f6b 100644
--- a/tests/integration/test_solvers/test_external_variables.py
+++ b/tests/integration/test_solvers/test_external_variables.py
@@ -3,6 +3,7 @@
 #
 import pybamm
 import numpy as np
+import os
 import unittest
 
 
@@ -49,6 +50,9 @@ def test_external_variables_SPMe(self):
         inputs = external_variables
         sim.built_model.variables[var].evaluate(t, y, inputs=inputs)
         sim.solution[var](t)
+        # test generate with external variable
+        sim.built_model.generate("test.c", ["Volume-averaged cell temperature"])
+        os.remove("test.c")
 
 
 if __name__ == "__main__":
diff --git a/tests/integration/test_spatial_methods/test_spectral_volume.py b/tests/integration/test_spatial_methods/test_spectral_volume.py
index 699e5f3afe..09b10d6426 100644
--- a/tests/integration/test_spatial_methods/test_spectral_volume.py
+++ b/tests/integration/test_spatial_methods/test_spectral_volume.py
@@ -8,8 +8,7 @@
 
 
 def get_mesh_for_testing(
-    xpts=None, rpts=10, ypts=15, zpts=15, geometry=None, cc_submesh=None,
-    order=2
+    xpts=None, rpts=10, ypts=15, zpts=15, geometry=None, cc_submesh=None, order=2
 ):
     param = pybamm.ParameterValues(
         values={
@@ -33,22 +32,19 @@ def get_mesh_for_testing(
 
     submesh_types = {
         "negative electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
+        ),
+        "separator": pybamm.MeshGenerator(
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
-        "separator": pybamm.MeshGenerator(pybamm.SpectralVolume1DSubMesh,
-                                          {"order": order}),
         "positive electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "negative particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "positive particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
     }
diff --git a/tests/unit/test_citations.py b/tests/unit/test_citations.py
index bc7c70a5a7..a2e243f552 100644
--- a/tests/unit/test_citations.py
+++ b/tests/unit/test_citations.py
@@ -107,6 +107,15 @@ def test_subramanian_2005(self):
         pybamm.particle.PolynomialManyParticles(None, "Negative", "quadratic profile")
         self.assertIn("subramanian2005", citations._papers_to_cite)
 
+    def test_brosaplanella_2020(self):
+        # Test that calling relevant bits of code adds the right paper to citations
+        citations = pybamm.citations
+
+        citations._reset()
+        self.assertNotIn("brosaplanella2020TSPMe", citations._papers_to_cite)
+        pybamm.electrolyte_conductivity.Integrated(None)
+        self.assertIn("brosaplanella2020TSPMe", citations._papers_to_cite)
+
     def test_scikit_fem(self):
         citations = pybamm.citations
 
diff --git a/tests/unit/test_discretisations/test_discretisation.py b/tests/unit/test_discretisations/test_discretisation.py
index 7ceff8746c..6cc507579c 100644
--- a/tests/unit/test_discretisations/test_discretisation.py
+++ b/tests/unit/test_discretisations/test_discretisation.py
@@ -619,8 +619,7 @@ def test_process_model_ode(self):
 
         # mass matrix is identity
         np.testing.assert_array_equal(
-            np.eye(combined_submesh.nodes.shape[0]),
-            model.mass_matrix.entries.toarray(),
+            np.eye(combined_submesh.nodes.shape[0]), model.mass_matrix.entries.toarray()
         )
 
         # Create StateVector to differentiate model with respect to
@@ -793,7 +792,7 @@ def test_process_model_dae(self):
             (
                 np.eye(np.size(combined_submesh.nodes)),
                 np.zeros(
-                    (np.size(combined_submesh.nodes), np.size(combined_submesh.nodes),)
+                    (np.size(combined_submesh.nodes), np.size(combined_submesh.nodes))
                 ),
             )
         )
@@ -1027,10 +1026,7 @@ def test_secondary_broadcast_2D(self):
         self.assertIsInstance(broad_to_edges_disc.children[1], pybamm.StateVector)
         self.assertEqual(
             broad_to_edges_disc.shape,
-            (
-                mesh["negative particle"].npts * (mesh["negative electrode"].npts + 1),
-                1,
-            ),
+            (mesh["negative particle"].npts * (mesh["negative electrode"].npts + 1), 1),
         )
 
     def test_concatenation(self):
@@ -1237,6 +1233,58 @@ def test_process_input_variable(self):
         n = disc.mesh.combine_submeshes(*a.domain).npts
         self.assertEqual(a_disc._expected_size, n)
 
+    def test_bc_symmetry(self):
+        # define model
+        model = pybamm.BaseModel()
+        c = pybamm.Variable("Concentration", domain="negative particle")
+        N = -pybamm.grad(c)
+        dcdt = -pybamm.div(N)
+        model.rhs = {c: dcdt}
+
+        # initial conditions
+        model.initial_conditions = {c: pybamm.Scalar(1)}
+
+        # define geometry
+        r = pybamm.SpatialVariable(
+            "r", domain=["negative particle"], coord_sys="spherical polar"
+        )
+        geometry = {
+            "negative particle": {r: {"min": pybamm.Scalar(0), "max": pybamm.Scalar(1)}}
+        }
+
+        # mesh
+        submesh_types = {
+            "negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)
+        }
+        var_pts = {r: 20}
+        mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
+
+        spatial_methods = {"negative particle": pybamm.FiniteVolume()}
+
+        # boundary conditions (Dirichlet)
+        lbc = pybamm.Scalar(0)
+        rbc = pybamm.Scalar(2)
+        model.boundary_conditions = {
+            c: {"left": (lbc, "Dirichlet"), "right": (rbc, "Neumann")}
+        }
+
+        # discretise
+        disc = pybamm.Discretisation(mesh, spatial_methods)
+        with self.assertRaisesRegex(pybamm.ModelError, "Boundary condition at r = 0"):
+            disc.process_model(model)
+
+        # boundary conditions (non-homog Neumann)
+        lbc = pybamm.Scalar(0)
+        rbc = pybamm.Scalar(2)
+        model.boundary_conditions = {
+            c: {"left": (rbc, "Neumann"), "right": (rbc, "Neumann")}
+        }
+
+        # discretise
+        disc = pybamm.Discretisation(mesh, spatial_methods)
+        with self.assertRaisesRegex(pybamm.ModelError, "Boundary condition at r = 0"):
+            disc.process_model(model)
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")
diff --git a/tests/unit/test_expression_tree/test_binary_operators.py b/tests/unit/test_expression_tree/test_binary_operators.py
index 5aa4e3ba6c..a714c544f4 100644
--- a/tests/unit/test_expression_tree/test_binary_operators.py
+++ b/tests/unit/test_expression_tree/test_binary_operators.py
@@ -143,12 +143,30 @@ def test_diff(self):
         self.assertEqual((a / a).diff(a).evaluate(y=y), 0)
         self.assertEqual((a / a).diff(b).evaluate(y=y), 0)
 
-    def test_addition_printing(self):
+    def test_printing(self):
+        # This in not an exhaustive list of all cases. More test cases may need to
+        # be added for specific combinations of binary operators
         a = pybamm.Symbol("a")
         b = pybamm.Symbol("b")
-        summ = pybamm.Addition(a, b)
-        self.assertEqual(summ.name, "+")
-        self.assertEqual(str(summ), "a + b")
+        c = pybamm.Symbol("c")
+        d = pybamm.Symbol("d")
+        self.assertEqual(str(a + b), "a + b")
+        self.assertEqual(str(a + b + c + d), "a + b + c + d")
+        self.assertEqual(str((a + b) + (c + d)), "a + b + c + d")
+        self.assertEqual(str(a + b - c), "a + b - c")
+        self.assertEqual(str(a + b - c + d), "a + b - c + d")
+        self.assertEqual(str((a + b) - (c + d)), "a + b - (c + d)")
+        self.assertEqual(str((a + b) - (c - d)), "a + b - (c - d)")
+
+        self.assertEqual(str((a + b) * (c + d)), "(a + b) * (c + d)")
+        self.assertEqual(str(a * b * (c + d)), "a * b * (c + d)")
+        self.assertEqual(str((a * b) * (c + d)), "a * b * (c + d)")
+        self.assertEqual(str(a * (b * (c + d))), "a * b * (c + d)")
+        self.assertEqual(str((a + b) / (c + d)), "(a + b) / (c + d)")
+        self.assertEqual(str(a + b / (c + d)), "a + b / (c + d)")
+        self.assertEqual(str(a * b / (c + d)), "a * b / (c + d)")
+        self.assertEqual(str((a * b) / (c + d)), "a * b / (c + d)")
+        self.assertEqual(str(a * (b / (c + d))), "a * b / (c + d)")
 
     def test_id(self):
         a = pybamm.Scalar(4)
@@ -303,6 +321,21 @@ def test_heaviside(self):
         self.assertEqual(heav.evaluate(y=np.array([0])), 1)
         self.assertEqual(str(heav), "y[0:1] <= 1.0")
 
+    def test_sigmoid(self):
+        a = pybamm.Scalar(1)
+        b = pybamm.StateVector(slice(0, 1))
+        sigm = pybamm.sigmoid(a, b, 10)
+        self.assertAlmostEqual(sigm.evaluate(y=np.array([2]))[0, 0], 1)
+        self.assertEqual(sigm.evaluate(y=np.array([1])), 0.5)
+        self.assertAlmostEqual(sigm.evaluate(y=np.array([0]))[0, 0], 0)
+        self.assertEqual(str(sigm), "(1.0 + tanh(10.0 * (y[0:1] - 1.0))) / 2.0")
+
+        sigm = pybamm.sigmoid(b, a, 10)
+        self.assertAlmostEqual(sigm.evaluate(y=np.array([2]))[0, 0], 0)
+        self.assertEqual(sigm.evaluate(y=np.array([1])), 0.5)
+        self.assertAlmostEqual(sigm.evaluate(y=np.array([0]))[0, 0], 1)
+        self.assertEqual(str(sigm), "(1.0 + tanh(10.0 * (1.0 - y[0:1]))) / 2.0")
+
     def test_modulo(self):
         a = pybamm.StateVector(slice(0, 1))
         b = pybamm.Scalar(3)
@@ -329,6 +362,43 @@ def test_minimum_maximum(self):
         self.assertEqual(maximum.evaluate(y=np.array([0])), 1)
         self.assertEqual(str(maximum), "maximum(1.0, y[0:1])")
 
+    def test_softminus_softplus(self):
+        a = pybamm.Scalar(1)
+        b = pybamm.StateVector(slice(0, 1))
+
+        minimum = pybamm.softminus(a, b, 50)
+        self.assertAlmostEqual(minimum.evaluate(y=np.array([2]))[0, 0], 1)
+        self.assertAlmostEqual(minimum.evaluate(y=np.array([0]))[0, 0], 0)
+        self.assertEqual(
+            str(minimum),
+            "log(1.9287498479639178e-22 + exp(-50.0 * y[0:1])) / -50.0",
+        )
+
+        maximum = pybamm.softplus(a, b, 50)
+        self.assertAlmostEqual(maximum.evaluate(y=np.array([2]))[0, 0], 2)
+        self.assertAlmostEqual(maximum.evaluate(y=np.array([0]))[0, 0], 1)
+        self.assertEqual(
+            str(maximum),
+            "log(5.184705528587072e+21 + exp(50.0 * y[0:1])) / 50.0",
+        )
+
+        # Test that smooth min/max are used when the setting is changed
+        pybamm.settings.min_smoothing = 10
+        pybamm.settings.max_smoothing = 10
+
+        self.assertEqual(str(pybamm.minimum(a, b)), str(pybamm.softminus(a, b, 10)))
+        self.assertEqual(str(pybamm.maximum(a, b)), str(pybamm.softplus(a, b, 10)))
+
+        # But exact min/max should still be used if both variables are constant
+        a = 1
+        b = pybamm.Parameter("b")
+        self.assertEqual(str(pybamm.minimum(a, b)), str(pybamm.Minimum(a, b)))
+        self.assertEqual(str(pybamm.maximum(a, b)), str(pybamm.Maximum(a, b)))
+
+        # Change setting back for other tests
+        pybamm.settings.min_smoothing = "exact"
+        pybamm.settings.max_smoothing = "exact"
+
 
 class TestIsZero(unittest.TestCase):
     def test_is_scalar_zero(self):
diff --git a/tests/unit/test_expression_tree/test_concatenations.py b/tests/unit/test_expression_tree/test_concatenations.py
index e87f2aaa29..01e7a07077 100644
--- a/tests/unit/test_expression_tree/test_concatenations.py
+++ b/tests/unit/test_expression_tree/test_concatenations.py
@@ -14,6 +14,7 @@ def test_base_concatenation(self):
         c = pybamm.Symbol("c")
         conc = pybamm.Concatenation(a, b, c)
         self.assertEqual(conc.name, "concatenation")
+        self.assertEqual(str(conc), "concatenation(a, b, c)")
         self.assertIsInstance(conc.children[0], pybamm.Symbol)
         self.assertEqual(conc.children[0].name, "a")
         self.assertEqual(conc.children[1].name, "b")
@@ -153,11 +154,15 @@ def test_numpy_domain_concatenation(self):
         )
         # test size and shape
         self.assertEqual(
-            conc.size, mesh[b_dom[0]].npts + mesh[a_dom[0]].npts + mesh[b_dom[1]].npts,
+            conc.size,
+            mesh[b_dom[0]].npts + mesh[a_dom[0]].npts + mesh[b_dom[1]].npts,
         )
         self.assertEqual(
             conc.shape,
-            (mesh[b_dom[0]].npts + mesh[a_dom[0]].npts + mesh[b_dom[1]].npts, 1,),
+            (
+                mesh[b_dom[0]].npts + mesh[a_dom[0]].npts + mesh[b_dom[1]].npts,
+                1,
+            ),
         )
 
     def test_domain_concatenation_domains(self):
diff --git a/tests/unit/test_expression_tree/test_functions.py b/tests/unit/test_expression_tree/test_functions.py
index e79d82b48f..14901582fc 100644
--- a/tests/unit/test_expression_tree/test_functions.py
+++ b/tests/unit/test_expression_tree/test_functions.py
@@ -6,6 +6,7 @@
 import unittest
 import numpy as np
 from scipy.interpolate import interp1d
+from scipy import special
 
 
 def test_function(arg):
@@ -36,6 +37,7 @@ def test_function_of_one_variable(self):
         a = pybamm.Symbol("a")
         funca = pybamm.Function(test_function, a)
         self.assertEqual(funca.name, "function (test_function)")
+        self.assertEqual(str(funca), "test_function(a)")
         self.assertEqual(funca.children[0].name, a.name)
 
         b = pybamm.Scalar(1)
@@ -95,6 +97,7 @@ def test_function_of_multiple_variables(self):
         b = pybamm.Parameter("b")
         func = pybamm.Function(test_multi_var_function, a, b)
         self.assertEqual(func.name, "function (test_multi_var_function)")
+        self.assertEqual(str(func), "test_multi_var_function(a, b)")
         self.assertEqual(func.children[0].name, a.name)
         self.assertEqual(func.children[1].name, b.name)
 
