From 4f35a988b5c00e4fcf88b2c720f75ed5fe85e2db Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Mon, 18 May 2020 11:09:36 +0100 Subject: [PATCH 1/9] #997 update current collector models --- .../anodes/graphite_Chen2020/README.md | 7 + .../graphite_LGM50_diffusivity_Chen2020.py | 33 ++ ...olyte_exchange_current_density_Chen2020.py | 39 ++ pouch.py | 163 ++++++ pybamm/__init__.py | 1 + pybamm/geometry/geometry.py | 34 ++ .../submodels/current_collector/__init__.py | 6 +- .../effective_resistance_current_collector.py | 502 ++++++++++++++---- pybamm/solvers/base_solver.py | 2 +- pybamm/solvers/processed_variable.py | 33 +- tests/unit/test_geometry/test_geometry.py | 27 + .../test_effective_current_collector.py | 64 ++- .../test_solvers/test_processed_variable.py | 3 +- 13 files changed, 773 insertions(+), 141 deletions(-) create mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md create mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py create mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py create mode 100644 pouch.py diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md b/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md new file mode 100644 index 0000000000..702df98440 --- /dev/null +++ b/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md @@ -0,0 +1,7 @@ +# LG M50 Graphite anode parameters + +Parameters for a LG M50 graphite anode, from the paper + +> 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." Submitted for publication (2020). + +and references therein. For more information or how to cite please contact Ferran.Brosa-Planella (at) warwick.ac.uk. diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py new file mode 100644 index 0000000000..a877cafc06 --- /dev/null +++ b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py @@ -0,0 +1,33 @@ +from pybamm import exp, constants + + +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]. + + 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." Submitted for + publication (2020). + + Parameters + ---------- + sto: :class:`pybamm.Symbol` + Electrode stochiometry + T: :class:`pybamm.Symbol` + Dimensional temperature + + Returns + ------- + :class:`pybamm.Symbol` + Solid diffusivity + """ + + D_ref = 3.3e-14 + E_D_s = 42770 + arrhenius = exp(E_D_s / constants.R * (1 / 298.15 - 1 / T)) + + return D_ref * arrhenius diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py new file mode 100644 index 0000000000..51b9a3e90b --- /dev/null +++ b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py @@ -0,0 +1,39 @@ +from pybamm import exp, constants, standard_parameters_lithium_ion + + +def graphite_LGM50_electrolyte_exchange_current_density_Chen2020(c_e, c_s_surf, T): + """ + Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in + EC:DMC. + + 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." Submitted for + publication (2020). + + 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 = 6.48e-7 # (A/m2)(mol/m3)**1.5 - includes ref concentrations + E_r = 35000 + arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T)) + + c_n_max = standard_parameters_lithium_ion.c_n_max + + return ( + m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_n_max - c_s_surf) ** 0.5 + ) diff --git a/pouch.py b/pouch.py new file mode 100644 index 0000000000..e2ca2b49f1 --- /dev/null +++ b/pouch.py @@ -0,0 +1,163 @@ +import pybamm +import numpy as np +import matplotlib.pyplot as plt + +pybamm.set_logging_level("DEBUG") + +# load model +options = { + "current collector": "potential pair", + "dimensionality": 2, + "thermal": "x-lumped", + # The below option replaces the PDEs in the particles with ODEs under the + # assumption of fast diffusion (so that the concentration is uniform within + # each particle). This will speed up the simulation and is an OK assumption + # for a lot of cases. Uncomment it to switch it on/off. + # "particle": "fast diffusion", +} +model = pybamm.lithium_ion.SPM(options) + +# parameters can be updated here +param = model.default_parameter_values + +# set mesh points +var = pybamm.standard_spatial_vars +var_pts = { + var.x_n: 10, + var.x_s: 10, + var.x_p: 10, + var.r_n: 10, + var.r_p: 10, + var.y: 10, + var.z: 10, +} + +# solver +# casadi fast mode is pretty quick, but doesn't support events out of the box +# solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-3, root_tol=1e-3, mode="fast") +# KLU is sometimes better for bigger problems and supports events +solver = pybamm.IDAKLUSolver(atol=1e-6, rtol=1e-3, root_tol=1e-6, root_method="hybr") +# KLU performs better if you convert the final model to a python function +if isinstance(solver, pybamm.IDAKLUSolver): + model.convert_to_format = "python" + +# simulation object +simulation = pybamm.Simulation( + model, parameter_values=param, var_pts=var_pts, solver=solver +) + +# build simulation +# by default pybamm performs some checks on the discretised model. this can +# be a little slow for bigger problems, so you can turn if off. if you start to +# get obscure errors when you change things, set this to True and the error should +# get caught sooner and give a more informative message +simulation.build(check_model=False) + +# solve simulation +t_eval = np.linspace(0, 3600, 100) # time in seconds +simulation.solve(t_eval=t_eval) +solution = simulation.solution + +# plotting +# TO DO: 2+1D automated plotting + +# post-process variables +phi_s_cn = solution["Negative current collector potential [V]"] +phi_s_cp = solution["Positive current collector potential [V]"] +I = solution["Current collector current density [A.m-2]"] +T = solution["X-averaged cell temperature [K]"] + +# get y and z points for plotting (these are non-dimensional) +l_y = phi_s_cp.y_sol[-1] +l_z = phi_s_cp.z_sol[-1] +y_plot = np.linspace(0, l_y, 21) +z_plot = np.linspace(0, l_z, 21) + +# Can multiply by L_z to get dimensional y and z. Note that both y and z are +# scaled with L_z +L_z = param.evaluate(pybamm.standard_parameters_lithium_ion.L_z) +y_plot_dim = np.linspace(0, l_y, 21) * L_z +z_plot_dim = np.linspace(0, l_z, 21) * L_z + + +# define plotting function +def plot(time_in_seconds): + fig, ax = plt.subplots(figsize=(15, 8)) + plt.tight_layout() + plt.subplots_adjust(left=-0.1) + + # get non-dim time + tau = param.evaluate(pybamm.standard_parameters_lithium_ion.tau_discharge) + t_non_dim = time_in_seconds / tau + + # negative current collector potential + plt.subplot(221) + phi_s_cn_plot = plt.pcolormesh( + y_plot_dim, + z_plot_dim, + np.transpose( + phi_s_cn(y=y_plot, z=z_plot, t=t_non_dim) + ), # accepts non-dim values + shading="gouraud", + ) + plt.axis([0, l_y * L_z, 0, l_z * L_z]) + plt.xlabel(r"$y$ [m]") + plt.ylabel(r"$z$ [m]") + plt.title(r"$\phi_{s,cn}$ [V]") + plt.set_cmap("cividis") + plt.colorbar(phi_s_cn_plot) + + # positive current collector potential + plt.subplot(222) + phi_s_cp_plot = plt.pcolormesh( + y_plot_dim, + z_plot_dim, + np.transpose( + phi_s_cp(y=y_plot, z=z_plot, t=t_non_dim) + ), # accepts non-dim values + shading="gouraud", + ) + plt.axis([0, l_y * L_z, 0, l_z * L_z]) + plt.xlabel(r"$y$ [m]") + plt.ylabel(r"$z$ [m]") + plt.title(r"$\phi_{s,cp}$ [V]") + plt.set_cmap("viridis") + plt.colorbar(phi_s_cp_plot) + + # through-cell current + plt.subplot(223) + I_plot = plt.pcolormesh( + y_plot_dim, + z_plot_dim, + np.transpose(I(y=y_plot, z=z_plot, t=t_non_dim)), # accepts non-dim values + shading="gouraud", + ) + plt.axis([0, l_y * L_z, 0, l_z * L_z]) + plt.xlabel(r"$y$ [m]") + plt.ylabel(r"$z$ [m]") + plt.title(r"$I$ [A.m-2]") + plt.set_cmap("plasma") + plt.colorbar(I_plot) + # temperature + plt.subplot(224) + T_plot = plt.pcolormesh( + y_plot_dim, + z_plot_dim, + np.transpose(T(y=y_plot, z=z_plot, t=t_non_dim)), # accepts non-dim values + shading="gouraud", + ) + plt.axis([0, l_y * L_z, 0, l_z * L_z]) + plt.xlabel(r"$y$ [m]") + plt.ylabel(r"$z$ [m]") + plt.title(r"$T$ [K]") + plt.set_cmap("inferno") + plt.colorbar(T_plot) + + plt.subplots_adjust( + top=0.92, bottom=0.15, left=0.10, right=0.9, hspace=0.5, wspace=0.5 + ) + plt.show() + + +# call plot +plot(1000) diff --git a/pybamm/__init__.py b/pybamm/__init__.py index 44033ec2df..2068d47bee 100644 --- a/pybamm/__init__.py +++ b/pybamm/__init__.py @@ -149,6 +149,7 @@ def version(formatted=False): Geometryxp1DMacro, Geometryxp0p1DMicro, Geometryxp1p1DMicro, + Geometry1DCurrentCollector, Geometry2DCurrentCollector, ) diff --git a/pybamm/geometry/geometry.py b/pybamm/geometry/geometry.py index 5b680f4dca..f36ec6168a 100644 --- a/pybamm/geometry/geometry.py +++ b/pybamm/geometry/geometry.py @@ -47,6 +47,7 @@ class Geometry(dict): along with the microscopic 1D particle geometry. - "(2+1)+1D micro": 1D macroscopic cell geometry, with 2D current collector model, along with the microscopic 1D particle geometry. + - "1D current collector": macroscopic 1D current collector geometry - "2D current collector": macroscopic 2D current collector geometry **Extends**: :class:`dict` @@ -84,6 +85,8 @@ def __init__(self, *geometries, custom_geometry={}): geometry = Geometryxp1p1DMicro(cc_dimension=1) elif geometry == "(2+1)+1D micro": geometry = Geometryxp1p1DMicro(cc_dimension=2) + elif geometry == "1D current collector": + geometry = Geometry1DCurrentCollector() elif geometry == "2D current collector": geometry = Geometry2DCurrentCollector() # avoid combining geometries that clash @@ -512,6 +515,37 @@ def __init__(self, cc_dimension=1, custom_geometry={}): self.update(custom_geometry) +class Geometry1DCurrentCollector(Geometry): + """ + A geometry class to store the details features of the macroscopic 1D + current collector geometry. + + **Extends**: :class:`Geometry` + + Parameters + ---------- + + custom_geometry : dict containing any extra user defined geometry + """ + + def __init__(self, custom_geometry={}): + super().__init__() + var = pybamm.standard_spatial_vars + + self["current collector"] = { + "primary": { + var.z: {"min": pybamm.Scalar(0), "max": pybamm.geometric_parameters.l_z} + }, + "tabs": { + "negative": {"z_centre": pybamm.geometric_parameters.centre_z_tab_n}, + "positive": {"z_centre": pybamm.geometric_parameters.centre_z_tab_p}, + }, + } + + # update with custom geometry if non empty + self.update(custom_geometry) + + class Geometry2DCurrentCollector(Geometry): """ A geometry class to store the details features of the macroscopic 2D diff --git a/pybamm/models/submodels/current_collector/__init__.py b/pybamm/models/submodels/current_collector/__init__.py index 1f765b4e30..daea5b0b24 100644 --- a/pybamm/models/submodels/current_collector/__init__.py +++ b/pybamm/models/submodels/current_collector/__init__.py @@ -1,7 +1,11 @@ from .base_current_collector import BaseModel from .homogeneous_current_collector import Uniform -from .effective_resistance_current_collector import EffectiveResistance2D +from .effective_resistance_current_collector import ( + EffectiveResistance1D, + EffectiveResistance2D, + AlternativeEffectiveResistance2D, +) from .potential_pair import ( BasePotentialPair, PotentialPair1plus1D, diff --git a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py index e74fe39cb2..01b890f4fb 100644 --- a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py +++ b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py @@ -1,118 +1,244 @@ # -# Class for calcuting the effective resistance of two-dimensional current collectors +# Classes for calcuting the effective resistance of current collectors in a pouch cell # import pybamm -class EffectiveResistance2D(pybamm.BaseModel): - """A model which calculates the effective Ohmic resistance of the current - collectors in the limit of large electrical conductivity. - Note: This submodel should be solved before a one-dimensional model to calculate - and return the effective current collector resistance. +class EffectiveResistance1D(pybamm.BaseModel): + """A model which calculates the effective Ohmic resistance of the 1D current + collectors in the limit of large electrical conductivity. For details see [1]_. + + References + ---------- + .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic + Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. **Extends:** :class:`pybamm.BaseModel` """ def __init__(self): super().__init__() - self.name = "Effective resistance in current collector model" + self.name = "Effective resistance in current collector model (1D)" self.param = pybamm.standard_parameters_lithium_ion - # Get useful parameters + # Get necessary parameters param = self.param l_cn = param.l_cn l_cp = param.l_cp - l_y = param.l_y sigma_cn_dbl_prime = param.sigma_cn_dbl_prime sigma_cp_dbl_prime = param.sigma_cp_dbl_prime - alpha_prime = param.alpha_prime + delta = param.delta # aspect ratio - # Set model variables - var = pybamm.standard_spatial_vars - - psi = pybamm.Variable( - "Current collector potential weighted sum", ["current collector"] + # Set model variables: Note: we solve using a scaled version that is + # better conditioned + R_cn_scaled = pybamm.Variable( + "Scaled negative current collector resistance", domain="current collector" ) - W = pybamm.Variable( - "Perturbation to current collector potential difference", - ["current collector"], + R_cp_scaled = pybamm.Variable( + "Scaled positive current collector resistance", domain="current collector" ) - c_psi = pybamm.Variable("Lagrange multiplier for variable `psi`") - c_W = pybamm.Variable("Lagrange multiplier for variable `W`") - - self.variables = { - "Current collector potential weighted sum": psi, - "Perturbation to current collector potential difference": W, - "Lagrange multiplier for variable `psi`": c_psi, - "Lagrange multiplier for variable `W`": c_W, - } + R_cn = delta * R_cn_scaled / (l_cn * sigma_cn_dbl_prime) + R_cp = delta * R_cp_scaled / (l_cp * sigma_cp_dbl_prime) - # Algebraic equations (enforce zero mean constraint through Lagrange multiplier) - # 0*LagrangeMultiplier hack otherwise gives KeyError + # Governing equations self.algebraic = { - psi: pybamm.laplacian(psi) - + c_psi * pybamm.DefiniteIntegralVector(psi, vector_type="column"), - W: pybamm.laplacian(W) - - pybamm.source(1, W) - + c_W * pybamm.DefiniteIntegralVector(W, vector_type="column"), - c_psi: pybamm.Integral(psi, [var.y, var.z]) + 0 * c_psi, - c_W: pybamm.Integral(W, [var.y, var.z]) + 0 * c_W, + R_cn_scaled: pybamm.laplacian(R_cn_scaled) - 1, + R_cp_scaled: pybamm.laplacian(R_cp_scaled) - 1, } # Boundary conditons - psi_neg_tab_bc = l_cn - psi_pos_tab_bc = -l_cp - W_neg_tab_bc = l_y / (alpha_prime * sigma_cn_dbl_prime) - W_pos_tab_bc = l_y / (alpha_prime * sigma_cp_dbl_prime) - self.boundary_conditions = { - psi: { - "negative tab": (psi_neg_tab_bc, "Neumann"), - "positive tab": (psi_pos_tab_bc, "Neumann"), + R_cn_scaled: { + "left": (0, "Neumann"), + "right": (0, "Dirichlet"), + # "negative tab": (0, "Dirichlet"), + # "positive tab": (0, "Neumann"), + # "no tab": (0, "Neumann"), }, - W: { - "negative tab": (W_neg_tab_bc, "Neumann"), - "positive tab": (W_pos_tab_bc, "Neumann"), + R_cp_scaled: { + "negative tab": (0, "Neumann"), + "positive tab": (0, "Dirichlet"), + "no tab": (0, "Neumann"), }, } # "Initial conditions" provides initial guess for solver - # TODO: better guess than zero? self.initial_conditions = { - psi: pybamm.Scalar(0), - W: pybamm.Scalar(0), - c_psi: pybamm.Scalar(0), - c_W: pybamm.Scalar(0), + R_cn_scaled: pybamm.Scalar(0), + R_cp_scaled: pybamm.Scalar(0), } # Define effective current collector resistance - psi_neg_tab = pybamm.BoundaryValue(psi, "negative tab") - psi_pos_tab = pybamm.BoundaryValue(psi, "positive tab") - W_neg_tab = pybamm.BoundaryValue(W, "negative tab") - W_pos_tab = pybamm.BoundaryValue(W, "positive tab") - - R_cc = ( - (alpha_prime / l_y) - * ( - sigma_cn_dbl_prime * l_cn * W_pos_tab - + sigma_cp_dbl_prime * l_cp * W_neg_tab - ) - - (psi_pos_tab - psi_neg_tab) - ) / (sigma_cn_dbl_prime * l_cn + sigma_cp_dbl_prime * l_cp) - - R_cc_dim = R_cc * param.potential_scale / param.I_typ - - self.variables.update( - { - "Current collector potential weighted sum (negative tab)": psi_neg_tab, - "Current collector potential weighted sum (positive tab)": psi_pos_tab, - "Perturbation to c.c. potential difference (negative tab)": W_neg_tab, - "Perturbation to c.c. potential difference (positive tab)": W_pos_tab, - "Effective current collector resistance": R_cc, - "Effective current collector resistance [Ohm]": R_cc_dim, - } + R_cc_n = -pybamm.z_average(R_cn) + R_cc_p = -pybamm.z_average(R_cp) + R_cc = R_cc_n + R_cc_p + R_scale = param.potential_scale / param.I_typ + + self.variables = { + "Negative current collector resistance": R_cn, + "Negative current collector resistance [Ohm]": R_cn * R_scale, + "Positive current collector resistance": R_cp, + "Positive current collector resistance [Ohm]": R_cp * R_scale, + "Effective current collector resistance": R_cc, + "Effective current collector resistance [Ohm]": R_cc * R_scale, + "Effective negative current collector resistance": R_cc_n, + "Effective negative current collector resistance [Ohm]": R_cc_n * R_scale, + "Effective positive current collector resistance": R_cc_p, + "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, + } + + def get_processed_potentials(self, solution, param_values, V_av, I_av): + """ + Calculates the potentials in the current collector given + the average voltage and current. + Note: This takes in the *processed* V_av and I_av from a 1D simulation + representing the average cell behaviour and returns a dictionary of + processed potentials. + """ + # Get required processed parameters + param = self.param + pot_scale = param_values.evaluate(param.potential_scale) + U_ref = param_values.evaluate(param.U_p_ref - param.U_n_ref) + + # Process resistances + R_cn = solution["Negative current collector resistance"] + R_cp = solution["Positive current collector resistance"] + + # Create callable combination of ProcessedVariable objects for potentials + def phi_s_cn(t, z): + return R_cn(z=z) * I_av(t=t) + + def phi_s_cp(t, z): + return V_av(t=t) - R_cp(z=z) * I_av(t=t) + + def V_cc(t, z): + return phi_s_cp(t, z) - phi_s_cn(t, z) + + def phi_s_cn_dim(t, z): + return phi_s_cn(t, z) * pot_scale + + def phi_s_cp_dim(t, z): + return U_ref + phi_s_cp(t, z) * pot_scale + + def V_cc_dim(t, z): + return U_ref + V_cc(t, z) * pot_scale + + potentials = { + "Negative current collector potential": phi_s_cn, + "Negative current collector potential [V]": phi_s_cn_dim, + "Positive current collector potential": phi_s_cp, + "Positive current collector potential [V]": phi_s_cp_dim, + "Local current collector potential difference": V_cc, + "Local current collector potential difference [V]": V_cc_dim, + } + return potentials + + @property + def default_parameter_values(self): + return pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019) + + @property + def default_geometry(self): + return pybamm.Geometry("1D current collector") + + @property + def default_var_pts(self): + var = pybamm.standard_spatial_vars + return {var.z: 32} + + @property + def default_submesh_types(self): + return {"current collector": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)} + + @property + def default_spatial_methods(self): + return {"current collector": pybamm.FiniteVolume()} + + @property + def default_solver(self): + return pybamm.CasadiAlgebraicSolver() + + +class EffectiveResistance2D(pybamm.BaseModel): + """A model which calculates the effective Ohmic resistance of the 2D current + collectors in the limit of large electrical conductivity. For details see [1]_. + Note that unlike the model in [1]_, this formulation assumes uniform potential + across the tabs. See :class:`pybamm.AlternativeEffectiveResistance2D` for the + exact formulation in [1]_ that assumes a uniform current density at the tabs. + + References + ---------- + .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic + Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + + **Extends:** :class:`pybamm.BaseModel` + """ + + def __init__(self): + super().__init__() + self.name = "Effective resistance in current collector model (2D)" + self.param = pybamm.standard_parameters_lithium_ion + + # Get necessary parameters + param = self.param + l_cn = param.l_cn + l_cp = param.l_cp + sigma_cn_dbl_prime = param.sigma_cn_dbl_prime + sigma_cp_dbl_prime = param.sigma_cp_dbl_prime + delta = param.delta # aspect ratio + + # Set model variables + R_cn = pybamm.Variable( + "Negative current collector resistance", domain="current collector" + ) + R_cp = pybamm.Variable( + "positive current collector resistance", domain="current collector" ) + # We solve using a scaled version that is better conditioned + R_cn_scaled = R_cn * l_cn * sigma_cn_dbl_prime / delta + R_cp_scaled = R_cp * l_cp * sigma_cp_dbl_prime / delta + + # Governing equations + self.algebraic = { + R_cn: pybamm.laplacian(R_cn_scaled) - pybamm.source(1, R_cn_scaled), + R_cp: pybamm.laplacian(R_cp_scaled) - pybamm.source(1, R_cp_scaled), + } + + # Boundary conditons + self.boundary_conditions = { + R_cn_scaled: { + "negative tab": (0, "Dirichlet"), + "positive tab": (0, "Neumann"), + }, + R_cp_scaled: { + "negative tab": (0, "Neumann"), + "positive tab": (0, "Dirichlet"), + }, + } + + # "Initial conditions" provides initial guess for solver + self.initial_conditions = {R_cn: pybamm.Scalar(0), R_cp: pybamm.Scalar(0)} + + # Define effective current collector resistance + R_cc_n = -pybamm.yz_average(R_cn) + R_cc_p = -pybamm.yz_average(R_cp) + R_cc = R_cc_n + R_cc_p + R_scale = param.potential_scale / param.I_typ + + self.variables = { + "Negative current collector resistance": R_cn, + "Negative current collector resistance [Ohm]": R_cn * R_scale, + "Positive current collector resistance": R_cp, + "Positive current collector resistance [Ohm]": R_cp * R_scale, + "Effective current collector resistance": R_cc, + "Effective current collector resistance [Ohm]": R_cc * R_scale, + "Effective negative current collector resistance": R_cc_n, + "Effective negative current collector resistance [Ohm]": R_cc_n * R_scale, + "Effective positive current collector resistance": R_cc_p, + "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, + } + def get_processed_potentials(self, solution, param_values, V_av, I_av): """ Calculates the potentials in the current collector given @@ -123,72 +249,212 @@ def get_processed_potentials(self, solution, param_values, V_av, I_av): """ # Get required processed parameters param = self.param - l_cn = param_values.evaluate(param.l_cn) - l_cp = param_values.evaluate(param.l_cp) - l_y = param_values.evaluate(param.l_y) - l_z = param_values.evaluate(param.l_z) - sigma_cn_prime = param_values.evaluate(param.sigma_cn_prime) - sigma_cp_prime = param_values.evaluate(param.sigma_cp_prime) - alpha = param_values.evaluate(param.alpha) pot_scale = param_values.evaluate(param.potential_scale) U_ref = param_values.evaluate(param.U_p_ref - param.U_n_ref) - # Process psi and W, and their (average) values at the negative tab - psi = solution["Current collector potential weighted sum"] - W = solution["Perturbation to current collector potential difference"] - psi_neg_tab = self.variables[ - "Current collector potential weighted sum (negative tab)" - ].evaluate(y=solution.y[:, 0])[0][0] - W_neg_tab = self.variables[ - "Perturbation to c.c. potential difference (negative tab)" - ].evaluate(y=solution.y[:, 0])[0][0] + # Process resistances + R_cn = solution["Negative current collector resistance"] + R_cp = solution["Positive current collector resistance"] # Create callable combination of ProcessedVariable objects for potentials + def phi_s_cn(t, y, z): + return R_cn(y=y, z=z) * I_av(t=t) + + def phi_s_cp(t, y, z): + return V_av(t=t) - R_cp(y=y, z=z) * I_av(t=t) + def V_cc(t, y, z): - return V_av(t) - alpha * I_av(t) * W(y=y, z=z) + return phi_s_cp(t, y, z) - phi_s_cn(t, y, z) + + def phi_s_cn_dim(t, y, z): + return phi_s_cn(t, y, z) * pot_scale + + def phi_s_cp_dim(t, y, z): + return U_ref + phi_s_cp(t, y, z) * pot_scale def V_cc_dim(t, y, z): return U_ref + V_cc(t, y, z) * pot_scale - denominator = sigma_cn_prime * l_cn + sigma_cn_prime * l_cp + potentials = { + "Negative current collector potential": phi_s_cn, + "Negative current collector potential [V]": phi_s_cn_dim, + "Positive current collector potential": phi_s_cp, + "Positive current collector potential [V]": phi_s_cp_dim, + "Local current collector potential difference": V_cc, + "Local current collector potential difference [V]": V_cc_dim, + } + return potentials + + @property + def default_parameter_values(self): + return pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019) + + @property + def default_geometry(self): + return pybamm.Geometry("2D current collector") + + @property + def default_var_pts(self): + var = pybamm.standard_spatial_vars + return {var.y: 32, var.z: 32} + + @property + def default_submesh_types(self): + return { + "current collector": pybamm.MeshGenerator(pybamm.ScikitUniform2DSubMesh) + } + + @property + def default_spatial_methods(self): + return {"current collector": pybamm.ScikitFiniteElement()} + + @property + def default_solver(self): + return pybamm.CasadiAlgebraicSolver() + + +class AlternativeEffectiveResistance2D(pybamm.BaseModel): + """A model which calculates the effective Ohmic resistance of the 2D current + collectors in the limit of large electrical conductivity. This model assumes + a uniform current density at the tabs and the solution is computed by first + solving and auxilliary problem which is the related to the resistances, see [1]_. + + References + ---------- + .