@@ -322,6 +325,38 @@ def test_tanh(self):
             places=5,
         )
 
+    def test_erf(self):
+        a = pybamm.InputParameter("a")
+        fun = pybamm.erf(a)
+        self.assertEqual(fun.evaluate(inputs={"a": 3}), special.erf(3))
+        h = 0.0000001
+        self.assertAlmostEqual(
+            fun.diff(a).evaluate(inputs={"a": 3}),
+            (
+                pybamm.erf(pybamm.Scalar(3 + h)).evaluate()
+                - fun.evaluate(inputs={"a": 3})
+            )
+            / h,
+            places=5,
+        )
+
+    def test_erfc(self):
+        a = pybamm.InputParameter("a")
+        fun = pybamm.erfc(a)
+        self.assertAlmostEqual(
+            fun.evaluate(inputs={"a": 3}), special.erfc(3), places=15
+        )
+        h = 0.0000001
+        self.assertAlmostEqual(
+            fun.diff(a).evaluate(inputs={"a": 3}),
+            (
+                pybamm.erfc(pybamm.Scalar(3 + h)).evaluate()
+                - fun.evaluate(inputs={"a": 3})
+            )
+            / h,
+            places=5,
+        )
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")
diff --git a/tests/unit/test_expression_tree/test_operations/test_convert_to_casadi.py b/tests/unit/test_expression_tree/test_operations/test_convert_to_casadi.py
index ef28a429ad..d2e13c88b3 100644
--- a/tests/unit/test_expression_tree/test_operations/test_convert_to_casadi.py
+++ b/tests/unit/test_expression_tree/test_operations/test_convert_to_casadi.py
@@ -6,6 +6,7 @@
 import pybamm
 import unittest
 from tests import get_mesh_for_testing, get_1p1d_discretisation_for_testing
+from scipy import special
 
 
 class TestCasadiConverter(unittest.TestCase):
@@ -15,6 +16,15 @@ def assert_casadi_equal(self, a, b, evalf=False):
         else:
             self.assertTrue((a - b).is_zero())
 
+    def assert_casadi_almost_equal(self, a, b, decimal=7, evalf=False):
+        tol = 1.5 * 10 ** (-decimal)
+        if evalf is True:
+            self.assertTrue(
+                (casadi.fabs(casadi.evalf(a) - casadi.evalf(b)) < tol).is_one()
+            )
+        else:
+            self.assertTrue((casadi.fabs(a - b) < tol).is_one())
+
     def test_convert_scalar_symbols(self):
         a = pybamm.Scalar(0)
         b = pybamm.Scalar(1)
@@ -104,6 +114,8 @@ def test_special_functions(self):
         self.assert_casadi_equal(
             pybamm.Function(np.abs, c).to_casadi(), casadi.MX(3), evalf=True
         )
+
+        # test functions with assert_casadi_equal
         for np_fun in [
             np.sqrt,
             np.tanh,
@@ -121,6 +133,15 @@ def test_special_functions(self):
                 pybamm.Function(np_fun, c).to_casadi(), casadi.MX(np_fun(3)), evalf=True
             )
 
+        # test functions with assert_casadi_almost_equal
+        for np_fun in [special.erf]:
+            self.assert_casadi_almost_equal(
+                pybamm.Function(np_fun, c).to_casadi(),
+                casadi.MX(np_fun(3)),
+                decimal=15,
+                evalf=True,
+            )
+
     def test_interpolation(self):
         x = np.linspace(0, 1)[:, np.newaxis]
         y = pybamm.StateVector(slice(0, 2))
diff --git a/tests/unit/test_expression_tree/test_operations/test_evaluate.py b/tests/unit/test_expression_tree/test_operations/test_evaluate.py
index 0e4e4b177f..5c063a36b8 100644
--- a/tests/unit/test_expression_tree/test_operations/test_evaluate.py
+++ b/tests/unit/test_expression_tree/test_operations/test_evaluate.py
@@ -130,17 +130,6 @@ def test_find_symbols(self):
             list(constant_symbols.values())[0].toarray(), A.entries.toarray()
         )
 
-        # test sparse to dense conversion
-        constant_symbols = OrderedDict()
-        variable_symbols = OrderedDict()
-        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[0, 2], [0, 4]])))
-        pybamm.find_symbols(A, constant_symbols, variable_symbols, to_dense=True)
-        self.assertEqual(len(variable_symbols), 0)
-        self.assertEqual(list(constant_symbols.keys())[0], A.id)
-        np.testing.assert_allclose(
-            list(constant_symbols.values())[0], A.entries.toarray()
-        )
-
         # test numpy concatentate
         constant_symbols = OrderedDict()
         variable_symbols = OrderedDict()
@@ -451,11 +440,11 @@ def test_evaluator_python(self):
 
         v = pybamm.StateVector(slice(0, 2))
         A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
-        expr = pybamm.Inner(A, v)
-        evaluator = pybamm.EvaluatorPython(expr)
-        for t, y in zip(t_tests, y_tests):
-            result = evaluator.evaluate(t=t, y=y).toarray()
-            np.testing.assert_allclose(result, expr.evaluate(t=t, y=y).toarray())
+        for expr in [pybamm.Inner(A, v), pybamm.Inner(v, A)]:
+            evaluator = pybamm.EvaluatorPython(expr)
+            for t, y in zip(t_tests, y_tests):
+                result = evaluator.evaluate(t=t, y=y).toarray()
+                np.testing.assert_allclose(result, expr.evaluate(t=t, y=y).toarray())
 
         y_tests = [np.array([[2], [3], [4], [5]]), np.array([[1], [3], [2], [1]])]
         t_tests = [1, 2]
@@ -467,13 +456,30 @@ def test_evaluator_python(self):
             result = evaluator.evaluate(t=t, y=y)
             np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
 
+    @unittest.skipIf(system() == "Windows", "JAX not supported on windows")
+    def test_find_symbols_jax(self):
+        # test sparse conversion
+        constant_symbols = OrderedDict()
+        variable_symbols = OrderedDict()
+        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[0, 2], [0, 4]])))
+        pybamm.find_symbols(A, constant_symbols, variable_symbols, output_jax=True)
+        self.assertEqual(len(variable_symbols), 0)
+        self.assertEqual(list(constant_symbols.keys())[0], A.id)
+        np.testing.assert_allclose(
+            list(constant_symbols.values())[0].toarray(), A.entries.toarray()
+        )
+
     @unittest.skipIf(system() == "Windows", "JAX not supported on windows")
     def test_evaluator_jax(self):
         a = pybamm.StateVector(slice(0, 1))
         b = pybamm.StateVector(slice(1, 2))
 
-        y_tests = [np.array([[2], [3]]), np.array([[1], [3]])]
-        t_tests = [1, 2]
+        y_tests = [
+            np.array([[2.0], [3.0]]),
+            np.array([[1.0], [3.0]]),
+            np.array([1.0, 3.0]),
+        ]
+        t_tests = [1.0, 2.0]
 
         # test a * b
         expr = a * b
@@ -558,7 +564,7 @@ def test_evaluator_jax(self):
             result = evaluator.evaluate(t=t, y=y)
             self.assertEqual(result, expr.evaluate(t=t, y=y))
 
-        # test something with a sparse matrix multiplication
+        # test something with a sparse matrix-vector multiplication
         A = pybamm.Matrix(np.array([[1, 2], [3, 4]]))
         B = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
         C = pybamm.Matrix(scipy.sparse.coo_matrix(np.array([[1, 0], [0, 4]])))
@@ -568,15 +574,40 @@ def test_evaluator_jax(self):
             result = evaluator.evaluate(t=t, y=y)
             np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
 
+        # test the sparse-scalar multiplication
+        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
+        for expr in [
+                A * pybamm.t @ pybamm.StateVector(slice(0, 2)),
+                pybamm.t * A @ pybamm.StateVector(slice(0, 2)),
+        ]:
+            evaluator = pybamm.EvaluatorJax(expr)
+            for t, y in zip(t_tests, y_tests):
+                result = evaluator.evaluate(t=t, y=y)
+                np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
+
+        # test the sparse-scalar division
+        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
+        expr = A / (1.0 + pybamm.t) @ pybamm.StateVector(slice(0, 2))
+        evaluator = pybamm.EvaluatorJax(expr)
+        for t, y in zip(t_tests, y_tests):
+            result = evaluator.evaluate(t=t, y=y)
+            np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
+
         # test sparse stack
         A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
         B = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[2, 0], [5, 0]])))
         a = pybamm.StateVector(slice(0, 1))
         expr = pybamm.SparseStack(A, a * B)
-        evaluator = pybamm.EvaluatorJax(expr)
-        for t, y in zip(t_tests, y_tests):
-            result = evaluator.evaluate(t=t, y=y)
-            np.testing.assert_allclose(result, expr.evaluate(t=t, y=y).toarray())
+        with self.assertRaises(NotImplementedError):
+            evaluator = pybamm.EvaluatorJax(expr)
+
+        # test sparse mat-mat mult
+        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1, 0], [0, 4]])))
+        B = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[2, 0], [5, 0]])))
+        a = pybamm.StateVector(slice(0, 1))
+        expr = A @ (a * B)
+        with self.assertRaises(NotImplementedError):
+            evaluator = pybamm.EvaluatorJax(expr)
 
         # test numpy concatenation
         a = pybamm.Vector(np.array([[1], [2]]))
@@ -588,17 +619,22 @@ def test_evaluator_jax(self):
             np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
 
         # test Inner
-        v = pybamm.Vector(np.ones(5), domain="test")
-        w = pybamm.Vector(2 * np.ones(5), domain="test")
-        expr = pybamm.Inner(v, w)
-        evaluator = pybamm.EvaluatorJax(expr)
-        result = evaluator.evaluate()
-        np.testing.assert_allclose(result, expr.evaluate())
+        A = pybamm.Matrix(scipy.sparse.csr_matrix(np.array([[1]])))
+        v = pybamm.StateVector(slice(0, 1))
+        for expr in [
+                pybamm.Inner(A, v) @ v,
+                pybamm.Inner(v, A) @ v,
+                pybamm.Inner(v, v) @ v
+        ]:
+            evaluator = pybamm.EvaluatorJax(expr)
+            for t, y in zip(t_tests, y_tests):
+                result = evaluator.evaluate(t=t, y=y)
+                np.testing.assert_allclose(result, expr.evaluate(t=t, y=y))
 
     @unittest.skipIf(system() == "Windows", "JAX not supported on windows")
     def test_evaluator_jax_jacobian(self):
         a = pybamm.StateVector(slice(0, 1))
-        y_tests = [np.array([[2.0]]), np.array([[1.0]])]
+        y_tests = [np.array([[2.0]]), np.array([[1.0]]), np.array([1.0])]
 
         expr = a ** 2
         expr_jac = 2 * a
@@ -618,6 +654,28 @@ def test_evaluator_jax_debug(self):
         evaluator = pybamm.EvaluatorJax(expr)
         evaluator.debug(y=y_test)
 
+    @unittest.skipIf(system() == "Windows", "JAX not supported on windows")
+    def test_evaluator_jax_inputs(self):
+        a = pybamm.InputParameter('a')
+        expr = a ** 2
+        evaluator = pybamm.EvaluatorJax(expr)
+        result = evaluator.evaluate(inputs={'a': 2})
+        self.assertEqual(result, 4)
+
+    @unittest.skipIf(system() == "Windows", "JAX not supported on windows")
+    def test_jax_coo_matrix(self):
+        import jax
+        A = pybamm.JaxCooMatrix([0, 1], [0, 1], [1.0, 2.0], (2, 2))
+        Adense = jax.numpy.array([[1.0, 0], [0, 2.0]])
+        v = jax.numpy.array([[2.0], [1.0]])
+
+        np.testing.assert_allclose(A.toarray(), Adense)
+        np.testing.assert_allclose(A @ v, Adense @ v)
+        np.testing.assert_allclose(A.scalar_multiply(3.0).toarray(), Adense * 3.0)
+
+        with self.assertRaises(NotImplementedError):
+            A.multiply(v)
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")
diff --git a/tests/unit/test_expression_tree/test_symbol.py b/tests/unit/test_expression_tree/test_symbol.py
index 2c23e09fc7..56d98e6745 100644
--- a/tests/unit/test_expression_tree/test_symbol.py
+++ b/tests/unit/test_expression_tree/test_symbol.py
@@ -135,6 +135,44 @@ def test_symbol_methods(self):
         ):
             a + "two"
 
+    def test_sigmoid(self):
+        # Test that smooth heaviside is used when the setting is changed
+        a = pybamm.Symbol("a")
+        b = pybamm.Symbol("b")
+
+        pybamm.settings.heaviside_smoothing = 10
+
+        self.assertEqual(str(a < b), str(pybamm.sigmoid(a, b, 10)))
+        self.assertEqual(str(a <= b), str(pybamm.sigmoid(a, b, 10)))
+        self.assertEqual(str(a > b), str(pybamm.sigmoid(b, a, 10)))
+        self.assertEqual(str(a >= b), str(pybamm.sigmoid(b, a, 10)))
+
+        # But exact heavisides should still be used if both variables are constant
+        a = 1
+        b = pybamm.Parameter("b")
+        self.assertEqual(str(a < b), str(pybamm.NotEqualHeaviside(a, b)))
+        self.assertEqual(str(a <= b), str(pybamm.EqualHeaviside(a, b)))
+        self.assertEqual(str(a > b), str(pybamm.NotEqualHeaviside(b, a)))
+        self.assertEqual(str(a >= b), str(pybamm.EqualHeaviside(b, a)))
+
+        # Change setting back for other tests
+        pybamm.settings.heaviside_smoothing = "exact"
+
+    def test_smooth_absolute_value(self):
+        # Test that smooth absolute value is used when the setting is changed
+        a = pybamm.Symbol("a")
+        pybamm.settings.abs_smoothing = 10
+        self.assertEqual(str(abs(a)), str(pybamm.smooth_absolute_value(a, 10)))
+
+        # But exact absolute value should still be used for constants
+        a = pybamm.Parameter("a")
+        self.assertEqual(str(abs(a)), str(pybamm.AbsoluteValue(a)))
+        a = -1
+        self.assertEqual(str(abs(a)), "1")
+
+        # Change setting back for other tests
+        pybamm.settings.abs_smoothing = "exact"
+
     def test_multiple_symbols(self):
         a = pybamm.Symbol("a")
         b = pybamm.Symbol("b")
@@ -187,12 +225,12 @@ def test_symbol_is_constant(self):
         a = pybamm.Parameter("a")
         self.assertTrue(a.is_constant())
 
-        a = pybamm.Scalar(1) * pybamm.Variable("a")
-        self.assertFalse(a.is_constant())
-
         a = pybamm.Scalar(1) * pybamm.Parameter("a")
         self.assertTrue(a.is_constant())
 
+        a = pybamm.Scalar(1) * pybamm.Variable("a")
+        self.assertFalse(a.is_constant())
+
         a = pybamm.Scalar(1) * pybamm.StateVector(slice(10))
         self.assertFalse(a.is_constant())
 
diff --git a/tests/unit/test_expression_tree/test_unary_operators.py b/tests/unit/test_expression_tree/test_unary_operators.py
index b5d6f6bdb0..1ea51478c3 100644
--- a/tests/unit/test_expression_tree/test_unary_operators.py
+++ b/tests/unit/test_expression_tree/test_unary_operators.py
@@ -16,6 +16,9 @@ def test_unary_operator(self):
         self.assertEqual(un.domain, a.domain)
 
         # with number
+        absval = pybamm.AbsoluteValue(-10)
+        self.assertEqual(absval.evaluate(), 10)
+
         log = pybamm.log(10)
         self.assertEqual(log.evaluate(), np.log(10))
 
@@ -39,6 +42,18 @@ def test_absolute(self):
         absb = pybamm.AbsoluteValue(b)
         self.assertEqual(absb.evaluate(), 4)
 
+    def test_smooth_absolute_value(self):
+        a = pybamm.StateVector(slice(0, 1))
+        expr = pybamm.smooth_absolute_value(a, 10)
+        self.assertAlmostEqual(expr.evaluate(y=np.array([1]))[0, 0], 1)
+        self.assertEqual(expr.evaluate(y=np.array([0])), 0)
+        self.assertAlmostEqual(expr.evaluate(y=np.array([-1]))[0, 0], 1)
+        self.assertEqual(
+            str(expr),
+            "y[0:1] * (exp(10.0 * y[0:1]) - exp(-10.0 * y[0:1])) "
+            "/ (exp(10.0 * y[0:1]) + exp(-10.0 * y[0:1]))",
+        )
+
     def test_sign(self):
         b = pybamm.Scalar(-4)
         signb = pybamm.sign(b)
@@ -460,7 +475,7 @@ def test_x_average(self):
             pybamm.x_average(symbol_on_edges)
 
         # Particle domains
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         l_n = geo.l_n
         l_p = geo.l_p
 
diff --git a/tests/unit/test_geometry/test_battery_geometry.py b/tests/unit/test_geometry/test_battery_geometry.py
index 668a4b2234..e2b11a064d 100644
--- a/tests/unit/test_geometry/test_battery_geometry.py
+++ b/tests/unit/test_geometry/test_battery_geometry.py
@@ -17,7 +17,7 @@ def test_geometry_keys(self):
 
     def test_geometry(self):
         var = pybamm.standard_spatial_vars
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         for cc_dimension in [0, 1, 2]:
             geometry = pybamm.battery_geometry(current_collector_dimension=cc_dimension)
             self.assertIsInstance(geometry, pybamm.Geometry)
@@ -42,7 +42,7 @@ class TestReadParameters(unittest.TestCase):
     # This is the most complicated geometry and should test the parameters are
     # all returned for the deepest dict
     def test_read_parameters(self):
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         L_n = geo.L_n
         L_s = geo.L_s
         L_p = geo.L_p
diff --git a/tests/unit/test_meshes/test_meshes.py b/tests/unit/test_meshes/test_meshes.py
index f8a3c50acd..ff71555293 100644
--- a/tests/unit/test_meshes/test_meshes.py
+++ b/tests/unit/test_meshes/test_meshes.py
@@ -107,6 +107,32 @@ def test_init_failure(self):
         with self.assertRaisesRegex(KeyError, "Points not given"):
             pybamm.Mesh(geometry, submesh_types, var_pts)
 
+        # Not processing geometry parameters
+        geometry = pybamm.battery_geometry()
+
+        var = pybamm.standard_spatial_vars
+        var_pts = {var.x_n: 10, var.x_s: 10, var.x_p: 12, var.r_n: 5, var.r_p: 6}
+
+        submesh_types = {
+            "negative electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
+            "separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
+            "positive electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
+            "negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
+            "positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
+            "current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
+        }
+
+        with self.assertRaisesRegex(pybamm.DiscretisationError, "Parameter values"):
+            pybamm.Mesh(geometry, submesh_types, var_pts)
+
+        # Geometry has an unrecognized variable type
+        var = pybamm.standard_spatial_vars
+        geometry["negative electrode"] = {
+            var.x_n: {"min": 0, "max": pybamm.Variable("var")}
+        }
+        with self.assertRaisesRegex(NotImplementedError, "for symbol var"):
+            pybamm.Mesh(geometry, submesh_types, var_pts)
+
     def test_mesh_sizes(self):
         param = pybamm.ParameterValues(
             values={
diff --git a/tests/unit/test_meshes/test_one_dimensional_submesh.py b/tests/unit/test_meshes/test_one_dimensional_submesh.py
index 8cb084e786..59d8013419 100644
--- a/tests/unit/test_meshes/test_one_dimensional_submesh.py
+++ b/tests/unit/test_meshes/test_one_dimensional_submesh.py
@@ -277,8 +277,7 @@ class TestSpectralVolume1DSubMesh(unittest.TestCase):
     def test_exceptions(self):
         edges = np.array([0, 0.3, 1])
         submesh_params = {"edges": edges}
-        mesh = pybamm.MeshGenerator(pybamm.SpectralVolume1DSubMesh,
-                                    submesh_params)
+        mesh = pybamm.MeshGenerator(pybamm.SpectralVolume1DSubMesh, submesh_params)
 
         x_n = pybamm.standard_spatial_vars.x_n
 
@@ -306,8 +305,7 @@ def test_mesh_creation_no_parameters(self):
         )
 
         geometry = {
-            "negative particle": {r: {"min": pybamm.Scalar(0),
-                                      "max": pybamm.Scalar(1)}}
+            "negative particle": {r: {"min": pybamm.Scalar(0), "max": pybamm.Scalar(1)}}
         }
 
         edges = np.array([0, 0.3, 1])
@@ -329,16 +327,17 @@ def test_mesh_creation_no_parameters(self):
 
         # check number of edges and nodes
         self.assertEqual(len(mesh["negative particle"].sv_nodes), var_pts[r])
-        self.assertEqual(len(mesh["negative particle"].nodes),
-                         order * var_pts[r])
+        self.assertEqual(len(mesh["negative particle"].nodes), order * var_pts[r])
         self.assertEqual(
             len(mesh["negative particle"].edges),
             len(mesh["negative particle"].nodes) + 1,
         )
 
         # check Chebyshev subdivision locations
-        for (a, b) in zip(mesh["negative particle"].edges.tolist(),
-                          [0, 0.075, 0.225, 0.3, 0.475, 0.825, 1]):
+        for (a, b) in zip(
+            mesh["negative particle"].edges.tolist(),
+            [0, 0.075, 0.225, 0.3, 0.475, 0.825, 1],
+        ):
             self.assertAlmostEqual(a, b)
 
         # test uniform submesh creation
@@ -352,8 +351,10 @@ def test_mesh_creation_no_parameters(self):
 
         # create mesh
         mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
-        for (a, b) in zip(mesh["negative particle"].edges.tolist(),
-                          [0.0, 0.125, 0.375, 0.5, 0.625, 0.875, 1.0]):
+        for (a, b) in zip(
+            mesh["negative particle"].edges.tolist(),
+            [0.0, 0.125, 0.375, 0.5, 0.625, 0.875, 1.0],
+        ):
             self.assertAlmostEqual(a, b)
 
 
diff --git a/tests/unit/test_meshes/test_scikit_fem_submesh.py b/tests/unit/test_meshes/test_scikit_fem_submesh.py
index ade3e4c760..207016bf1c 100644
--- a/tests/unit/test_meshes/test_scikit_fem_submesh.py
+++ b/tests/unit/test_meshes/test_scikit_fem_submesh.py
@@ -77,7 +77,10 @@ def test_init_failure(self):
         var = pybamm.standard_spatial_vars
         var_pts = {var.x_n: 10, var.x_s: 10, var.x_p: 10, var.y: 10, var.z: 10}
         # there are parameters in the variables that need to be processed
-        with self.assertRaises(NotImplementedError):
+        with self.assertRaisesRegex(
+            pybamm.DiscretisationError,
+            "Parameter values have not yet been set for geometry",
+        ):
             pybamm.Mesh(geometry, submesh_types, var_pts)
 
         lims = {var.x_n: {"min": pybamm.Scalar(0), "max": pybamm.Scalar(1)}}
diff --git a/tests/unit/test_models/test_base_model.py b/tests/unit/test_models/test_base_model.py
index de41f240f8..a054067539 100644
--- a/tests/unit/test_models/test_base_model.py
+++ b/tests/unit/test_models/test_base_model.py
@@ -1,8 +1,13 @@
 #
 # Tests for the base model class
 #
+import casadi
 import pybamm
+import numpy as np
 import unittest
+import os
+import subprocess  # nosec
+import platform
 
 
 class TestBaseModel(unittest.TestCase):
@@ -501,6 +506,124 @@ def test_check_well_posedness_output_variables(self):
         model.initial_conditions[d] = 1
         model.check_well_posedness()
 