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic + Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + + **Extends:** :class:`pybamm.BaseModel` + """ + + def __init__(self): + super().__init__() + self.name = "Effective resistance in current collector model (2D)" + self.param = pybamm.standard_parameters_lithium_ion + + # Get necessary parameters + param = self.param + l_y = param.l_y + l_z = param.l_z + l_cn = param.l_cn + l_cp = param.l_cp + l_tab_p = param.l_tab_p + A_tab_p = l_cp * l_tab_p + sigma_cn_dbl_prime = param.sigma_cn_dbl_prime + sigma_cp_dbl_prime = param.sigma_cp_dbl_prime + delta = param.delta + + # Set model variables -- we solve a auxilliary problem in each current collector + # then relate this to the potentials and resistances later + f_n = pybamm.Variable( + "Unit solution in negative current collector", domain="current collector" + ) + f_p = pybamm.Variable( + "Unit solution in positive current collector", domain="current collector" + ) + + # Governing equations -- we impose that the average of f_p is zero + # by introducing a Lagrange multiplier + c = pybamm.Variable("Lagrange multiplier") - # The method only defines psi up to an arbitrary function of time. This - # is fixed by ensuring phi_s_cn = 0 on the negative tab when reconstructing - # the potentials - def phi_s_cn_tab(t): - phi_s_cn_tab = ( - I_av(t) * l_y * l_z * psi_neg_tab - - sigma_cp_prime * l_cp * (V_av(t) - alpha * I_av(t) * W_neg_tab) - ) / denominator - return phi_s_cn_tab + self.algebraic = { + f_n: pybamm.laplacian(f_n) + pybamm.source(1, f_n), + c: pybamm.laplacian(f_p) + - pybamm.source(1, f_p) + + c * pybamm.DefiniteIntegralVector(f_p, vector_type="column"), + f_p: pybamm.yz_average(f_p) + 0 * c, + } + + # Boundary conditons + pos_tab_bc = l_y * l_z * l_cp / A_tab_p + self.boundary_conditions = { + f_n: {"negative tab": (0, "Dirichlet"), "positive tab": (0, "Neumann")}, + f_p: { + "negative tab": (0, "Neumann"), + "positive tab": (pos_tab_bc, "Neumann"), + }, + } + + # "Initial conditions" provides initial guess for solver + self.initial_conditions = { + f_n: pybamm.Scalar(0), + f_p: pybamm.Scalar(0), + c: pybamm.Scalar(0), + } + + # Define effective current collector resistance + R_cc_n = ( + delta * pybamm.yz_average(f_n) / (l_y * l_z * l_cn * sigma_cn_dbl_prime) + ) + R_cc_p = ( + delta + * pybamm.BoundaryIntegral(f_p, "positive tab") + / (l_y * l_z * l_cp * sigma_cp_dbl_prime) + ) + R_cc = R_cc_n + R_cc_p + R_scale = param.potential_scale / param.I_typ + + self.variables = { + "Unit solution in negative current collector": f_n, + "Unit solution in positive current collector": f_p, + "Effective current collector resistance": R_cc, + "Effective current collector resistance [Ohm]": R_cc * R_scale, + "Effective negative current collector resistance": R_cc_n, + "Effective negative current collector resistance [Ohm]": R_cc_n * R_scale, + "Effective positive current collector resistance": R_cc_p, + "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, + } + def get_processed_potentials(self, solution, param_values, V_av, I_av): + """ + Calculates the potentials in the current collector given + the average voltage and current. + Note: This takes in the *processed* V_av and I_av from a 1D simulation + representing the average cell behaviour and returns a dictionary of + processed potentials. + """ + # Get evaluated parameters + param = self.param + delta = param_values.evaluate(param.delta) + l_cn = param_values.evaluate(param.l_cn) + l_cp = param_values.evaluate(param.l_cp) + sigma_cn_dbl_prime = param_values.evaluate(param.sigma_cn_dbl_prime) + sigma_cp_dbl_prime = param_values.evaluate(param.sigma_cp_dbl_prime) + pot_scale = param_values.evaluate(param.potential_scale) + U_ref = param_values.evaluate(param.U_p_ref - param.U_n_ref) + + # Process unit solutions + f_n = solution["Unit solution in negative current collector"] + f_p = solution["Unit solution in positive current collector"] + + # Create callable combination of ProcessedVariable objects for potentials def phi_s_cn(t, y, z): - phi_s_cn = ( - I_av(t) * l_y * l_z * psi(y=y, z=z) - - sigma_cp_prime * l_cp * V_cc(t, y, z) - ) / denominator - return phi_s_cn - phi_s_cn_tab(t) + return -(delta * I_av(t=t) / l_cn / sigma_cn_dbl_prime) * f_n(y=y, z=z) + + def phi_s_cp(t, y, z): + return V_av(t=t) + (delta * I_av(t=t) / l_cp / sigma_cp_dbl_prime) * f_p( + y=y, z=z + ) + + def V_cc(t, y, z): + return phi_s_cp(t, y, z) - phi_s_cn(t, y, z) def phi_s_cn_dim(t, y, z): return phi_s_cn(t, y, z) * pot_scale - def phi_s_cp(t, y, z): - phi_s_cp = ( - I_av(t) * l_y * l_z * psi(y=y, z=z) - + sigma_cn_prime * l_cn * V_cc(t, y, z) - ) / denominator - return phi_s_cp - phi_s_cn_tab(t) - def phi_s_cp_dim(t, y, z): return U_ref + phi_s_cp(t, y, z) * pot_scale + def V_cc_dim(t, y, z): + return U_ref + V_cc(t, y, z) * pot_scale + potentials = { "Negative current collector potential": phi_s_cn, "Negative current collector potential [V]": phi_s_cn_dim, "Positive current collector potential": phi_s_cp, "Positive current collector potential [V]": phi_s_cp_dim, - "Local voltage": V_cc, - "Local voltage [V]": V_cc_dim, + "Local current collector potential difference": V_cc, + "Local current collector potential difference [V]": V_cc_dim, } return potentials diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py index a8cc53eacd..ad34a98ff6 100644 --- a/pybamm/solvers/base_solver.py +++ b/pybamm/solvers/base_solver.py @@ -591,7 +591,7 @@ def solve(self, model, t_eval=None, external_variables=None, inputs=None): model.y0 = last_state if len(model.algebraic) > 0: model.y0 = self.calculate_consistent_state( - model, t_eval_dimensionless[end_index], ext_and_inputs, + model, t_eval_dimensionless[end_index], ext_and_inputs ) # restore old y0 diff --git a/pybamm/solvers/processed_variable.py b/pybamm/solvers/processed_variable.py index e36ff46701..c158e66d96 100644 --- a/pybamm/solvers/processed_variable.py +++ b/pybamm/solvers/processed_variable.py @@ -64,10 +64,16 @@ def __init__(self, base_variable, solution, known_evals=None): # check variable shape else: if len(solution.t) == 1: - raise pybamm.SolverError( - "Solution time vector must have length > 1. Check whether " - "simulation terminated too early." - ) + # 1D function of space only + n = self.mesh[0].npts + base_shape = self.base_eval.shape[0] + if base_shape in [n, n + 1]: + self.initialise_1D(fixed_t=True) + else: + raise pybamm.SolverError( + "Solution time vector must have length > 1. Check whether " + "simulation terminated too early." + ) elif ( isinstance(self.base_eval, numbers.Number) or len(self.base_eval.shape) == 0 @@ -120,7 +126,7 @@ def initialise_0D(self): self.entries = entries self.dimensions = 0 - def initialise_1D(self): + def initialise_1D(self, fixed_t=False): len_space = self.base_eval.shape[0] entries = np.empty((len_space, len(self.t_sol))) @@ -181,10 +187,21 @@ def initialise_1D(self): # set up interpolation # note that the order of 't' and 'space' is the reverse of what you'd expect + # TODO: fix processing when variable is a function of space only + if fixed_t: + # Hack for 1D space only - self._interpolation_function = interp.interp2d( - self.t_sol, space, entries_for_interp, kind="linear", fill_value=np.nan - ) + def interp_fun(t, z): + out = interp.interp1d( + space, entries_for_interp[:, 