+    def test_export_casadi(self):
+        model = pybamm.BaseModel()
+        t = pybamm.t
+        a = pybamm.Variable("a")
+        b = pybamm.Variable("b")
+        p = pybamm.InputParameter("p")
+        q = pybamm.InputParameter("q")
+        model.rhs = {a: -a * p}
+        model.algebraic = {b: a - b}
+        model.initial_conditions = {a: q, b: 1}
+        model.variables = {"a+b": a + b - t}
+
+        out = model.export_casadi_objects(["a+b"])
+
+        # Try making a function from the outputs
+        t, x, z, p = out["t"], out["x"], out["z"], out["inputs"]
+        x0, z0 = out["x0"], out["z0"]
+        rhs, alg = out["rhs"], out["algebraic"]
+        var = out["variables"]["a+b"]
+        jac_rhs, jac_alg = out["jac_rhs"], out["jac_algebraic"]
+        x0_fn = casadi.Function("x0", [p], [x0])
+        z0_fn = casadi.Function("x0", [p], [z0])
+        rhs_fn = casadi.Function("rhs", [t, x, z, p], [rhs])
+        alg_fn = casadi.Function("alg", [t, x, z, p], [alg])
+        jac_rhs_fn = casadi.Function("jac_rhs", [t, x, z, p], [jac_rhs])
+        jac_alg_fn = casadi.Function("jac_alg", [t, x, z, p], [jac_alg])
+        var_fn = casadi.Function("var", [t, x, z, p], [var])
+
+        # Test that function values are as expected
+        self.assertEqual(x0_fn([0, 5]), 5)
+        self.assertEqual(z0_fn([0, 0]), 1)
+        self.assertEqual(rhs_fn(0, 3, 2, [7, 2]), -21)
+        self.assertEqual(alg_fn(0, 3, 2, [7, 2]), 1)
+        np.testing.assert_array_equal(np.array(jac_rhs_fn(5, 6, 7, [8, 9])), [[-8, 0]])
+        np.testing.assert_array_equal(np.array(jac_alg_fn(5, 6, 7, [8, 9])), [[1, -1]])
+        self.assertEqual(var_fn(6, 3, 2, [7, 2]), -1)
+
+        # Now change the order of input parameters
+        out = model.export_casadi_objects(["a+b"], input_parameter_order=["q", "p"])
+
+        # Try making a function from the outputs
+        t, x, z, p = out["t"], out["x"], out["z"], out["inputs"]
+        x0, z0 = out["x0"], out["z0"]
+        rhs, alg = out["rhs"], out["algebraic"]
+        var = out["variables"]["a+b"]
+        jac_rhs, jac_alg = out["jac_rhs"], out["jac_algebraic"]
+        x0_fn = casadi.Function("x0", [p], [x0])
+        z0_fn = casadi.Function("x0", [p], [z0])
+        rhs_fn = casadi.Function("rhs", [t, x, z, p], [rhs])
+        alg_fn = casadi.Function("alg", [t, x, z, p], [alg])
+        jac_rhs_fn = casadi.Function("jac_rhs", [t, x, z, p], [jac_rhs])
+        jac_alg_fn = casadi.Function("jac_alg", [t, x, z, p], [jac_alg])
+        var_fn = casadi.Function("var", [t, x, z, p], [var])
+
+        # Test that function values are as expected
+        self.assertEqual(x0_fn([5, 0]), 5)
+        self.assertEqual(z0_fn([0, 0]), 1)
+        self.assertEqual(rhs_fn(0, 3, 2, [2, 7]), -21)
+        self.assertEqual(alg_fn(0, 3, 2, [2, 7]), 1)
+        np.testing.assert_array_equal(np.array(jac_rhs_fn(5, 6, 7, [9, 8])), [[-8, 0]])
+        np.testing.assert_array_equal(np.array(jac_alg_fn(5, 6, 7, [9, 8])), [[1, -1]])
+        self.assertEqual(var_fn(6, 3, 2, [2, 7]), -1)
+
+        # Test model with external variable runs
+        model_options = {"thermal": "lumped", "external submodels": ["thermal"]}
+        model = pybamm.lithium_ion.SPMe(model_options)
+        sim = pybamm.Simulation(model)
+        sim.build()
+        variable_names = ["Volume-averaged cell temperature"]
+        out = sim.built_model.export_casadi_objects(variable_names)
+
+        # Test fails if not discretised
+        with self.assertRaisesRegex(
+            pybamm.DiscretisationError, "Cannot automatically discretise model"
+        ):
+            model.export_casadi_objects(["Electrolyte concentration"])
+
+    @unittest.skipIf(platform.system() == "Windows", "Skipped for Windows")
+    def test_generate_casadi(self):
+        model = pybamm.BaseModel()
+        t = pybamm.t
+        a = pybamm.Variable("a")
+        b = pybamm.Variable("b")
+        p = pybamm.InputParameter("p")
+        q = pybamm.InputParameter("q")
+        model.rhs = {a: -a * p}
+        model.algebraic = {b: a - b}
+        model.initial_conditions = {a: q, b: 1}
+        model.variables = {"a+b": a + b - t}
+
+        # Generate C code
+        model.generate("test.c", ["a+b"])
+
+        # Compile
+        subprocess.run(["gcc", "-fPIC", "-shared", "-o", "test.so", "test.c"])  # nosec
+
+        # Read the generated functions
+        x0_fn = casadi.external("x0", "./test.so")
+        z0_fn = casadi.external("z0", "./test.so")
+        rhs_fn = casadi.external("rhs_", "./test.so")
+        alg_fn = casadi.external("alg_", "./test.so")
+        jac_rhs_fn = casadi.external("jac_rhs", "./test.so")
+        jac_alg_fn = casadi.external("jac_alg", "./test.so")
+        var_fn = casadi.external("variables", "./test.so")
+
+        # Test that function values are as expected
+        self.assertEqual(x0_fn([0, 5]), 5)
+        self.assertEqual(z0_fn([0, 0]), 1)
+        self.assertEqual(rhs_fn(0, 3, 2, [7, 2]), -21)
+        self.assertEqual(alg_fn(0, 3, 2, [7, 2]), 1)
+        np.testing.assert_array_equal(np.array(jac_rhs_fn(5, 6, 7, [8, 9])), [[-8, 0]])
+        np.testing.assert_array_equal(np.array(jac_alg_fn(5, 6, 7, [8, 9])), [[1, -1]])
+        self.assertEqual(var_fn(6, 3, 2, [7, 2]), -1)
+
+        # Remove generated files.
+        os.remove("test.c")
+        os.remove("test.so")
+
 
 class TestStandardBatteryBaseModel(unittest.TestCase):
     def test_default_solver(self):
@@ -536,7 +659,6 @@ def test_default_parameters(self):
         )
 
         # change path and try again
-        import os
 
         cwd = os.getcwd()
         os.chdir("..")
diff --git a/tests/unit/test_models/test_full_battery_models/test_base_battery_model.py b/tests/unit/test_models/test_full_battery_models/test_base_battery_model.py
index b50bd1534f..48ad9ef44d 100644
--- a/tests/unit/test_models/test_full_battery_models/test_base_battery_model.py
+++ b/tests/unit/test_models/test_full_battery_models/test_base_battery_model.py
@@ -149,6 +149,10 @@ def test_options(self):
             pybamm.BaseBatteryModel({"particle shape": "bad particle shape"})
         with self.assertRaisesRegex(pybamm.OptionError, "operating mode"):
             pybamm.BaseBatteryModel({"operating mode": "bad operating mode"})
+        with self.assertRaisesRegex(pybamm.OptionError, "electrolyte conductivity"):
+            pybamm.BaseBatteryModel(
+                {"electrolyte conductivity": "bad electrolyte conductivity"}
+            )
 
         # SEI options
         with self.assertRaisesRegex(pybamm.OptionError, "sei"):
@@ -162,6 +166,9 @@ def test_options(self):
         self.assertEqual(model.options["sei film resistance"], None)
         model = pybamm.BaseBatteryModel({"sei": "constant"})
         self.assertEqual(model.options["sei film resistance"], "distributed")
+        # crack model
+        with self.assertRaisesRegex(pybamm.OptionError, "particle cracking"):
+            pybamm.BaseBatteryModel({"particle cracking": "bad particle cracking"})
 
     def test_build_twice(self):
         model = pybamm.lithium_ion.SPM()  # need to pick a model to set vars and build
diff --git a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
index 7088c3f0e9..de1776b229 100644
--- a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
+++ b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_dfn.py
@@ -118,6 +118,11 @@ def test_surface_form_algebraic(self):
         model = pybamm.lithium_ion.DFN(options)
         model.check_well_posedness()
 
+    def test_electrolyte_options(self):
+        options = {"electrolyte conductivity": "integrated"}
+        with self.assertRaisesRegex(pybamm.OptionError, "electrolyte conductivity"):
+            pybamm.lithium_ion.DFN(options)
+
 
 class TestDFNWithSEI(unittest.TestCase):
     def test_well_posed_constant(self):
@@ -156,6 +161,33 @@ def test_well_posed_ec_reaction_limited(self):
         model.check_well_posedness()
 
 
+class TestDFNWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.DFN(options)
+        model.check_well_posedness()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.DFN(options)
+        model.check_well_posedness()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.DFN(options)
+        model.check_well_posedness()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.DFN(options)
+        model.check_well_posedness()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.DFN(options)
+        model.check_well_posedness()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spm.py b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
index 460d711825..84606408d3 100644
--- a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
+++ b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spm.py
@@ -119,6 +119,11 @@ def test_surface_form_algebraic(self):
         model = pybamm.lithium_ion.SPM(options)
         model.check_well_posedness()
 
+    def test_electrolyte_options(self):
+        options = {"electrolyte conductivity": "full"}
+        with self.assertRaisesRegex(pybamm.OptionError, "electrolyte conductivity"):
+            pybamm.lithium_ion.SPM(options)
+
     def test_new_model(self):
         model = pybamm.lithium_ion.SPM({"thermal": "x-full"})
         new_model = model.new_copy()
@@ -188,6 +193,33 @@ def test_well_posed_ec_reaction_limited(self):
         model.check_well_posedness()
 
 
+class TestSPMWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.SPM(options)
+        model.check_well_posedness()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.SPM(options)
+        model.check_well_posedness()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.SPM(options)
+        model.check_well_posedness()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.SPM(options)
+        model.check_well_posedness()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.SPM(options)
+        model.check_well_posedness()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spme.py b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
index 41579dad6b..bf16934b4c 100644
--- a/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
+++ b/tests/unit/test_models/test_full_battery_models/test_lithium_ion/test_spme.py
@@ -110,14 +110,24 @@ def test_particle_shape_user(self):
 
     def test_surface_form_differential(self):
         options = {"surface form": "differential"}
-        model = pybamm.lithium_ion.SPMe(options)
-        model.check_well_posedness()
+        with self.assertRaises(NotImplementedError):
+            pybamm.lithium_ion.SPMe(options)
 
     def test_surface_form_algebraic(self):
         options = {"surface form": "algebraic"}
+        with self.assertRaises(NotImplementedError):
+            pybamm.lithium_ion.SPMe(options)
+
+    def test_integrated_conductivity(self):
+        options = {"electrolyte conductivity": "integrated"}
         model = pybamm.lithium_ion.SPMe(options)
         model.check_well_posedness()
 
+    def test_electrolyte_options(self):
+        options = {"electrolyte conductivity": "full"}
+        with self.assertRaisesRegex(pybamm.OptionError, "electrolyte conductivity"):
+            pybamm.lithium_ion.SPMe(options)
+
 
 class TestSPMeWithSEI(unittest.TestCase):
     def test_well_posed_reaction_limited(self):
@@ -146,6 +156,33 @@ def test_well_posed_ec_reaction_limited(self):
         model.check_well_posedness()
 
 
+class TestSPMeWithCrack(unittest.TestCase):
+    def test_well_posed_none_crack(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": None}
+        model = pybamm.lithium_ion.SPMe(options)
+        model.check_well_posedness()
+
+    def test_well_posed_no_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "no cracking"}
+        model = pybamm.lithium_ion.SPMe(options)
+        model.check_well_posedness()
+
+    def test_well_posed_anode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "anode"}
+        model = pybamm.lithium_ion.SPMe(options)
+        model.check_well_posedness()
+
+    def test_well_posed_cathode_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "cathode"}
+        model = pybamm.lithium_ion.SPMe(options)
+        model.check_well_posedness()
+
+    def test_well_posed_both_cracking(self):
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.SPMe(options)
+        model.check_well_posedness()
+
+
 if __name__ == "__main__":
     print("Add -v for more debug output")
     import sys
diff --git a/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_full_conductivity.py b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_full_conductivity.py
index 575898299d..5675654696 100644
--- a/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_full_conductivity.py
+++ b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_full_conductivity.py
@@ -11,7 +11,7 @@ class TestFull(unittest.TestCase):
     def test_public_functions(self):
         param = pybamm.LithiumIonParameters()
         a = pybamm.Scalar(0)
-        surf = "surface area per unit volume distribution in x"
+        surf = "electrode surface area per unit volume"
         variables = {
             "Electrolyte tortuosity": a,
             "Electrolyte concentration": pybamm.FullBroadcast(
diff --git a/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_integrated.py b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_integrated.py
new file mode 100644
index 0000000000..84554d68eb
--- /dev/null
+++ b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_integrated.py
@@ -0,0 +1,42 @@
+#
+# Test integrated Stefan Maxwell electrolyte conductivity submodel
+#
+
+import pybamm
+import tests
+import unittest
+
+
+class TestFull(unittest.TestCase):
+    def test_public_functions(self):
+        param = pybamm.LithiumIonParameters()
+        a = pybamm.PrimaryBroadcast(0, "current collector")
+        c_e_n = pybamm.standard_variables.c_e_n
+        c_e_s = pybamm.standard_variables.c_e_s
+        c_e_p = pybamm.standard_variables.c_e_p
+        variables = {
+            "X-averaged electrolyte concentration": a,
+            "Leading-order current collector current density": a,
+            "Negative electrolyte concentration": c_e_n,
+            "Separator electrolyte concentration": c_e_s,
+            "Positive electrolyte concentration": c_e_p,
+            "X-averaged negative electrode surface potential difference": a,
+            "X-averaged negative electrode potential": a,
+            "Negative electrolyte tortuosity": a,
+            "Separator tortuosity": a,
+            "Positive electrolyte tortuosity": a,
+            "X-averaged cell temperature": a,
+        }
+        submodel = pybamm.electrolyte_conductivity.Integrated(param)
+        std_tests = tests.StandardSubModelTests(submodel, variables)
+        std_tests.test_all()
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_surface_form/test_full_surface_form_conductivity.py b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_surface_form/test_full_surface_form_conductivity.py
index 327f8e85b0..3dbe5e2bcf 100644
--- a/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_surface_form/test_full_surface_form_conductivity.py
+++ b/tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_surface_form/test_full_surface_form_conductivity.py
@@ -25,7 +25,7 @@ def test_public_functions(self):
             "Negative electrode porosity": a_n,
             "Negative electrolyte tortuosity": a_n,
             "Negative electrode tortuosity": a_n,
-            "Negative surface area per unit volume distribution in x": a_n,
+            "Negative electrode surface area per unit volume": a_n,
             "Negative electrolyte concentration": a_n,
             "Sum of negative electrode interfacial current densities": a_n,
             "Electrolyte potential": pybamm.Concatenation(a_n, a_s, a_p),
@@ -55,7 +55,7 @@ def test_public_functions(self):
             "Positive electrode porosity": a_p,
             "Positive electrolyte tortuosity": a_p,
             "Positive electrode tortuosity": a_p,
-            "Positive surface area per unit volume distribution in x": a_p,
+            "Positive electrode surface area per unit volume": a_p,
             "Positive electrolyte concentration": a_p,
             "Sum of positive electrode interfacial current densities": a_p,
             "Positive electrode temperature": a_p,
diff --git a/tests/unit/test_models/test_submodels/test_mechanical/__init__.py b/tests/unit/test_models/test_submodels/test_mechanical/__init__.py
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/unit/test_models/test_submodels/test_mechanical/test_base_cracking.py b/tests/unit/test_models/test_submodels/test_mechanical/test_base_cracking.py
new file mode 100644
index 0000000000..3aaceff1b8
--- /dev/null
+++ b/tests/unit/test_models/test_submodels/test_mechanical/test_base_cracking.py
@@ -0,0 +1,30 @@
+#
+# Test base cracking submodel
+#
+
+import pybamm
+import tests
+import unittest
+
+
+class TestBaseCracking(unittest.TestCase):
+    def test_public_functions(self):
+        variables = {
+            "Negative particle crack length": pybamm.Scalar(0),
+            "Negative particle concentration": pybamm.Scalar(0),
+            "Positive particle crack length": pybamm.Scalar(0),
+            "Positive particle concentration": pybamm.Scalar(0),
+        }
+        submodel = pybamm.particle_cracking.BaseCracking(None, "Negative")
+        std_tests = tests.StandardSubModelTests(submodel, variables)
+        std_tests.test_all()
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_models/test_submodels/test_mechanical/test_crack_propagation.py b/tests/unit/test_models/test_submodels/test_mechanical/test_crack_propagation.py
new file mode 100644
index 0000000000..cd838cd9c1
--- /dev/null
+++ b/tests/unit/test_models/test_submodels/test_mechanical/test_crack_propagation.py
@@ -0,0 +1,52 @@
+#
+# Test base particle submodel
+#
+
+import pybamm
+import tests
+import unittest
+
+
+class TestCrackPropagation(unittest.TestCase):
+    def test_public_functions(self):
+        a_n = pybamm.FullBroadcast(
+            pybamm.Scalar(0), ["negative electrode"], "current collector"
+        )
+        a_p = pybamm.FullBroadcast(
+            pybamm.Scalar(0), ["positive electrode"], "current collector"
+        )
+        a = pybamm.Scalar(0)
+        variables = {
+            "Negative particle crack length": a_n,
+            "Negative particle surface concentration": a_n,
+            "R-averaged negative particle concentration": a_n,
+            "Average negative particle concentration": a,
+            "X-averaged cell temperature": a,
+            "Negative electrode temperature": a_n,
+            "Positive particle crack length": a_p,
+            "Positive particle surface concentration": a_p,
+            "R-averaged positive particle concentration": a_p,
+            "Average positive particle concentration": a,
+            "Positive electrode temperature": a_p,
+        }
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        param = pybamm.LithiumIonParameters(options)
+        submodel = pybamm.particle_cracking.CrackPropagation(param, "Negative")
+        std_tests = tests.StandardSubModelTests(submodel, variables)
+        std_tests.test_all()
+        submodel = pybamm.particle_cracking.CrackPropagation(param, "Positive")
+        std_tests = tests.StandardSubModelTests(submodel, variables)
+        std_tests.test_all()
+        submodel = pybamm.particle_cracking.NoCracking(param, "Positive")
+        std_tests = tests.StandardSubModelTests(submodel, variables)
+        std_tests.test_all()
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_models/test_submodels/test_thermal/coupled_variables.py b/tests/unit/test_models/test_submodels/test_thermal/coupled_variables.py
index 9fde9fd885..7fdc1fa565 100644
--- a/tests/unit/test_models/test_submodels/test_thermal/coupled_variables.py
+++ b/tests/unit/test_models/test_submodels/test_thermal/coupled_variables.py
@@ -10,6 +10,8 @@
 b = pybamm.PrimaryBroadcast(pybamm.Scalar(1), "current collector")
 
 coupled_variables = {
+    "Negative electrode surface area per unit volume": a_n,
+    "Positive electrode surface area per unit volume": a_p,
     "Negative electrode interfacial current density": a_n,
     "Positive electrode interfacial current density": a_p,
     "Negative electrode reaction overpotential": a_n,
diff --git a/tests/unit/test_parameters/data/process_symbol_test_function.py b/tests/unit/test_parameters/data/process_symbol_test_function.py
index 5ed5288a7a..29bc56662f 100644
--- a/tests/unit/test_parameters/data/process_symbol_test_function.py
+++ b/tests/unit/test_parameters/data/process_symbol_test_function.py
@@ -7,5 +7,5 @@ def process_symbol_test_function(var):
     var: numeric
         Some variable
 
-   """
+    """
     return 123 * var
diff --git a/tests/unit/test_parameters/test_current_functions.py b/tests/unit/test_parameters/test_current_functions.py
index b640842d69..2222d3d3b8 100644
--- a/tests/unit/test_parameters/test_current_functions.py
+++ b/tests/unit/test_parameters/test_current_functions.py
@@ -10,7 +10,7 @@
 class TestCurrentFunctions(unittest.TestCase):
     def test_constant_current(self):
         # test simplify
-        param = pybamm.ElectricalParameters()
+        param = pybamm.electrical_parameters
         current = param.current_with_time
         parameter_values = pybamm.ParameterValues(
             {
@@ -24,7 +24,7 @@ def test_constant_current(self):
 
     def test_get_current_data(self):
         # test process parameters
-        param = pybamm.ElectricalParameters()
+        param = pybamm.electrical_parameters
         dimensional_current = param.dimensional_current_with_time
         parameter_values = pybamm.ParameterValues(
             {
@@ -47,7 +47,7 @@ def my_fun(t, A, omega):
             return A * pybamm.sin(2 * np.pi * omega * t)
 
         # choose amplitude and frequency
-        param = pybamm.ElectricalParameters()
+        param = pybamm.electrical_parameters
         A = param.I_typ
         omega = pybamm.Parameter("omega")
 
diff --git a/tests/unit/test_parameters/test_electrical_parameters.py b/tests/unit/test_parameters/test_electrical_parameters.py
index 0a51f7bb9e..dd513d1d42 100644
--- a/tests/unit/test_parameters/test_electrical_parameters.py
+++ b/tests/unit/test_parameters/test_electrical_parameters.py
@@ -9,7 +9,7 @@
 class TestElectricalParameters(unittest.TestCase):
     def test_current_functions(self):
         # create current functions
-        param = pybamm.ElectricalParameters()
+        param = pybamm.electrical_parameters
         dimensional_current = param.dimensional_current_with_time
         dimensional_current_density = param.dimensional_current_density_with_time
         dimensionless_current = param.current_with_time
diff --git a/tests/unit/test_parameters/test_geometric_parameters.py b/tests/unit/test_parameters/test_geometric_parameters.py
index 63df878fac..69c769830c 100644
--- a/tests/unit/test_parameters/test_geometric_parameters.py
+++ b/tests/unit/test_parameters/test_geometric_parameters.py
@@ -8,7 +8,7 @@
 
 class TestGeometricParameters(unittest.TestCase):
     def test_macroscale_parameters(self):
-        geo = pybamm.GeometricParameters()
+        geo = pybamm.geometric_parameters
         L_n = geo.L_n
         L_s = geo.L_s
         L_p = geo.L_p
diff --git a/tests/unit/test_parameters/test_lead_acid_parameters.py b/tests/unit/test_parameters/test_lead_acid_parameters.py
index 787e304f81..2e7be47a38 100644
--- a/tests/unit/test_parameters/test_lead_acid_parameters.py
+++ b/tests/unit/test_parameters/test_lead_acid_parameters.py
@@ -103,8 +103,8 @@ def test_functions_lead_acid(self):
         parameters = {
             "D_e_1": param.D_e(pybamm.Scalar(1), pybamm.Scalar(0)),
             "kappa_e_0": param.kappa_e(pybamm.Scalar(0), pybamm.Scalar(0)),
-            "chi_1": param.chi(pybamm.Scalar(1)),
-            "chi_0.5": param.chi(pybamm.Scalar(0.5)),
+            "chi_1": param.chi(pybamm.Scalar(1), pybamm.Scalar(0)),
+            "chi_0.5": param.chi(pybamm.Scalar(0.5), pybamm.Scalar(0)),
             "U_n_1": param.U_n(pybamm.Scalar(1), pybamm.Scalar(0)),
             "U_n_0.5": param.U_n(pybamm.Scalar(0.5), pybamm.Scalar(0)),
             "U_p_1": param.U_p(pybamm.Scalar(1), pybamm.Scalar(0)),
diff --git a/tests/unit/test_parameters/test_lithium_ion_parameters.py b/tests/unit/test_parameters/test_lithium_ion_parameters.py
index 8d48a84b10..9288d9bfef 100644
--- a/tests/unit/test_parameters/test_lithium_ion_parameters.py
+++ b/tests/unit/test_parameters/test_lithium_ion_parameters.py
@@ -11,6 +11,8 @@ class TestDimensionlessParameterValues(unittest.TestCase):
     def test_options(self):
         with self.assertRaisesRegex(pybamm.OptionError, "particle shape"):
             pybamm.LithiumIonParameters({"particle shape": "bad shape"})
+        with self.assertRaisesRegex(pybamm.OptionError, "particle cracking"):
+            pybamm.LithiumIonParameters({"particle cracking": "bad crack"})
 
     def test_lithium_ion(self):
         """This test checks that all the dimensionless parameters are being calculated
@@ -23,26 +25,33 @@ def test_lithium_ion(self):
         c_rate = param.i_typ / 24  # roughly for the numbers I used before
 
         "particle geometry"
+        # Note: in general these can be functions, but are constant for this
+        # set, so we just arbitrarily evaluate at 0
+
         # a_n dimensional
         np.testing.assert_almost_equal(
-            values.evaluate(param.a_n_dim), 0.18 * 10 ** (6), 2
+            values.evaluate(param.a_n_dimensional(0)), 0.18 * 10 ** (6), 2
         )
         # R_n dimensional
-        np.testing.assert_almost_equal(values.evaluate(param.R_n), 1 * 10 ** (-5), 2)
+        np.testing.assert_almost_equal(
+            values.evaluate(param.R_n_dimensional(0)), 1 * 10 ** (-5), 2
+        )
 
-        # a_n
-        np.testing.assert_almost_equal(values.evaluate(param.a_n), 1.8, 2)
+        # a_R_n = a_n_typ * R_n_typ
+        np.testing.assert_almost_equal(values.evaluate(param.a_R_n), 1.8, 2)
 
         # a_p dimensional
         np.testing.assert_almost_equal(
-            values.evaluate(param.a_p_dim), 0.15 * 10 ** (6), 2
+            values.evaluate(param.a_p_dimensional(0)), 0.15 * 10 ** (6), 2
         )
 
         # R_p dimensional
-        np.testing.assert_almost_equal(values.evaluate(param.R_n), 1 * 10 ** (-5), 2)
+        np.testing.assert_almost_equal(
+            values.evaluate(param.R_n_dimensional(0)), 1 * 10 ** (-5), 2
+        )
 
-        # a_p
-        np.testing.assert_almost_equal(values.evaluate(param.a_p), 1.5, 2)
+        # a_p = a_p_typ * R_p_typ
+        np.testing.assert_almost_equal(values.evaluate(param.a_R_p), 1.5, 2)
 