0], kind="linear", fill_value=np.nan + )(z) + return out[:, np.newaxis] + + self._interpolation_function = interp_fun + else: + self._interpolation_function = interp.interp2d( + self.t_sol, space, entries_for_interp, kind="linear", fill_value=np.nan + ) def initialise_2D(self): """ diff --git a/tests/unit/test_geometry/test_geometry.py b/tests/unit/test_geometry/test_geometry.py index eff357b31b..f60c72ed90 100644 --- a/tests/unit/test_geometry/test_geometry.py +++ b/tests/unit/test_geometry/test_geometry.py @@ -299,6 +299,33 @@ def test_combine_geometries_strings(self): ) +class TestGeometry1DCurrentCollector(unittest.TestCase): + def test_add_custom_geometry(self): + geometry = pybamm.Geometry1DCurrentCollector() + whole_cell = ["negative electrode", "separator", "positive electrode"] + x = pybamm.SpatialVariable("x", whole_cell) + custom_geometry = { + "negative electrode": { + "primary": {x: {"min": pybamm.Scalar(1), "max": pybamm.Scalar(2)}} + } + } + + geometry.update(custom_geometry) + self.assertEqual( + geometry["negative electrode"], custom_geometry["negative electrode"] + ) + + def test_geometry_keys(self): + geometry = pybamm.Geometry1DCurrentCollector() + for prim_sec_vars in geometry.values(): + for spatial_vars in prim_sec_vars.values(): + all( + self.assertIsInstance(spatial_var, pybamm.SpatialVariable) + for spatial_var in spatial_vars.keys() + if spatial_var not in ["negative", "positive"] + ) + + class TestGeometry2DCurrentCollector(unittest.TestCase): def test_add_custom_geometry(self): geometry = pybamm.Geometry2DCurrentCollector() diff --git a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py index 66a17b5a1c..3d6079be86 100644 --- a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py +++ b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py @@ -1,11 +1,27 @@ # -# Tests for the Effective Current Collector Resistance model +# Tests for the Effective Current Collector Resistance models # import pybamm import unittest import numpy as np +class TestEffectiveResistance1D(unittest.TestCase): + def test_well_posed(self): + model = pybamm.current_collector.EffectiveResistance1D() + model.check_well_posedness() + + def test_default_geometry(self): + model = pybamm.current_collector.EffectiveResistance1D() + self.assertIsInstance(model.default_geometry, pybamm.Geometry) + self.assertTrue("current collector" in model.default_geometry) + self.assertNotIn("negative electrode", model.default_geometry) + + def test_default_solver(self): + model = pybamm.current_collector.EffectiveResistance1D() + self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) + + class TestEffectiveResistance2D(unittest.TestCase): def test_well_posed(self): model = pybamm.current_collector.EffectiveResistance2D() @@ -21,11 +37,31 @@ def test_default_solver(self): model = pybamm.current_collector.EffectiveResistance2D() self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) + +class TestAlternativeEffectiveResistance2D(unittest.TestCase): + def test_well_posed(self): + model = pybamm.current_collector.AlternativeEffectiveResistance2D() + model.check_well_posedness() + + def test_default_geometry(self): + model = pybamm.current_collector.AlternativeEffectiveResistance2D() + self.assertIsInstance(model.default_geometry, pybamm.Geometry) + self.assertTrue("current collector" in model.default_geometry) + self.assertNotIn("negative electrode", model.default_geometry) + + def test_default_solver(self): + model = pybamm.current_collector.AlternativeEffectiveResistance2D() + self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) + + +class TestEffectiveResistancePotentials(unittest.TestCase): def test_get_processed_potentials(self): # solve cheap SPM to test processed potentials (think of an alternative test?) models = [ - pybamm.current_collector.EffectiveResistance2D(), pybamm.lithium_ion.SPM(), + pybamm.current_collector.EffectiveResistance1D(), + # pybamm.current_collector.EffectiveResistance2D(), + # pybamm.current_collector.AlternativeEffectiveResistance2D(), ] var = pybamm.standard_spatial_vars var_pts = { @@ -37,7 +73,7 @@ def test_get_processed_potentials(self): var.y: 5, var.z: 5, } - param = models[1].default_parameter_values + param = models[0].default_parameter_values meshes = [None] * len(models) for i, model in enumerate(models): param.process_model(model) @@ -46,19 +82,23 @@ def test_get_processed_potentials(self): meshes[i] = pybamm.Mesh(geometry, model.default_submesh_types, var_pts) disc = pybamm.Discretisation(meshes[i], model.default_spatial_methods) disc.process_model(model) - solutions = [None] * len(models) t_eval = np.linspace(0, 100, 10) - solutions[0] = models[0].default_solver.solve(models[0]) - solutions[1] = models[1].default_solver.solve(models[1], t_eval) - + solution_1D = models[0].default_solver.solve(models[0], t_eval) # Process SPM V and I - V = solutions[1]["Terminal voltage"] - I = solutions[1]["Total current density"] + V = solution_1D["Terminal voltage"] + I = solution_1D["Total current density"] # Test potential can be constructed and evaluated without raising error - potentials = models[0].get_processed_potentials(solutions[0], param, V, I) - for var, processed_var in potentials.items(): - processed_var(0.05, 0.5, 0.5) + # for each current collector model + for model in models[1:]: + solution = model.default_solver.solve(model) + potentials = model.get_processed_potentials(solution, param, V, I) + pts = np.array([0.1, 0.5, 0.9]) + for var, processed_var in potentials.items(): + if isinstance(model, pybamm.current_collector.EffectiveResistance1D): + processed_var(t=solution_1D.t[5], z=pts) + else: + processed_var(t=solution_1D.t[5], y=pts, z=pts) if __name__ == "__main__": diff --git a/tests/unit/test_solvers/test_processed_variable.py b/tests/unit/test_solvers/test_processed_variable.py index 224fe24d22..a2cc6a8174 100644 --- a/tests/unit/test_solvers/test_processed_variable.py +++ b/tests/unit/test_solvers/test_processed_variable.py @@ -522,7 +522,8 @@ def test_solution_too_short(self): t = pybamm.t y = pybamm.StateVector(slice(0, 1)) var = t * y - var.mesh = None + disc = tests.get_2p1d_discretisation_for_testing() + var.mesh = disc.mesh["current collector"] t_sol = np.array([1]) y_sol = np.array([np.linspace(0, 5)]) with self.assertRaisesRegex( From a17bf1e915643c0b0caf0c1d9fec2c76d34aeee0 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Mon, 18 May 2020 17:42:06 +0100 Subject: [PATCH 2/9] #997 add notebook --- .../Creating Models/2-a-pde-model.ipynb | 2 +- .../notebooks/models/pouch_cell_model.ipynb | 644 ++++++++++++++++++ old.py | 257 +++++++ .../full_battery_models/base_battery_model.py | 12 +- 4 files changed, 906 insertions(+), 9 deletions(-) create mode 100644 examples/notebooks/models/pouch_cell_model.ipynb create mode 100644 old.py diff --git a/examples/notebooks/Creating Models/2-a-pde-model.ipynb b/examples/notebooks/Creating Models/2-a-pde-model.ipynb index 09acd1e1c5..384f016072 100644 --- a/examples/notebooks/Creating Models/2-a-pde-model.ipynb +++ b/examples/notebooks/Creating Models/2-a-pde-model.ipynb @@ -298,7 +298,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.5" + "version": "3.6.9" } }, "nbformat": 4, diff --git a/examples/notebooks/models/pouch_cell_model.ipynb b/examples/notebooks/models/pouch_cell_model.ipynb new file mode 100644 index 0000000000..74507b1b8f --- /dev/null +++ b/examples/notebooks/models/pouch_cell_model.ipynb @@ -0,0 +1,644 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pybamm\n", + "import sys\n", + "import pickle\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import scipy.interpolate as interp\n", + "\n", + "# increase recursion limit for large expression trees\n", + "sys.setrecursionlimit(100000)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "comsol_results_path = pybamm.get_parameters_filepath(\n", + " \"input/comsol_results/comsol_1plus1D_3C.pickle\"\n", + ")\n", + "comsol_variables = pickle.load(open(comsol_results_path, \"rb\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:253: 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" + ] + } + ], + "source": [ + "cc_model = pybamm.current_collector.EffectiveResistance1D()\n", + "dfn_av = pybamm.lithium_ion.DFN({\"thermal\": \"x-lumped\"}, name=\"Average DFN\")\n", + "dfn = pybamm.lithium_ion.DFN(\n", + " {\"current collector\": \"potential pair\", \"dimensionality\": 1, \"thermal\": \"x-lumped\"},\n", + " name=\"1+1D DFN\",\n", + ")\n", + "models = {\"Current collector\": cc_model, \"Average DFN\": dfn_av, \"1+1D DFN\": dfn}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "param = dfn.default_parameter_values\n", + "I_1C = param[\"Cell capacity [A.h]\"] # 1C current is cell capacity multipled by 1 hour\n", + "param.update(\n", + " {\n", + " \"Current function [A]\": I_1C * 3,\n", + " \"Negative electrode diffusivity [m2.s-1]\": 3.9 * 10 ** (-14),\n", + " \"Positive electrode diffusivity [m2.s-1]\": 10 ** (-13),\n", + " \"Negative current collector surface heat transfer coefficient [W.m-2.K-1]\": 10,\n", + " \"Positive current collector surface heat transfer coefficient [W.m-2.K-1]\": 10,\n", + " \"Negative tab heat transfer coefficient [W.m-2.K-1]\": 10,\n", + " \"Positive tab heat transfer coefficient [W.m-2.K-1]\": 10,\n", + " \"Edge heat transfer coefficient [W.m-2.K-1]\": 10,\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "meshes = {}\n", + "for name, model in models.items():\n", + " param.process_model(model)\n", + " geometry = model.default_geometry\n", + " param.process_geometry(geometry)\n", + "\n", + " # set mesh\n", + " var = pybamm.standard_spatial_vars\n", + " submesh_types = model.default_submesh_types\n", + " # set npts\n", + " var = pybamm.standard_spatial_vars\n", + " npts = 16\n", + " var_pts = {\n", + " var.x_n: npts,\n", + " var.x_s: npts,\n", + " var.x_p: npts,\n", + " var.r_n: npts,\n", + " var.r_p: npts,\n", + " var.z: npts,\n", + " }\n", + " meshes[name] = pybamm.Mesh(geometry, submesh_types, var_pts)\n", + " disc = pybamm.Discretisation(meshes[name], model.default_spatial_methods)\n", + " disc.process_model(model, check_model=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "t_eval = comsol_variables[\"time\"]\n", + "solutions = {}\n", + "for name, model in models.items():\n", + " if name == \"Current collector\":\n", + " solver = pybamm.CasadiAlgebraicSolver(tol=1e-6)\n", + " solutions[name] = solver.solve(model)\n", + " else:\n", + " solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-6, root_tol=1e-6, mode=\"fast\")\n", + " solutions[name] = solver.solve(model, t_eval)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "R_cc = param.process_symbol(\n", + " cc_model.variables[\"Effective current collector resistance\"]\n", + ").evaluate(t=solutions[\"Current collector\"].t, y=solutions[\"Current collector\"].y)[0][0]\n", + "pot_scale = param.evaluate(pybamm.standard_parameters_lithium_ion.potential_scale)\n", + "U_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.U_p_ref) - param.evaluate(\n", + " pybamm.standard_parameters_lithium_ion.U_n_ref\n", + ")\n", + "V_av_1D = solutions[\"Average DFN\"][\"Terminal voltage\"]\n", + "I_av = solutions[\"Average DFN\"][\"Total current density\"]\n", + "\n", + "\n", + "def V_av(t):\n", + " \"Include effect of current collector resistance\"\n", + " return V_av_1D(t) - I_av(t) * R_cc\n", + "\n", + "\n", + "def V_av_dim(t):\n", + " return U_ref + V_av(t) * pot_scale\n", + "\n", + "potentials = cc_model.get_processed_potentials(\n", + " solutions[\"Current collector\"], param, V_av, I_av\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "tau = param.evaluate(pybamm.standard_parameters_lithium_ion.tau_discharge)\n", + "comsol_t = comsol_variables[\"time\"]\n", + "pybamm_t = comsol_t / tau\n", + "L_z = param.evaluate(pybamm.standard_parameters_lithium_ion.L_z)\n", + "pybamm_z = meshes[\"1+1D DFN\"][\"current collector\"][0].nodes\n", + "z_interp = pybamm_z * L_z\n", + "\n", + " \n", + "def get_interp_fun_curr_coll(variable_name):\n", + " \"\"\"\n", + " Create a :class:`pybamm.Function` object using the variable, to allow plotting with\n", + " :class:`pybamm.QuickPlot` (interpolate in space to match edges, and then create\n", + " function to interpolate in time)\n", + " \"\"\"\n", + "\n", + " comsol_z = comsol_variables[variable_name + \"_z\"]\n", + " variable = comsol_variables[variable_name]\n", + " variable = interp.interp1d(comsol_z, variable, axis=0, kind=\"linear\")(z_interp)\n", + "\n", + " def myinterp(t):\n", + " return interp.interp1d(comsol_t, variable, kind=\"linear\")(t)[:, np.newaxis]\n", + "\n", + " # Make sure to use dimensional time\n", + " fun = pybamm.Function(myinterp, pybamm.t * tau, name=variable_name + \"_comsol\")\n", + " fun.domain = \"current collector\"\n", + " fun.mesh = meshes[\"1+1D DFN\"].combine_submeshes(\"current collector\")\n", + " fun.secondary_mesh = None\n", + " \n", + " return fun" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "comsol_voltage = pybamm.Function(\n", + " interp.interp1d(comsol_t, comsol_variables[\"voltage\"], kind=\"linear\"),\n", + " pybamm.t * tau,\n", + " name=\"voltage_comsol\",\n", + ")\n", + "comsol_voltage.mesh = None\n", + "comsol_voltage.secondary_mesh = None\n", + "comsol_vol_av_temperature = pybamm.Function(\n", + " interp.interp1d(\n", + " comsol_t, comsol_variables[\"volume-averaged temperature\"], kind=\"linear\"\n", + " ),\n", + " pybamm.t * tau,\n", + " name=\"av_temperature_comsol\",\n", + ")\n", + "comsol_vol_av_temperature.mesh = None\n", + "comsol_vol_av_temperature.secondary_mesh = None\n", + "comsol_phi_s_cn = get_interp_fun_curr_coll(\"phi_s_cn\")\n", + "comsol_phi_s_cp = get_interp_fun_curr_coll(\"phi_s_cp\")\n", + "comsol_current = get_interp_fun_curr_coll(\"current\")\n", + "comsol_temperature = get_interp_fun_curr_coll(\"temperature\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "comsol_model = pybamm.BaseModel()\n", + "comsol_model.variables = {\n", + " \"Terminal voltage [V]\": comsol_voltage,\n", + " \"Volume-averaged cell temperature [K]\": comsol_vol_av_temperature,\n", + " \"Negative current collector potential [V]\": comsol_phi_s_cn,\n", + " \"Positive current collector potential [V]\": comsol_phi_s_cp,\n", + " \"Current collector current density [A.m-2]\": comsol_current,\n", + " \"X-averaged cell temperature [K]\": comsol_temperature,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "comsol_solution = pybamm.Solution(solutions[\"1+1D DFN\"].t, solutions[\"1+1D DFN\"].y)\n", + "comsol_solution.model = comsol_model" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "def plot(\n", + " t_plot,\n", + " z_plot,\n", + " t_slices,\n", + " var_name,\n", + " units,\n", + " comsol_var_fun,\n", + " pybamm_var_fun,\n", + " pybamm_bar_var_fun,\n", + " param,\n", + " cmap=\"viridis\",\n", + "):\n", + " # non-dimensionalise t and z\n", + " z_plot_non_dim = z_plot / L_z\n", + " t_non_dim = t_plot / tau\n", + " t_slices_non_dim = t_slices / tau\n", + "\n", + " fig, ax = plt.subplots(2, 2, figsize=(13, 7))\n", + " fig.subplots_adjust(\n", + " left=0.15, bottom=0.1, right=0.95, top=0.95, wspace=0.4, hspace=0.8\n", + " )\n", + " # plot comsol var\n", + " comsol_var = comsol_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", + " comsol_var_plot = ax[0, 0].pcolormesh(\n", + " z_plot * 1e3, t_plot, np.transpose(comsol_var), shading=\"gouraud\", cmap=cmap\n", + " )\n", + " if \"cn\" in var_name:\n", + " format = \"%.0e\"\n", + " elif \"cp\" in var_name:\n", + " format = \"%.0e\"\n", + " else:\n", + " format = None\n", + " fig.colorbar(\n", + " comsol_var_plot,\n", + " ax=ax,\n", + " format=format,\n", + " location=\"top\",\n", + " shrink=0.42,\n", + " aspect=20,\n", + " anchor=(0.0, 0.0),\n", + " )\n", + "\n", + " # plot slices\n", + " ccmap = plt.get_cmap(\"inferno\")\n", + " for ind, t in enumerate(t_slices_non_dim):\n", + " color = ccmap(float(ind) / len(t_slices))\n", + " comsol_var_slice = comsol_var_fun(t=t, z=z_plot_non_dim)\n", + " pybamm_var_slice = pybamm_var_fun(t=t, z=z_plot_non_dim)\n", + " pybamm_bar_var_slice = pybamm_bar_var_fun(t=np.array([t]), z=z_plot_non_dim)\n", + " ax[0, 1].plot(\n", + " z_plot * 1e3, comsol_var_slice, \"o\", fillstyle=\"none\", color=color\n", + " )\n", + " ax[0, 1].plot(\n", + " z_plot * 1e3,\n", + " pybamm_var_slice,\n", + " \"-\",\n", + " color=color,\n", + " label=\"{:.0f} s\".format(t_slices[ind]),\n", + " )\n", + " ax[0, 