         # j0_m
         np.testing.assert_almost_equal(
@@ -194,7 +203,7 @@ def test_thermal_parameters(self):
         #     values.evaluate(param.tau_th_yz), 1.4762 * 10 ** (3), 2
         # )
 
-        # thermal = pybamm.ThermalParameters()
+        # thermal = pybamm.thermal_parameters
         # np.testing.assert_almost_equal(
         # values.evaluate(thermal.rho_eff_dim), 1.8116 * 10 ** (6), 2
         # )
diff --git a/tests/unit/test_parameters/test_parameter_sets/test_LCO_Ai2020.py b/tests/unit/test_parameters/test_parameter_sets/test_LCO_Ai2020.py
new file mode 100644
index 0000000000..81dfccab3c
--- /dev/null
+++ b/tests/unit/test_parameters/test_parameter_sets/test_LCO_Ai2020.py
@@ -0,0 +1,57 @@
+#
+# Tests for Ai (2020) Enertech parameter set loads
+#
+import pybamm
+import unittest
+
+
+class TestAi2020(unittest.TestCase):
+    def test_load_params(self):
+        anode = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/anodes/graphite_Ai2020/parameters.csv"
+            )
+        )
+        self.assertEqual(anode["Negative electrode porosity"], "0.33")
+
+        cathode = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/cathodes/lico2_Ai2020/parameters.csv"
+            )
+        )
+        self.assertEqual(cathode["Positive electrode porosity"], "0.32")
+
+        electrolyte = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/electrolytes/lipf6_Enertech_Ai2020/"
+                + "parameters.csv"
+            )
+        )
+        self.assertEqual(electrolyte["Cation transference number"], "0.38")
+
+        cell = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/cells/Enertech_Ai2020/parameters.csv"
+            )
+        )
+        self.assertAlmostEqual(cell["Negative current collector thickness [m]"], 10e-6)
+
+    def test_standard_lithium_parameters(self):
+
+        chemistry = pybamm.parameter_sets.Ai2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        options = {"particle": "Fickian diffusion", "particle cracking": "both"}
+        model = pybamm.lithium_ion.DFN(options)
+        sim = pybamm.Simulation(model, parameter_values=parameter_values)
+        sim.set_parameters()
+        sim.build()
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_parameters/test_parameter_sets/test_LFP_Prada2013.py b/tests/unit/test_parameters/test_parameter_sets/test_LFP_Prada2013.py
new file mode 100644
index 0000000000..e8af896605
--- /dev/null
+++ b/tests/unit/test_parameters/test_parameter_sets/test_LFP_Prada2013.py
@@ -0,0 +1,42 @@
+#
+# Tests for LFP Prada 2013 parameter set
+#
+import pybamm
+import unittest
+
+
+class TestLFPPrada2013(unittest.TestCase):
+    def test_load_params(self):
+        cathode = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/cathodes/LFP_Prada2013/parameters.csv"
+            )
+        )
+        self.assertEqual(cathode["Positive electrode porosity"], "0.12728395")
+
+        cell = pybamm.ParameterValues({}).read_parameters_csv(
+            pybamm.get_parameters_filepath(
+                "input/parameters/lithium-ion/cells/A123_Lain2019/parameters.csv"
+            )
+        )
+        self.assertAlmostEqual(cell["Negative current collector thickness [m]"], 1e-5)
+
+    def test_standard_lithium_parameters(self):
+
+        chemistry = pybamm.parameter_sets.Prada2013
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+
+        model = pybamm.lithium_ion.DFN()
+        sim = pybamm.Simulation(model, parameter_values=parameter_values)
+        sim.set_parameters()
+        sim.build()
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_parameters/test_parameter_sets/test_Landesfeind2019.py b/tests/unit/test_parameters/test_parameter_sets/test_Landesfeind2019.py
index f469793a21..f2e008e189 100644
--- a/tests/unit/test_parameters/test_parameter_sets/test_Landesfeind2019.py
+++ b/tests/unit/test_parameters/test_parameter_sets/test_Landesfeind2019.py
@@ -68,14 +68,14 @@ def test_load_params(self):
 
             for i, _ in enumerate(T):
                 self.assertAlmostEqual(
-                    sigma_e(c[i], T[i]).value, data_sigma_e[solvent][i], places=5,
+                    sigma_e(c[i], T[i]).value, data_sigma_e[solvent][i], places=5
                 )
                 self.assertAlmostEqual(
-                    D_e(c[i], T[i]).value, data_D_e[solvent][i], places=5,
+                    D_e(c[i], T[i]).value, data_D_e[solvent][i], places=5
                 )
                 self.assertAlmostEqual(TDF(c[i], T[i]), data_TDF[solvent][i], places=5)
                 self.assertAlmostEqual(
-                    tplus(c[i], T[i]), data_tplus[solvent][i], places=5,
+                    tplus(c[i], T[i]), data_tplus[solvent][i], places=5
                 )
 
     def test_standard_lithium_parameters(self):
diff --git a/tests/unit/test_parameters/test_parameter_values.py b/tests/unit/test_parameters/test_parameter_values.py
index ce107d0b6f..f00006473b 100644
--- a/tests/unit/test_parameters/test_parameter_values.py
+++ b/tests/unit/test_parameters/test_parameter_values.py
@@ -103,6 +103,12 @@ def test_check_parameter_values(self):
             pybamm.ParameterValues({"Negative surface area density": 1})
         with self.assertRaisesRegex(ValueError, "reaction rate"):
             pybamm.ParameterValues({"Negative reaction rate": 1})
+        with self.assertRaisesRegex(ValueError, "particle distribution"):
+            pybamm.ParameterValues({"Negative particle distribution in x": 1})
+        with self.assertRaisesRegex(ValueError, "surface area per unit volume"):
+            pybamm.ParameterValues(
+                {"Negative electrode surface area per unit volume distribution in x": 1}
+            )
 
     def test_process_symbol(self):
         parameter_values = pybamm.ParameterValues({"a": 1, "b": 2, "c": 3})
diff --git a/tests/unit/test_parameters/test_parameters_cli.py b/tests/unit/test_parameters/test_parameters_cli.py
index 4b84eae329..7c8402c178 100644
--- a/tests/unit/test_parameters/test_parameters_cli.py
+++ b/tests/unit/test_parameters/test_parameters_cli.py
@@ -12,7 +12,7 @@
 import platform
 
 
-@unittest.skipUnless(platform.system() != "Windows", "Skipped for Windows")
+@unittest.skipIf(platform.system() == "Windows", "Skipped for Windows")
 class TestParametersCLI(unittest.TestCase):
     def test_add_rm_param(self):
         # Read a parameter file thta is shipped with PyBaMM
@@ -82,11 +82,7 @@ def test_edit_param(self):
         sandbox_dir = tempfile.TemporaryDirectory()
 
         # Copy temporary dir in package to current working directory
-        cmd = [
-            "pybamm_edit_parameter",
-            "-f",
-            chemistry,
-        ]
+        cmd = ["pybamm_edit_parameter", "-f", chemistry]
         subprocess.run(cmd, cwd=sandbox_dir.name)
 
         # Read and compare copied parameters.csv file
diff --git a/tests/unit/test_quick_plot.py b/tests/unit/test_quick_plot.py
index 6308864f9f..ca821b5c04 100644
--- a/tests/unit/test_quick_plot.py
+++ b/tests/unit/test_quick_plot.py
@@ -452,6 +452,39 @@ def test_failure(self):
         with self.assertRaisesRegex(TypeError, "solutions must be"):
             pybamm.QuickPlot(1)
 
+    def test_model_with_inputs(self):
+        chemistry = pybamm.parameter_sets.Chen2020
+        parameter_values = pybamm.ParameterValues(chemistry=chemistry)
+        model = pybamm.lithium_ion.SPMe()
+        parameter_values.update({"Electrode height [m]": "[input]"})
+        solver = pybamm.CasadiSolver(mode="safe")
+        sim1 = pybamm.Simulation(
+            model, parameter_values=parameter_values, solver=solver
+        )
+        inputs1 = {"Electrode height [m]": 1.00}
+        sol1 = sim1.solve(t_eval=np.linspace(0, 1000, 101), inputs=inputs1)
+        sim2 = pybamm.Simulation(
+            model, parameter_values=parameter_values, solver=solver
+        )
+        inputs2 = {"Electrode height [m]": 2.00}
+        sol2 = sim2.solve(t_eval=np.linspace(0, 1000, 101), inputs=inputs2)
+        output_variables = [
+            "Terminal voltage [V]",
+            "Current [A]",
+            "Negative electrode potential [V]",
+            "Positive electrode potential [V]",
+            "Electrolyte potential [V]",
+            "Electrolyte concentration",
+            "Negative particle surface concentration",
+            "Positive particle surface concentration",
+        ]
+        quick_plot = pybamm.QuickPlot(
+            solutions=[sol1, sol2], output_variables=output_variables
+        )
+        quick_plot.dynamic_plot(testing=True)
+        quick_plot.slider_update(1)
+        pybamm.close_plots()
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")
diff --git a/tests/unit/test_settings.py b/tests/unit/test_settings.py
new file mode 100644
index 0000000000..28ca922fcf
--- /dev/null
+++ b/tests/unit/test_settings.py
@@ -0,0 +1,40 @@
+#
+# Tests the settings class.
+#
+import pybamm
+import unittest
+
+
+class TestSettings(unittest.TestCase):
+    def test_smoothing_parameters(self):
+        self.assertEqual(pybamm.settings.min_smoothing, "exact")
+        self.assertEqual(pybamm.settings.max_smoothing, "exact")
+        self.assertEqual(pybamm.settings.heaviside_smoothing, "exact")
+        self.assertEqual(pybamm.settings.abs_smoothing, "exact")
+
+        pybamm.settings.set_smoothing_parameters(10)
+        self.assertEqual(pybamm.settings.min_smoothing, 10)
+        self.assertEqual(pybamm.settings.max_smoothing, 10)
+        self.assertEqual(pybamm.settings.heaviside_smoothing, 10)
+        self.assertEqual(pybamm.settings.abs_smoothing, 10)
+        pybamm.settings.set_smoothing_parameters("exact")
+
+        # Test errors
+        with self.assertRaisesRegex(ValueError, "strictly positive"):
+            pybamm.settings.min_smoothing = -10
+        with self.assertRaisesRegex(ValueError, "strictly positive"):
+            pybamm.settings.max_smoothing = -10
+        with self.assertRaisesRegex(ValueError, "strictly positive"):
+            pybamm.settings.heaviside_smoothing = -10
+        with self.assertRaisesRegex(ValueError, "strictly positive"):
+            pybamm.settings.abs_smoothing = -10
+
+
+if __name__ == "__main__":
+    print("Add -v for more debug output")
+    import sys
+
+    if "-v" in sys.argv:
+        debug = True
+    pybamm.settings.debug_mode = True
+    unittest.main()
diff --git a/tests/unit/test_simulation.py b/tests/unit/test_simulation.py
index b3fc6d2954..f7bf53d7a0 100644
--- a/tests/unit/test_simulation.py
+++ b/tests/unit/test_simulation.py
@@ -387,6 +387,18 @@ def test_t_eval(self):
         sim.solve(t_eval=[0, 10])
         np.testing.assert_array_almost_equal(sim.t_eval, np.linspace(0, 10, 100))
 
+    def test_battery_model_with_input_height(self):
+        # load model
+        model = pybamm.lithium_ion.SPM()
+        # load parameter values and process model and geometry
+        param = model.default_parameter_values
+        param.update({"Electrode height [m]": "[input]"})
+        # solve model for 1 minute
+        t_eval = np.linspace(0, 60, 11)
+        inputs = {"Electrode height [m]": 0.2}
+        sim = pybamm.Simulation(model=model, parameter_values=param)
+        sim.solve(t_eval=t_eval, inputs=inputs)
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")
diff --git a/tests/unit/test_solvers/test_base_solver.py b/tests/unit/test_solvers/test_base_solver.py
index 9d60ebd16f..3703bdefad 100644
--- a/tests/unit/test_solvers/test_base_solver.py
+++ b/tests/unit/test_solvers/test_base_solver.py
@@ -276,9 +276,11 @@ def test_timescale_input_fail(self):
         model.initial_conditions = {v: 1}
         a = pybamm.InputParameter("a")
         model.timescale = a
-        solver = pybamm.BaseSolver()
+        solver = pybamm.CasadiSolver()
+        solver.set_up(model, inputs={"a": 10})
+        sol = solver.step(old_solution=None, model=model, dt=1.0, inputs={"a": 10})
         with self.assertRaisesRegex(pybamm.SolverError, "The model timescale"):
-            solver.set_up(model, inputs={"a": 10})
+            sol = solver.step(old_solution=sol, model=model, dt=1.0, inputs={"a": 20})
 
 
 if __name__ == "__main__":
diff --git a/tests/unit/test_solvers/test_casadi_algebraic_solver.py b/tests/unit/test_solvers/test_casadi_algebraic_solver.py
index 1d8422318f..862ea298ca 100644
--- a/tests/unit/test_solvers/test_casadi_algebraic_solver.py
+++ b/tests/unit/test_solvers/test_casadi_algebraic_solver.py
@@ -105,6 +105,26 @@ def test_model_solver_with_time(self):
             sol[1, :],
         )
 
+    def test_model_solver_with_time_not_changing(self):
+        # Create model
+        model = pybamm.BaseModel()
+        var1 = pybamm.Variable("var1")
+        var2 = pybamm.Variable("var2")
+        model.algebraic = {var1: var1 - 3, var2: 2 * var1 - var2}
+        model.initial_conditions = {var1: pybamm.Scalar(1), var2: pybamm.Scalar(4)}
+        model.variables = {"var1": var1, "var2": var2}
+
+        disc = pybamm.Discretisation()
+        disc.process_model(model)
+
+        # Solve
+        t_eval = np.linspace(0, 1)
+        solver = pybamm.CasadiAlgebraicSolver()
+        solution = solver.solve(model, t_eval)
+
+        sol = np.vstack((3 + 0 * t_eval, 6 + 0 * t_eval))
+        np.testing.assert_array_almost_equal(solution.y, sol)
+
     def test_model_solver_with_bounds(self):
         # Note: we need a better test case to test this functionality properly
         # Create model
diff --git a/tests/unit/test_solvers/test_jax_bdf_solver.py b/tests/unit/test_solvers/test_jax_bdf_solver.py
index 1ec810c09d..70ae7dc26e 100644
--- a/tests/unit/test_solvers/test_jax_bdf_solver.py
+++ b/tests/unit/test_solvers/test_jax_bdf_solver.py
@@ -5,6 +5,7 @@
 import time
 import numpy as np
 from platform import system
+
 if system() != "Windows":
     import jax
 
@@ -40,8 +41,7 @@ def fun(y, t):
         t1 = time.perf_counter() - t0
 
         # test accuracy
-        np.testing.assert_allclose(y[:, 0], np.exp(0.1 * t_eval),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(y[:, 0], np.exp(0.1 * t_eval), rtol=1e-6, atol=1e-6)
 
         t0 = time.perf_counter()
         y = pybamm.jax_bdf_integrate(fun, y0, t_eval, rtol=1e-8, atol=1e-8)
@@ -51,23 +51,16 @@ def fun(y, t):
         self.assertLess(t2, t1)
 
         # test second run is accurate
-        np.testing.assert_allclose(y[:, 0], np.exp(0.1 * t_eval),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(y[:, 0], np.exp(0.1 * t_eval), rtol=1e-6, atol=1e-6)
 
     def test_mass_matrix(self):
         # Solve
         t_eval = np.linspace(0.0, 1.0, 80)
 
         def fun(y, t):
-            return jax.numpy.stack([
-                0.1 * y[0],
-                y[1] - 2.0 * y[0],
-            ])
+            return jax.numpy.stack([0.1 * y[0], y[1] - 2.0 * y[0]])
 
-        mass = jax.numpy.array([
-            [2.0, 0.0],
-            [0.0, 0.0],
-        ])
+        mass = jax.numpy.array([[2.0, 0.0], [0.0, 0.0]])
 
         # give some bad initial conditions, solver should calculate correct ones using
         # this as a guess
@@ -79,10 +72,8 @@ def fun(y, t):
 
         # test accuracy
         soln = np.exp(0.05 * t_eval)
-        np.testing.assert_allclose(y[:, 0], soln,
-                                   rtol=1e-7, atol=1e-7)
-        np.testing.assert_allclose(y[:, 1], 2.0 * soln,
-                                   rtol=1e-7, atol=1e-7)
+        np.testing.assert_allclose(y[:, 0], soln, rtol=1e-7, atol=1e-7)
+        np.testing.assert_allclose(y[:, 1], 2.0 * soln, rtol=1e-7, atol=1e-7)
 
         t0 = time.perf_counter()
         y = pybamm.jax_bdf_integrate(fun, y0, t_eval, mass=mass, rtol=1e-8, atol=1e-8)
@@ -92,8 +83,7 @@ def fun(y, t):
         self.assertLess(t2, t1)
 
         # test second run is accurate
-        np.testing.assert_allclose(y[:, 0], np.exp(0.05 * t_eval),
-                                   rtol=1e-7, atol=1e-7)
+        np.testing.assert_allclose(y[:, 0], np.exp(0.05 * t_eval), rtol=1e-7, atol=1e-7)
 
     def test_solver_sensitivities(self):
         # Create model
@@ -125,9 +115,9 @@ def fun(y, t, inputs):
         @jax.jit
         def solve_bdf(rate):
             return jax.numpy.sum(
-                pybamm.jax_bdf_integrate(fun, y0, t_eval,
-                                         {'rate': rate},
-                                         rtol=1e-9, atol=1e-9)
+                pybamm.jax_bdf_integrate(
+                    fun, y0, t_eval, {"rate": rate}, rtol=1e-9, atol=1e-9
+                )
             )
 
         # check answers with finite difference
@@ -145,15 +135,9 @@ def test_mass_matrix_with_sensitivities(self):
         t_eval = np.linspace(0.0, 1.0, 80)
 
         def fun(y, t, inputs):
-            return jax.numpy.stack([
-                inputs['rate'] * y[0],
-                y[1] - 2.0 * y[0],
-            ])
+            return jax.numpy.stack([inputs["rate"] * y[0], y[1] - 2.0 * y[0]])
 
-        mass = jax.numpy.array([
-            [2.0, 0.0],
-            [0.0, 0.0],
-        ])
+        mass = jax.numpy.array([[2.0, 0.0], [0.0, 0.0]])
 
         y0 = jax.numpy.array([1.0, 2.0])
 
@@ -164,10 +148,9 @@ def fun(y, t, inputs):
         @jax.jit
         def solve_bdf(rate):
             return jax.numpy.sum(
-                pybamm.jax_bdf_integrate(fun, y0, t_eval,
-                                         {'rate': rate},
-                                         mass=mass,
-                                         rtol=1e-9, atol=1e-9)
+                pybamm.jax_bdf_integrate(
+                    fun, y0, t_eval, {"rate": rate}, mass=mass, rtol=1e-9, atol=1e-9
+                )
             )
 
         # check answers with finite difference
@@ -203,8 +186,9 @@ def test_solver_with_inputs(self):
         def fun(y, t, inputs):
             return rhs.evaluate(t=t, y=y, inputs=inputs).reshape(-1)
 
-        y = pybamm.jax_bdf_integrate(fun, y0, t_eval, {
-            "rate": 0.1}, rtol=1e-9, atol=1e-9)
+        y = pybamm.jax_bdf_integrate(
+            fun, y0, t_eval, {"rate": 0.1}, rtol=1e-9, atol=1e-9
+        )
 
         np.testing.assert_allclose(y[:, 0].reshape(-1), np.exp(-0.1 * t_eval))
 
diff --git a/tests/unit/test_solvers/test_jax_solver.py b/tests/unit/test_solvers/test_jax_solver.py
index d30f3f76b6..3c6f727583 100644
--- a/tests/unit/test_solvers/test_jax_solver.py
+++ b/tests/unit/test_solvers/test_jax_solver.py
@@ -5,6 +5,7 @@
 import time
 import numpy as np
 from platform import system
+
 if system() != "Windows":
     import jax
 
@@ -27,18 +28,17 @@ def test_model_solver(self):
         disc = pybamm.Discretisation(mesh, spatial_methods)
         disc.process_model(model)
 
-        for method in ['RK45', 'BDF']:
+        for method in ["RK45", "BDF"]:
             # Solve
-            solver = pybamm.JaxSolver(
-                method=method, rtol=1e-8, atol=1e-8
-            )
+            solver = pybamm.JaxSolver(method=method, rtol=1e-8, atol=1e-8)
             t_eval = np.linspace(0, 1, 80)
             t0 = time.perf_counter()
             solution = solver.solve(model, t_eval)
             t_first_solve = time.perf_counter() - t0
             np.testing.assert_array_equal(solution.t, t_eval)
-            np.testing.assert_allclose(solution.y[0], np.exp(0.1 * solution.t),
-                                       rtol=1e-6, atol=1e-6)
+            np.testing.assert_allclose(
+                solution.y[0], np.exp(0.1 * solution.t), rtol=1e-6, atol=1e-6
+            )
 
             # Test time
             self.assertEqual(
@@ -73,19 +73,15 @@ def test_semi_explicit_model(self):
         disc.process_model(model)
 
         # Solve
-        solver = pybamm.JaxSolver(
-            method='BDF', rtol=1e-8, atol=1e-8
-        )
+        solver = pybamm.JaxSolver(method="BDF", rtol=1e-8, atol=1e-8)
         t_eval = np.linspace(0, 1, 80)
         t0 = time.perf_counter()
         solution = solver.solve(model, t_eval)
         t_first_solve = time.perf_counter() - t0
         np.testing.assert_array_equal(solution.t, t_eval)
         soln = np.exp(0.1 * solution.t)
-        np.testing.assert_allclose(solution.y[0], soln,
-                                   rtol=1e-7, atol=1e-7)
-        np.testing.assert_allclose(solution.y[-1], 2 * soln,
-                                   rtol=1e-7, atol=1e-7)
+        np.testing.assert_allclose(solution.y[0], soln, rtol=1e-7, atol=1e-7)
+        np.testing.assert_allclose(solution.y[-1], 2 * soln, rtol=1e-7, atol=1e-7)
 
         # Test time
         self.assertEqual(
@@ -116,23 +112,21 @@ def test_solver_sensitivities(self):
         disc = pybamm.Discretisation(mesh, spatial_methods)
         disc.process_model(model)
 
-        for method in ['RK45', 'BDF']:
+        for method in ["RK45", "BDF"]:
             # Solve
-            solver = pybamm.JaxSolver(
-                method=method, rtol=1e-8, atol=1e-8
-            )
+            solver = pybamm.JaxSolver(method=method, rtol=1e-8, atol=1e-8)
             t_eval = np.linspace(0, 1, 80)
 
             h = 0.0001
             rate = 0.1
 
             # need to solve the model once to get it set up by the base solver
-            solver.solve(model, t_eval, inputs={'rate': rate})
+            solver.solve(model, t_eval, inputs={"rate": rate})
             solve = solver.get_solve(model, t_eval)
 
             # create a dummy "model" where we calculate the sum of the time series
             def solve_model(rate):
-                return jax.numpy.sum(solve({'rate': rate}))
+                return jax.numpy.sum(solve({"rate": rate}))
 
             # check answers with finite difference
             eval_plus = solve_model(rate + h)
@@ -216,15 +210,17 @@ def test_model_solver_with_inputs(self):
         solution = solver.solve(model, t_eval, inputs={"rate": 0.1})
         t_first_solve = time.perf_counter() - t0
 
-        np.testing.assert_allclose(solution.y[0], np.exp(-0.1 * solution.t),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(
+            solution.y[0], np.exp(-0.1 * solution.t), rtol=1e-6, atol=1e-6
+        )
 
         t0 = time.perf_counter()
         solution = solver.solve(model, t_eval, inputs={"rate": 0.2})
         t_second_solve = time.perf_counter() - t0
 
-        np.testing.assert_allclose(solution.y[0], np.exp(-0.2 * solution.t),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(
+            solution.y[0], np.exp(-0.2 * solution.t), rtol=1e-6, atol=1e-6
+        )
 
         self.assertLess(t_second_solve, t_first_solve)
 
@@ -247,7 +243,7 @@ def test_get_solve(self):
 
         # test that another method string gives error
         with self.assertRaises(ValueError):
-            solver = pybamm.JaxSolver(method='not_real')
+            solver = pybamm.JaxSolver(method="not_real")
 
         # Solve
         solver = pybamm.JaxSolver(rtol=1e-8, atol=1e-8)
@@ -260,13 +256,11 @@ def test_get_solve(self):
         solver = solver.get_solve(model, t_eval)
         y = solver({"rate": 0.1})
 
-        np.testing.assert_allclose(y[0], np.exp(-0.1 * t_eval),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(y[0], np.exp(-0.1 * t_eval), rtol=1e-6, atol=1e-6)
 
         y = solver({"rate": 0.2})
 
-        np.testing.assert_allclose(y[0], np.exp(-0.2 * t_eval),
-                                   rtol=1e-6, atol=1e-6)
+        np.testing.assert_allclose(y[0], np.exp(-0.2 * t_eval), rtol=1e-6, atol=1e-6)
 
 
 if __name__ == "__main__":
diff --git a/tests/unit/test_solvers/test_processed_symbolic_variable.py b/tests/unit/test_solvers/test_processed_symbolic_variable.py
index c179562d3b..1346de88a2 100644
--- a/tests/unit/test_solvers/test_processed_symbolic_variable.py
+++ b/tests/unit/test_solvers/test_processed_symbolic_variable.py
@@ -132,7 +132,7 @@ def test_processed_variable_1D_with_scalar_inputs(self):
 
         # Test values
         np.testing.assert_array_equal(
-            processed_eqn.value({"p": 27, "q": -42}), 27 * y_sol - 84,
+            processed_eqn.value({"p": 27, "q": -42}), 27 * y_sol - 84
         )
 
         # Test sensitivities
@@ -152,8 +152,7 @@ def test_processed_variable_1D_with_scalar_inputs(self):
 
         # Test values
         np.testing.assert_array_equal(
-            processed_eqn.value({"p": 27, "q": -42}),
-            (27 * y_sol - 84).T.reshape(-1, 1),
+            processed_eqn.value({"p": 27, "q": -42}), (27 * y_sol - 84).T.reshape(-1, 1)
         )
 
         # Test sensitivities
@@ -192,7 +191,7 @@ def test_processed_variable_1D_with_vector_inputs(self):
         # Test values - varying p
         p = np.linspace(0, 1, n)
         np.testing.assert_array_equal(
-            processed_eqn.value({"p": p, "q": 3}), (p[:, np.newaxis] * y_sol) ** 2 + 6,
+            processed_eqn.value({"p": p, "q": 3}), (p[:, np.newaxis] * y_sol) ** 2 + 6
         )
 
         # Test sensitivities - constant p
diff --git a/tests/unit/test_solvers/test_scikits_solvers.py b/tests/unit/test_solvers/test_scikits_solvers.py
index bc8d5a22c1..8e06a9465b 100644
--- a/tests/unit/test_solvers/test_scikits_solvers.py
+++ b/tests/unit/test_solvers/test_scikits_solvers.py
@@ -353,10 +353,7 @@ def test_model_solver_dae_multiple_nonsmooth_python(self):
         ]
         for discontinuity in discontinuities:
             model.events.append(
-                pybamm.Event(
-                    "nonsmooth rate",
-                    pybamm.Scalar(discontinuity),
-                )
+                pybamm.Event("nonsmooth rate", pybamm.Scalar(discontinuity))
             )
         disc = get_discretisation_for_testing()
         disc.process_model(model)
@@ -760,10 +757,7 @@ def test_model_step_nonsmooth_events(self):
         ]
         for discontinuity in discontinuities:
             model.events.append(
-                pybamm.Event(
-                    "nonsmooth rate",
-                    pybamm.Scalar(discontinuity),
-                )
+                pybamm.Event("nonsmooth rate", pybamm.Scalar(discontinuity))
             )
         disc = get_discretisation_for_testing()
         disc.process_model(model)
@@ -781,12 +775,8 @@ def test_model_step_nonsmooth_events(self):
         np.testing.assert_array_less(step_solution.y[-1], 1.2)
         var1_soln = (step_solution.t % a) ** 2 / 2 + a ** 2 / 2 * (step_solution.t // a)
         var2_soln = 2 * var1_soln
-        np.testing.assert_array_almost_equal(
-            step_solution.y[0], var1_soln, decimal=5
-        )
-        np.testing.assert_array_almost_equal(
-            step_solution.y[-1], var2_soln, decimal=5
-        )
+        np.testing.assert_array_almost_equal(step_solution.y[0], var1_soln, decimal=5)
+        np.testing.assert_array_almost_equal(step_solution.y[-1], var2_soln, decimal=5)
 
     def test_model_solver_dae_nonsmooth(self):
         whole_cell = ["negative electrode", "separator", "positive electrode"]
diff --git a/tests/unit/test_solvers/test_scipy_solver.py b/tests/unit/test_solvers/test_scipy_solver.py
index fae2775b3f..7f8d30dcae 100644
--- a/tests/unit/test_solvers/test_scipy_solver.py
+++ b/tests/unit/test_solvers/test_scipy_solver.py
@@ -305,9 +305,7 @@ def test_model_solver_inputs_in_initial_conditions(self):
         model = pybamm.BaseModel()
         var1 = pybamm.Variable("var1")
         model.rhs = {var1: pybamm.InputParameter("rate") * var1}
-        model.initial_conditions = {
-            var1: pybamm.InputParameter("ic 1"),
-        }
+        model.initial_conditions = {var1: pybamm.InputParameter("ic 1")}
 
         # Solve
         solver = pybamm.ScipySolver(rtol=1e-8, atol=1e-8)
diff --git a/tests/unit/test_solvers/test_solution.py b/tests/unit/test_solvers/test_solution.py
index 65e1c223cb..2bc57f14c0 100644
--- a/tests/unit/test_solvers/test_solution.py
+++ b/tests/unit/test_solvers/test_solution.py
@@ -31,6 +31,7 @@ def test_append(self):
         y1 = np.tile(t1, (20, 1))
         sol1 = pybamm.Solution(t1, y1)
         sol1.solve_time = 1.5
+        sol1.integration_time = 0.3
         sol1.model = pybamm.BaseModel()
         sol1.inputs = {"a": 1}
 
@@ -39,11 +40,13 @@ def test_append(self):
         y2 = np.tile(t2, (20, 1))
         sol2 = pybamm.Solution(t2, y2)
         sol2.solve_time = 1
+        sol2.integration_time = 0.5
         sol2.inputs = {"a": 2}
         sol1.append(sol2, create_sub_solutions=True)
 
         # Test
         self.assertEqual(sol1.solve_time, 2.5)
+        self.assertEqual(sol1.integration_time, 0.8)
         np.testing.assert_array_equal(sol1.t, np.concatenate([t1, t2[1:]]))
         np.testing.assert_array_equal(sol1.y, np.concatenate([y1, y2[:, 1:]], axis=1))
         np.testing.assert_array_equal(
@@ -96,14 +99,29 @@ def test_getitem(self):
         np.testing.assert_array_equal(twoc_sol.entries, twoc_sol(solution.t))
         np.testing.assert_array_equal(twoc_sol.entries, 2 * c_sol.entries)
 
+    def test_plot(self):
+        model = pybamm.BaseModel()
+        c = pybamm.Variable("c")
+        model.rhs = {c: -c}
+        model.initial_conditions = {c: 1}
+        model.variables["c"] = c
+        model.variables["2c"] = 2 * c
+
+        disc = pybamm.Discretisation()
+        disc.process_model(model)
+        solution = pybamm.ScipySolver().solve(model, np.linspace(0, 1))
+
+        solution.plot(["c", "2c"], testing=True)
+
     def test_save(self):
         model = pybamm.BaseModel()
+        model.length_scales = {"negative electrode": pybamm.Scalar(1)}
         # create both 1D and 2D variables
         c = pybamm.Variable("c")
         d = pybamm.Variable("d", domain="negative electrode")
         model.rhs = {c: -c, d: 1}
         model.initial_conditions = {c: 1, d: 2}
-        model.variables = {"c": c, "d": d, "2c": 2 * c}
+        model.variables = {"c": c, "d": d, "2c": 2 * c, "c + d": c + d}
 
         disc = get_discretisation_for_testing()
         disc.process_model(model)
@@ -125,6 +143,17 @@ def test_save(self):
         np.testing.assert_array_equal(solution.data["c"], data_load["c"].flatten())
         np.testing.assert_array_equal(solution.data["d"], data_load["d"])
 
+        # to matlab with bad variables name fails
+        solution.update(["c + d"])
+        with self.assertRaisesRegex(ValueError, "Invalid character"):
+            solution.save_data("test.mat", to_format="matlab")
+        # Works if providing alternative name
+        solution.save_data(
+            "test.mat", to_format="matlab", short_names={"c + d": "c_plus_d"}
+        )
+        data_load = loadmat("test.mat")
+        np.testing.assert_array_equal(solution.data["c + d"], data_load["c_plus_d"])
+
         # to csv
         with self.assertRaisesRegex(
             ValueError, "only 0D variables can be saved to csv"
@@ -138,9 +167,7 @@ def test_save(self):
         np.testing.assert_array_almost_equal(df["2c"], solution.data["2c"])
 
         # raise error if format is unknown
-        with self.assertRaisesRegex(
-            ValueError, "format 'wrong_format' not recognised"
-        ):
+        with self.assertRaisesRegex(ValueError, "format 'wrong_format' not recognised"):
             solution.save_data("test.csv", to_format="wrong_format")
 
         # test save whole solution
diff --git a/tests/unit/test_spatial_methods/test_finite_volume/test_finite_volume.py b/tests/unit/test_spatial_methods/test_finite_volume/test_finite_volume.py
index b6d4f4ed8f..3e9f81285e 100644
--- a/tests/unit/test_spatial_methods/test_finite_volume/test_finite_volume.py
+++ b/tests/unit/test_spatial_methods/test_finite_volume/test_finite_volume.py
@@ -1303,7 +1303,7 @@ def test_discretise_spatial_variable(self):
         r_disc = disc.process_symbol(r)
         self.assertIsInstance(r_disc, pybamm.Vector)
         np.testing.assert_array_equal(
-            r_disc.evaluate(), 3 * disc.mesh["negative particle"].nodes[:, np.newaxis],
+            r_disc.evaluate(), 3 * disc.mesh["negative particle"].nodes[:, np.newaxis]
         )
 
     def test_mass_matrix_shape(self):
@@ -1348,7 +1348,7 @@ def test_p2d_mass_matrix_shape(self):
         model.rhs = {c: pybamm.div(N)}
         model.initial_conditions = {c: pybamm.Scalar(0)}
         model.boundary_conditions = {
-            c: {"left": (0, "Dirichlet"), "right": (0, "Dirichlet")}
+            c: {"left": (0, "Neumann"), "right": (0, "Dirichlet")}
         }
         model.variables = {"c": c, "N": N}
         mesh = get_p2d_mesh_for_testing()
diff --git a/tests/unit/test_spatial_methods/test_spectral_volume.py b/tests/unit/test_spatial_methods/test_spectral_volume.py
index 425bc0fabc..0e9d89920c 100644
--- a/tests/unit/test_spatial_methods/test_spectral_volume.py
+++ b/tests/unit/test_spatial_methods/test_spectral_volume.py
@@ -8,8 +8,7 @@
 
 
 def get_mesh_for_testing(
-    xpts=None, rpts=10, ypts=15, zpts=15, geometry=None, cc_submesh=None,
-    order=2
+    xpts=None, rpts=10, ypts=15, zpts=15, geometry=None, cc_submesh=None, order=2
 ):
     param = pybamm.ParameterValues(
         values={
@@ -33,22 +32,19 @@ def get_mesh_for_testing(
 
     submesh_types = {
         "negative electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
+        ),
+        "separator": pybamm.MeshGenerator(
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
-        "separator": pybamm.MeshGenerator(pybamm.SpectralVolume1DSubMesh,
-                                          {"order": order}),
         "positive electrode": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "negative particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "positive particle": pybamm.MeshGenerator(
-            pybamm.SpectralVolume1DSubMesh,
-            {"order": order}
+            pybamm.SpectralVolume1DSubMesh, {"order": order}
         ),
         "current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
     }
diff --git a/tests/unit/test_timer.py b/tests/unit/test_timer.py
index 74d8eabcd6..531479881f 100644
--- a/tests/unit/test_timer.py
+++ b/tests/unit/test_timer.py
@@ -29,20 +29,19 @@ def test_timing(self):
         self.assertLess(b, a)
 
     def test_timer_format(self):
-        import sys
-
         t = pybamm.Timer()
-        self.assertEqual(t.format(1e-3), "0.001 seconds")
-        self.assertEqual(t.format(0.000123456789), "0.000123456789 seconds")
-        self.assertEqual(t.format(0.123456789), "0.12 seconds")
-        if sys.hexversion < 0x3000000:
-            self.assertEqual(t.format(2), "2.0 seconds")
-        else:
-            self.assertEqual(t.format(2), "2 seconds")
-        self.assertEqual(t.format(2.5), "2.5 seconds")
-        self.assertEqual(t.format(12.5), "12.5 seconds")
-        self.assertEqual(t.format(59.41), "59.41 seconds")
-        self.assertEqual(t.format(59.4126347547), "59.41 seconds")
+        self.assertEqual(t.format(1e-9), "1.000 ns")
+        self.assertEqual(t.format(0.000000123456789), "123.457 ns")
+        self.assertEqual(t.format(1e-6), "1.000 us")
+        self.assertEqual(t.format(0.000123456789), "123.457 us")
+        self.assertEqual(t.format(0.999e-3), "999.000 us")
+        self.assertEqual(t.format(1e-3), "1.000 ms")
+        self.assertEqual(t.format(0.123456789), "123.457 ms")
+        self.assertEqual(t.format(2), "2.000 s")
+        self.assertEqual(t.format(2.5), "2.500 s")
+        self.assertEqual(t.format(12.5), "12.500 s")
+        self.assertEqual(t.format(59.41), "59.410 s")
+        self.assertEqual(t.format(59.4126347547), "59.413 s")
         self.assertEqual(t.format(60.2), "1 minute, 0 seconds")
         self.assertEqual(t.format(61), "1 minute, 1 second")
         self.assertEqual(t.format(121), "2 minutes, 1 second")
diff --git a/tox.ini b/tox.ini
index c4dddc8549..4e90a958c3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -45,9 +45,12 @@ deps = flake8>=3
 commands = python -m flake8
 
 [testenv:coverage]
-skip_install = true
-deps = coverage
-commands = python -m coverage run run-tests.py --nosub
+deps = 
+     coverage
+     scikits.odes
+commands = 
+     coverage run run-tests.py --nosub
+     coverage xml
 
 [testenv:docs]
 skipdist = false
@@ -58,7 +61,7 @@ deps =
      guzzle-sphinx-theme
      sphinx-autobuild
 changedir = docs
-commands = sphinx-autobuild -BqT . {envtmpdir}/html
+commands = sphinx-autobuild --open-browser -qT . {envtmpdir}/html
 
 [flake8]
 max-line-length = 88