1].plot(z_plot * 1e3, pybamm_bar_var_slice, \":\", color=color)\n", + " # add dummy points for legend of styles\n", + " comsol_p, = ax[0, 1].plot(np.nan, np.nan, \"ko\", fillstyle=\"none\")\n", + " pybamm_p, = ax[0, 1].plot(np.nan, np.nan, \"k-\", fillstyle=\"none\")\n", + " pybamm_bar_p, = ax[0, 1].plot(np.nan, np.nan, \"k:\", fillstyle=\"none\")\n", + "\n", + " # compute errors\n", + " pybamm_var = pybamm_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", + " pybamm_bar_var = pybamm_bar_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", + " error = np.abs(comsol_var - pybamm_var)\n", + " error_bar = np.abs(comsol_var - pybamm_bar_var)\n", + "\n", + " # plot time averaged error\n", + " ax[1, 0].plot(z_plot * 1e3, np.mean(error, axis=1), \"k-\", label=r\"$1+1$D\")\n", + " ax[1, 0].plot(z_plot * 1e3, np.mean(error_bar, axis=1), \"k:\", label=\"DFNCC\")\n", + "\n", + " # plot z averaged error\n", + " ax[1, 1].plot(t_plot, np.mean(error, axis=0), \"k-\", label=r\"$1+1$D\")\n", + " ax[1, 1].plot(t_plot, np.mean(error_bar, axis=0), \"k:\", label=\"DFNCC\")\n", + "\n", + " # set ticks\n", + " ax[0, 0].tick_params(which=\"both\")\n", + " ax[0, 1].tick_params(which=\"both\")\n", + " ax[1, 0].tick_params(which=\"both\")\n", + " if var_name in [\"$\\mathcal{I}^*$\"]:\n", + " ax[1, 0].set_yscale(\"log\")\n", + " ax[1, 0].set_yticks = [1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e-2, 1e-1, 1]\n", + " else:\n", + " ax[1, 0].ticklabel_format(style=\"sci\", scilimits=(-2, 2), axis=\"y\")\n", + " ax[1, 1].tick_params(which=\"both\")\n", + " if var_name in [\"$\\phi^*_{\\mathrm{s,cn}}$\", \"$\\phi^*_{\\mathrm{s,cp}} - V^*$\"]:\n", + " ax[1, 0].ticklabel_format(style=\"sci\", scilimits=(-2, 2), axis=\"y\")\n", + " else:\n", + " ax[1, 1].set_yscale(\"log\")\n", + " ax[1, 1].set_yticks = [1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e-2, 1e-1, 1]\n", + "\n", + " # set labels\n", + " ax[0, 0].set_xlabel(r\"$z^*$ [mm]\")\n", + " ax[0, 0].set_ylabel(r\"$t^*$ [s]\")\n", + " ax[0, 0].set_title(r\"{} {}\".format(var_name, units), y=1.5)\n", + " ax[0, 1].set_xlabel(r\"$z^*$ [mm]\")\n", + " ax[0, 1].set_ylabel(r\"{}\".format(var_name))\n", + " ax[1, 0].set_xlabel(r\"$z^*$ [mm]\")\n", + " ax[1, 0].set_ylabel(\"Time-averaged\" + \"\\n\" + r\"absolute error {}\".format(units))\n", + " ax[1, 1].set_xlabel(r\"$t^*$ [s]\")\n", + " ax[1, 1].set_ylabel(\"Space-averaged\" + \"\\n\" + r\"absolute error {}\".format(units))\n", + "\n", + " ax[0, 0].text(-0.1, 1.6, \"(a)\", transform=ax[0, 0].transAxes)\n", + " ax[0, 1].text(-0.1, 1.6, \"(b)\", transform=ax[0, 1].transAxes)\n", + " ax[1, 0].text(-0.1, 1.2, \"(c)\", transform=ax[1, 0].transAxes)\n", + " ax[1, 1].text(-0.1, 1.2, \"(d)\", transform=ax[1, 1].transAxes)\n", + "\n", + " leg1 = ax[0, 1].legend(\n", + " bbox_to_anchor=(0, 1.1, 1.0, 0.102),\n", + " loc=\"lower left\",\n", + " borderaxespad=0.0,\n", + " ncol=3,\n", + " mode=\"expand\",\n", + " )\n", + "\n", + " leg2 = ax[0, 1].legend(\n", + " [comsol_p, pybamm_p, pybamm_bar_p],\n", + " [\"COMSOL\", r\"$1+1$D\", \"DFNCC\"],\n", + " bbox_to_anchor=(0, 1.5, 1.0, 0.102),\n", + " loc=\"lower left\",\n", + " borderaxespad=0.0,\n", + " ncol=3,\n", + " mode=\"expand\",\n", + " )\n", + " ax[0, 1].add_artist(leg1)\n", + "\n", + " ax[1, 0].legend(\n", + " bbox_to_anchor=(0.0, 1.1, 1.0, 0.102),\n", + " loc=\"lower right\",\n", + " borderaxespad=0.0,\n", + " ncol=3,\n", + " )\n", + " ax[1, 1].legend(\n", + " bbox_to_anchor=(0.0, 1.1, 1.0, 0.102),\n", + " loc=\"lower right\",\n", + " borderaxespad=0.0,\n", + " ncol=3,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "t_plot = comsol_t\n", + "z_plot = z_interp\n", + "t_slices = np.array([600, 1200, 1800, 2400, 3000]) / 3" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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MJaL5AI7CXPMiCIIgCIIg1BIiXgRBAzM/AuARX/IwmLuB2XkYwFRfng+sD6yF+lfWlo+CIAiCIAjHGiJeBCEmzLwIslheEIT6g2EYBiUSCVm8KghCo8EwDAJghJ1vvPvNCYIgCELjpmznzp1trD/0giAIDR7DMGjnzp1tAIS+ZkIiL4IgCILQAKmqqvrh9u3bn9q+fftgyMNIQRAaBwaAsqqqqh+GZZCtkgVBEARBEARBaBDIkxpBEARBEARBEBoEIl4EQRAEQRAEQWgQiHgRBEEQBEEQBKFBIOJFEARBEARBEIQGgYgXQRAEQRAEQRAaBI1OvBDRiURURUTfTrEcEdGjRLSWiJYT0TDf+dZEtIWIftuQfSKi8yxbnxDRYiIaLT7Vb3+sMpdZtj4logVENDQVnywbt1o+rSaic3zncojoP0Q0t4H71J+IPiKiCiK6KVV/asmn04mo3LqfPiGiOzLlExFtsPr/EyJanKpdQRAEQWhoNKr3vBBRDoD7AcxLo/g4AH2sz0gAs6yfNncD+LAR+PQugDnMzEQ0BMDfAPQXn+q1PwCwHsBpzLyXiMYBeNJnMxIiGgjgUgCDAHQB8A4R9WXmaivL9QBWAmjdwH3aA+AnAM5PoUxt+wQA/2LmCbXk0xnMvCsd24IgCILQ0GhskZcfA3gRwFdqIhH9jIj+bT0lviuk7HkAnmWThQDaElFnq/xwAIVIT4DUK5+Y+SC7L/dpCcB50Y/4VD/9sXxawMx7rcOFALoqPn2PiBZZT9+fsASzzqfnmbmCmdcDWAtghFW+K4DxAJ5qBD59xcz/BnDUfy5bPkVRU58EQRAE4Vij0YgXIioCcAHMp9xq+hiYT8BHADgBwHAiOlVjogjAZuV4C4AiIkoAeBBAylNQ6qNPVv0XENEqAK8BmCw+1X9/fPwAwBuWTwMATALwTWY+AUA1gMvi+mR9fwTAzTDfatuYfHKoBz6dRETLiOgNIhqUQZ8YwDwiWkJEV6fhlyAIgiA0KBrTtLFHAPycmQ0iUtPHWJ//WMetYA5A407bmQrgdWbe4rPbUH0CM78M4GVr4H03gLPFp/rtjw0RnQFTKNjrcM4CMBzAvy2bzeGL8iWxNwHAV8y8hIhObyw+acimT0sBlDDzQSL6FoBXYN43NfLJYjQzbyWi4wC8TUSrmDnl6a2CIAiC0FBo0OKFiK4DMMU6bAPgeWsQUADgW0RUBYAA/IaZn4go+y0AWwF0U7J0tdJOAnAKEU2FOVhtSkQHmfmWBurTt5j5SwBg5g+JqCcRFRzrPtU3f0LsFsCcsjSOmXfb2QD8iZlv9ZW9AMCd1uEPI3w6F8C51qA6D0BrIvp/zPy9huqTfe382eqDT8z8OhE9rtxPNfEJzGz//IqIXoYZFRTxIgiCIDRemLnRfQD8EcC3re9jAHwMoJV1XATgOE2Z8TCnvRCAUQAWafJcCeC3DdknAL0BkPV9GMxBEIlP9dcfK38xzLUOJ/vSBwL43PYDQHuYT/n95QcBWAagGYAeANYByPHlOR3A3Ibsk1LulwBuqg8+Aeik3E8jAGyy7o0a+QRzPVa+laclgAUAxqbaV/KRj3zkIx/5NKRPg468xIGZ51lzyz+yIiAHAXwPwekZr8N8krwWwCEAVzVSny4CcDkRHQVwGMAkZrbnzYtP9dMfALgDQAcAj1t1VzFzKTOvIKL/tnxLwFyofh2AjWphZv6MiP4GYAWAKgDXsbtbVaPxiYg6AVgMczcwg4imAxiY5X76NoBrrajrYQCXWvdTjXwiokKYUxsBM4r+V2Z+s4a+CoIgCEK9xn4aKAiCIAiCIAiCUK9p9JEXQRAEQWiMLFmy5Ljc3NynAAxGI9o9VBCEYxoDQFlVVdUPhw8frt3ERsSLIAiCIDRAcnNzn+rUqdOAjh077k0kEjKNQhCEBo9hGLRz586B27dvfwrmZjkB5EmNIAiCIDRMBnfs2HG/CBdBEBoLiUSCO3bsWA4zoqzPU4f+CIIgCIKQORIiXARBaGxY/66FahQRL4IgCIIgpMzatWubjBw5sm+vXr0G9e7de9Ddd999nH1ux44dOSeffHKfkpKSwSeffHKfnTt35gCAYRi48soruxUXFw/u27fvwPnz57fIXguEOOzatStn7NixPXv06DGoZ8+eg955552WgFzjxsTFF1/cvX379kP79OkzSE1P5xo/9thjHUpKSgaXlJQMfuyxxzrUhr/HtHghoquz7YOf+uZTffMHEJ/iIj4lp775A9RPnwRBR5MmTfDggw9u+eKLLz7797//vfLpp58+bsmSJXkAcOedd3Y+/fTTD2zcuLHs9NNPP3DHHXd0AoD//d//bbNu3bq8DRs2lM2aNWvj1KlTi7PbCiEZV199dbcxY8bsX79+/WcrVqxYccIJJxwB5Bo3JiZPnrxrzpw5n/vTU73GO3bsyLn//vu7LFq0aOXixYtX3n///V1swZNJjmnxAqA+DhLqm0/1zR9AfIqL+JSc+uYPUD99EoQAJSUlR0ePHn0IANq1a2f06tXr8KZNm5oCwJtvvtn2mmuu2Q0A11xzze433nijHQC8+uqrbS+77LLdiUQCZ5111tf79+/P3bhxYxPV7v79+xOnn3567379+g3s06fPoD/84Q/t6rptgsnu3btzPv744/zp06fvAoC8vDwuKCioBuQaNybGjRt3sGPHjlX+9FSv8SuvvNLm1FNP3V9YWFjdsWPH6lNPPXX/Sy+91MZvd+rUqUW9evUa1Ldv34FXX31111T9ld3GBEEQBEGoEatXr266YsWKFqeddtpBANi9e3duSUnJUQDo1q3b0d27d+cCwLZt25p079690i7XuXPnyo0bNzax8wLASy+91LpTp05HP/jgg7WWrYw/uRXisXr16qbt27evuvjii7uvWLGixZAhQ77+wx/+sLl169aGXOPGT6rXeOvWrU26du3qpBcVFVVu3brVI1y3b9+e8/rrr7dbt25dWSKRwK5du1K+9seUeKEWxzGMSgBkJuS2AOW1dxc7EvlL6I+T5nOTyZeLlO/qSftrTtN8NGtV6PgUqErnVWQe9iToPKXAF/ewWfNWaN32OFYTQ1qr9cM163UgzEaUfbtcy5b5KOhYGFikGtYObZLPWW2dyXxRLmLr1q3RuXNnj0/+axzH11T9COtzAGjXrjVKunVmfX9474uo+iOva1hfU3ANMQHoWJCPPj0LOfI+IMW/lPzh6PY4B26XdC5siUH9Ctit1zwfXZ+TXVOfrl81l4B0l4VBBHTr0gzDjm/NnrLk9Svs+tkJS5Z//RYzjw1UITRaJk+e0q2srCyjawsGDx58aPbsP2xOlq+8vDxx4YUX9rrvvvs2t2/f3vCfTyQSoKh/rHwMGzbs8C9+8Ytu1157bdF5551XPnbs2IMput4oefe2Z7vtXrM1o9e4Q9+iQ2fde3noNa6qqqKVK1e2mDlz5qYzzzzz66uuuqrb7bff3mnmzJlfqvnkGmcGY+GPuvG+FRm9xtR24KHEqN8n/T1ORqrXOIwOHTpUN2vWzJg0aVL3CRMm7Js0aVJ5qjaOKfGC6kqg2+kAJcyPM4KyjongzKRz8iTc0YtzrJwDzPO2PWVUSgTkEpBjDTRyCcghIAdAgswPACTAzrGbBhCZ6QQ3naw8ZA10ADh5SClvH5M1SPLkVfI77jv5/eU1eZOUdwSaJy+FlkegvC+vzyaIQuonTxtcGxT0yU7z2PCWV/M4/qs2FQMBu/7+oHB/g33I+n7VXRtfmqce6x7R5+UQm7r0GGnkr09pg3XOvYfZkw5N3U55T35fXuUcfPnsvAm4x2H5gj4o5TVpbjt96cRIaNLcegzFrpJOhi+vgYRT3nDSzHRDSTec3wenAQnz36REp4UFEIQ6oKKigsaPH9/r4osv3nPFFVfss9M7dOhQZT9t37hxY5P27dtXAUDnzp2Pbtiwoamdb9u2bU3VJ/IAMGTIkIqlS5euePHFF9vcfvvtRe+8887+GTNmbKu7Vgk23bt3rywsLKw888wzvwaASZMm7b3vvvs6AXKNjwVSvcZFRUVH//nPf+bb6Vu3bm162mmnHVBtNmnSBJ988snKOXPmtP773//ebtasWcctXLhwTSp+HVviRRAEQRAaIXEiJJnGMAxceumlJX379j3yy1/+cod67pxzztn3xBNPdLj33nu3P/HEEx3Gjh27DwDOPffcfY8//vhxU6ZM2fP++++3zM/Pr/YPbDds2NDkuOOOq5o6deqedu3aVT/99NMixgFERUhqi+Li4qpOnTpVLlu2rNnQoUMr5s2b17pfv35HALnGtUEmIiSZJNVrfP7555f/6le/KrIX6f/zn/9s/fDDD29RbZaXlycOHjyYmDRpUvnZZ599sFevXsen6peIF0EQBEEQUubtt99u9corr3To06fP4f79+w8EgLvuumvrpEmTyu+6665tF1xwQa+SkpKCoqKiypdffvkLALjkkkvKX3vttTYlJSWDmzdvbjz11FMb/HaXLFnS/NZbb+2aSCSQm5vLjz/++MY6bpqg8Nhjj2267LLLelZWVlJxcXHFc889twEA5Bo3HiZOnNhj4cKF+Xv37s0tLCwccsstt3x5ww037Er1GhcWFlb/7Gc/+3L48OEDAODmm2/+srCwsFqta9++fTkTJkzoXVFRQQBw9913pyzYiPnYeb8VNWvLMm3MOx3Jcd/J7y+vyZukvG7alEwbC/c32IcybUymjdV42tgSZi6F0KhZtmzZhqFDh+7Kth+CIAiZZtmyZQVDhw7trjt3rG+VLAiCIAiCIAhCA0HEiyAIgiAIgiAIDQIRL4IgCIIgCIIgNAhEvAiCIAiCIAiC0CAQ8SIIgiAIgiAIQoNAxIsgCIIgCIIgCA0CES+CIAiCIKRNVVUVBgwYMPCMM87obaetWrWq6ZAhQ/oXFxcPHj9+fM8jR44QABw+fJjGjx/fs7i4ePCQIUP6r169umm4ZaE+cNdddx3Xu3fvQX369Bk0ceLEHocOHSJArrGQPUS8CIIgCIKQNvfcc09h7969D6tpN954Y9dp06bt2LRpU1mbNm2qZs6cWQAAM2fOLGjTpk3Vpk2byqZNm7bjxhtv7Jodr4U4rF+/vsmTTz5Z+Mknn6z4/PPPP6uurqannnqqPSDXWMgeIl4EQRAEQUiLL774oslbb73VZsqUKc7LMg3DwEcffZR/1VVX7QWAyZMn7/7HP/7RFgDmzp3bdvLkybsB4Kqrrtq7YMGCfMMwPDY3btzYpLS0tF///v0H9unTZ9Cbb77Zqg6bJPiorq6mr7/+OnH06FEcPnw40bVr16NyjYVsIuJFEARBEIS0uO6667r9z//8z5ZEwh1O7NixIzc/P7+6SZMmAIDu3btX7tixo6l1rmmPHj0qAaBJkyZo1apV9Y4dO3JVm7Nnz25/1llnla9atWrFypUrPxs5cuShumuRoNKjR4+j11133fYePXoMOe6444bm5+dXX3jhhfvlGgvZJDd5FkEQBEEQ6jMP/OjZbutXfNkikzZ7DOxy6Ge/v3xz2PnnnnuuTUFBQdUpp5xyaO7cufmZqnfUqFFfX3PNNd2PHj2a+Pa3v7335JNPPpy8VONn52/v7Va5aV1Gr3HT4p6HOk67LfQa79y5M+e1115ru3bt2k87dOhQPX78+J6PP/54+wsuuGB/TeqVayzUhGNLvFSWv4UvXi2oq+oYwFHrIwiCUIfsSp5FEGrG/PnzW7399ttti4qK2lRUVCS+/vrrxHnnndfj5ZdfXn/gwIGco0ePokmTJtiwYUPTwsLCSgAoLCysXL9+fdNevXodPXr0KA4ePJhTWFhYpdodN27cwQ8//HD1iy++2Gby5Mk9pk2btmPatGm7s9PKY5t//OMfrYuLiyu6dOlSBQDnn3/+vgULFrT60Y9+tEeusZAtjinxwsxjs+2DIAiCIGSaqAhJbfG73/1u6+9+97utADB37tz8Bx98sPDVV19dDwCjRo068Mwzz7S7+uqr986ePbvDhAkT9gHA+PHj982ePbvD2Wef/fUzzzzT7qSTTjqgTjkDgDVr1jTt2bNn5U9/+tNdFRUVtHTp0hYAjvmBbVSEpLbo3r175dKlS1sdOHAg0bIXJacAACAASURBVLJlS+O9997LHz58+KFEIiHXWMgax5R4EQRBEASh9nnwwQe3TJo0qdc999xTNGjQoEPXX3/9LgC4/vrrd1100UU9iouLB7dp06b6hRde+MJf9q233sp/9NFHO+Xm5nKLFi2q//KXv6yv+xYIAHDmmWd+PXHixL1DhgwZkJubi0GDBh268cYbdwJyjYXsQcycbR8EQRAEQUiRZcuWbRg6dKhMERQEodGxbNmygqFDh3bXnZPdxgRBEARBEARBaBCIeBEEQRAEQRAEoUEg4kUQBEEQBEEQhAaBiBdBEARBaJgYhmFQtp0QBEHIJNa/a0bYeREvgiAIgtAwKdu5c2cbETCCIDQWDMOgnTt3tgFQFpZHtkoWBEEQhAZIVVXVD7dv3/7U9u3bB0MeRgqC0DgwAJRVVVX9MCyDbJUsCIIgCIIgCEKDQJ7UCIIgCIIgCILQIBDxIgiCIAiCIAhCg0DEiyAIgiAIgiAIDQIRL4IgCIIgCIIgNAhEvAiCIAiCIAiC0CAQ8SIIgiAIgiAIQoNAxIsgCIIgCIIgCA2COhcvRDSbiL4iojIl7QEiWkVEy4noZSJqq5y7lYjWEtFqIjpHSR9rpa0lolvquh2CIAiCIAiCINQt2Yi8/BHAWF/a2wAGM/MQAGsA3AoARDQQwKUABlllHieiHCLKAfA7AOMADATwHSuvIAiCIAiCIAiNlDoXL8z8IYA9vrR5zFxlHS4E0NX6fh6A55m5gpnXA1gLYIT1WcvM65i5EsDzVl5BEARBEARBEBopudl2QMNkAC9Y34tgihmbLVYaAGz2pY/UGSOiqwFcbR7kDEeTVvG8oLjuxs4YMy+lZjKuzdjm4uaNl49iNocAJGJWTYjnJoFjN4ec/2nS1eMUujJue+LmAwEU4kC6fprXJ1Znxr8+ZNcfXSBBrMnDTn3evNrkoM2wxzGa8okEJ7FmkhMzHxHHskkAEglD517ggMCghBHdbjLr/KTswC5m7hjLWaFRUFBQwN27d8+2G4IgCBlnyZIloX/T6pV4IaJfAKgC8JdM2WTmJwE8CQDUrC2j62npeBZxKhFzHE9mXt0oyk8i7mXJsWwmqzoHSOTEsEcA5cI3egrJmkBOIsc5rctG1qepr9kE/fe8HLYGqRzZPTkE5Gqao9ozjxl5TYJ5dOTmqAPfYP32cSIBNM0l7bkom2H9AzBycyjQnrDBbNMm4WpQbX+zpkBCvTdCyiQSQJNc9R5yM/qFZ7NmQA7leHNq7CZygCY5wXuIYIV6leMWzZVsEb8aubmMHE0fuULJpEnOUeTlKed9BlXbTZtUIZGwBIIvg3rd8vIq0TSHXb+JnWvnFCEAMJDXzAwgJ8CeC2IKFlfYtGx+CE2auAKGSBEo5Ipuoio0a1Zpmkq4dQLm7wol2EnL7/mvjRCOKbp3747Fixdn2w1BEISMQ0Shf9PqjXghoisBTABwFjPbf6G3AuimZOtqpSEiPZNeZdAWA+wOgBD1gJbjPel1DCV7zJ6KOSBes9mbTfcMPZlJe9jlFzHJHQg2yN+til5KgeiO8oujTJDUJoV8D0lmWLdDyo5qBBkDTOG3V7Jr7rdMcHuYfO1K516ybbBVIDTKF2JQ7Sa2/VBtKpUxmd6b/UJgcoWLm5UcIcPWd1J+59kwv9gihtmyaZ9X7Jj1s0ec2aaI2Dk2f/1jxc4EQRAEoVFQL8QLEY0FcDOA05j5kHJqDoC/EtFDALoA6ANgEcy/4X2IqAdM0XIpgO9m3rOwwWwNhgoZNWmNylSboaO3FM2qZGBkxMoA0jcuBABUK1WHRT3C3NPZNOAOLPVxBR3uWdbUxJbhZP7p0sOugPPcPCLqEJWu2nYG4poODpRXrwUD8E3hYuULa8rpjikki+2PWoM9EDfYnBLmv+7s6w9dX9p2LV0BZsBQbIX+WihGPW1zgxgeVWNUG0CON78qepzIDbn96Z53HSKrtGEA5h2qiBDPFEd22uUKGVXE2J3DIKvdDO80NEEQBEHIJvOnj8UJfRcjr81hHClvjk/WlGL0I29mxHY2tkp+DsBHAPoR0RYi+gGA3wLIB/A2EX1CRL8HAGb+DMDfAKwA8CaA65i52lrcPw3AWwBWAviblbe2vUe8oXQUvvyZepxf52EBAwbUIVjNzBPcg6A99nySDeTVMSg0x8mJLpG6vWgI7lP0sPOpYhjWoFYnROOqL00WrU37HJL3iyePIjr8NlO6ne0IhFWQjaA9rUhh7xlPMIhhLyVxoi0wrPSAA6Z8sc/puteJhlmG2VGs5K47Ylv9mBaciJLjg2vQjTKp8UtBEARByD7zp4/F8AGLsHjLuTgyZiMWbzkXwwcswvzp/s2G06POIy/M/B1N8tMR+X8N4Nea9NcBvJ5B12KgG5qlov80A4zYUY6aDE7SeZ6fmk1dNMVzHBUFUI1oozPqc+70cYZ55FrUt8ILhXxn5afOZlTvhvWTOuj2T61KF2bFR2VAHO2Rz4b9P+fpv1LK3+CIyxRokpJgWOVyNK6ETV3ziIVAhCJY3nNfOf/jYBN8oRq28jj9wAgsN2O7oE8F2VERXUSKyIqkEKzpYHYt/tiR1wAHhHwm5bQgCIIgpM8JfRfj4zVnoGf+P7HsL4/j9Htn44PbgNK+czJiPxvveTmGqckAI8lzbY742HN/Ah/2fVKrUueCPxLjn7qjfgLlOVil16b1pDqJH8me2oc96U/VTjKbrCmsjd2FVOL0RRrCJax/7clF6dyJ2qhWzL60owWeSILfsIXBbuRIzaIx6RXHqnjy2YyKGNl3lKNllA85YRNN2w3zo/OJiAEyrI++Vtsv10eypoQpUophrmkJRFpU6awNBwmCIAhCVshrcxgj+r6PLr23I2f9uwCA0hv+B3ltDmfEvoiXOqemT0hDBi/R6gVwJnkZMcuwMndG99E/u1fHj+q4zjMFJ4VWqmXiDOa1g3YEe4NhDpKr2fxpTtsKxmFiaT7rBFuD7mpDtZncF20j1KfsEQPv2ChTjWx7hsdmdAVqZII0J5iVwXySixDadnbvE2vcbvajxhetaLHr0ShkT3SG1dQQb1RfrLz+ep3F9OrNbosWRVDoBKu95bX5w/SByPy4U8r8BV2HyPrPdULUiyAIgpBdKg8fwua7egAAcppW4f8+vwKjZv4TALD44ZtxpLx5VPHYiHhJi6j4QZxyqZ2KtpdqdZExiRr4oq8+br7QaAyCw0s2wkWA/7tukKwrw8ww/wuXf1H489hTgqLwj7kDiRqbaWELDOj9TFZUFS6BvtOIEfV74NrqIi/+sopBe2yvdTMkXGZrbtVvnU3A8PjlETu+KJEdm7F3FAtcO6tzDOse0ph07Dp+WZWYu4VRUF2DwMww2LXqlLeNs+VTKi8gEgRBEIQMs/Kt11D+aF906fMVjMocGJUEPnoEB3fuwge3TcbIklfwyZrSjNQl4iVlajJI0AzBaiQUIuyF2owxJI8zSPYN7Mh7KlB9WOwmWfNJKeHKi0i30oJDnl7X1eUJRAZSECpJNWqErVhrSZTEsGsdKUZCDQbvIXtgToAb9PO1QdccgmZgr1ZJ8Kx7saQA2L7DfEb94scT4LBFB+BESzwXzReRA3vLu+9wIbf/yRIxRCB7upkbzlEiVnbd5NlGWaSLIAiCkC2WTD8RvbdPQtsu+7Bk0QlIfG83lqw8CaVd5yBvXglKu87BkpUjMrbbWL3YKrlhUAvDgxqbtCVATcqrjlD4qRik4olfNauDVq8DyfJ5z0WJqFDB4Mlrp7I2b+QDbt85XfTFf8V0kQWPkNE57kO1qbmSKaCv0ONvEp8IwStnz8ZLKHkcgaLYScVnO0KTCBNFEcbs+tXrY18HR1yovwoJXXl/R7BrWBUxlqIipVeC38hzXi/9vUfsaXsySS8IgiAImefQ3r3YcO9pGHriF4BB+HDN93DmI78HAI9QaQVgdAbrFfGSlEyLlhjziWKjPK+ONEkIbI1UI3vwTsGBPrtOLOikgVeweJZPR1euseGP6EQJFk+6MhBM5rv/8oV6qosAaE5H+pnGrZL+03j/ldCc8rc9ZiUBWxF24pi0hY8tYjyCQ3d9klwH9cAWB+quZ6wIDPUFlf4GOP8nOAKHAOfdLKS8T8cVT8q0MI9lO039fXTjL/b6IkroJKMgCIIg1B4f/PLHGNb+efT7xiFsXV2Igyc/ijO/P6FO6hbxkpSwQUG6AoRqxWQ2UKtNFgOKEi3uGm/9TmLRz6HD69GNZaO7Si9c1LMJja4LFUSRdak1IlIvRgkZXd+wquDC8pKv/oj6WM0Y0Xhtf2t8VgUHQ/mpnk/Wz2oZVcSoNjTuevwlt7zfL0DZ0IABc8tjq5y1tbElZYLXh5R8nnNsvkVTESL24nx74b7ZJv8cNluc2HX5Wim6RRAEQahD/jl9IkaXvgcAWPjxSfjmzHfqtH4RLylTU6Vgz03JhC+KSSDCZhqjm6Q2DRjI0UYNUvXAeW5MppBJZyGWZ5zpeBhMi4YUW3qPDSOtGXWR7VcFR6q3RdhkI8MAKKEM0BGSMcqmpqFRGxHo2qjb7lgdetvrQigRLjjtY499ddzuExxORMIn0Ah+I15h5vilzgADwIZhvqAycLOz5zuxN1ndeM2xTQwwg609lp3dxpyO8No1F/K7LTBsAUO21GdwjbeiEwRBEITkrFv0EfjVyzF6xJeoKG+GjzdMwBkzn61zP0S8pEy6AwXSjX602YKjw4hn8nHm7WizRJSLNYJWB/pJogYhEQNdREQdpHqLcSBvGGp5htdm9BP91K5tPJvJcfqCFd9rYlDB84JKnx2vyfgVOC+o1BVJwU9P5ES5aFrxGmLXuW+U8s57IpW2B+p0SkdPQbRT2IqSOPVpFCGbi1zcyItthQAm385mUIUdgRI6ic3eJM81NDevCERpBEEQBKEWeP/OaRjd649IDGJ88WkxCqe/izMKu2TFFxEvDYJ0nvWr6MrpbFrD6Mi5ROqBd9hvF1MHn/6lxGFP1gHziTkndINHs0QqIiOsp+zBvH/6lzsdR+9vlN1omzF802R0BEKG9gN03kHKQCKhqzJ5fIq9Y3NP1MR01voRcnn861occalUbb9IM6Dhk4gXXf22r36x5brHVjH76vtCMHYZjfixX06pXp9AFIwY6tuOvFPC7KiJWQc7U8zYK7a0QtH9bdNOMxMEQRCEDFF19CgW3XQORg9bBBCwYmlvHD9jWVZ9kq2SGxSqRADSFzNRNn2EBovCpYTOIvk+qXhkH9uv14wqr9qPnKrF1pvcA5nS71PbphqRiVVOl2jrSAbSmRUUeslI42d4icDZUPFmT9dKcoFCr7/votsv/DTUuX86O7qbSlOJLWLs6IkdmXGiI6pw8dn0rMRS/HCiOwxna2VTdDFAhifRNefvSXval/lxhYy9bTKUd7ionaS8b0bdM1kQBEEQMsQnL76Aiqc6YeTIj3FgVz5WtZqddeECZCHyQkSzAUwA8BUzD7bS2gN4AUB3ABsAXMLMe8n8qz0TwLcAHAJwJTMvtcpcAeC/LbP3MPOf6rIdmREO6ZpMYTTrzjOJbzPFpoU9IDcA5GhqiRuRUJ9RkyY9qmxYmg6DbT+DlnXxqWQCyolyhJ3XlFenUIXZTIsIR+PaVIfbft/9/aNrOymZ2UoIdUsTvjPCbs3Q8Jp7jnxptohxIyMae+xeC7fNwbCSHdlRbXqmh7FOU7ATVfK+WNKKpChlmMnqT3V6mLKtsiJqRLsIgiAINWX+9LE4oe9i5LU5jMqDzTCgSRVyWldjxxcFaHdDGY5vlZ9tFwFkJ/LyRwBjfWm3AHiXmfsAeNc6BoBxAPpYn6sBzAIcsXMngJEARgC4k4ja1brnAOLFDnSkE92I40umbSJpMMa2739IrT7FJnjn4+siKQiUDVTh2HRfUFk7U2TsCUR+TwIpUQNvP5qMUW1VHEmZSDEQdetReEadr7rjqP4IiA1NRMTzcdSAFbiwRYE9Fcxn3x+HdISBpu6gn8pdqvPLMp6wy1uCI0HmFMGEXcx21LpDDSXCY3erR7AoddnRlQSR8yFnupkZymJmd0MHR+EqL6qs0S+7IAiCIJjCZfiARVi0/hxsKCtC05YVyGlajbXLi9Hl9o1oXk+EC5AF8cLMHwLY40s+D4AdOfkTgPOV9GfZZCGAtkTUGcA5AN5m5j3MvBfA2wgKogyT4QFC1Kg9NiFzaTJhM2UbtmCJfiBuPxTX5iP/ueCAOs7Y3m8/vh5w64vTjqTWfBGDqC712GR/QjRauzUQw6GiheCdHhXDIsOMUKiRkEB5RxiE2GbvsVb8+gqpb7T3pCtt8VThn1JGcNUJ+ev3OasahzvJzJyaR0HBovhopwRlPgXyO1MICeZaG3IzyLoXQRAEoSac0HcxPl55Mkb0eBM9jt+K/TtaY/7SMehasjPbrgWoLwv2C5l5m/V9O4BC63sRgM1Kvi1WWlh65oizWhgwRxGxB4rk+1lTdPNjwvLFhQKmo/LZgiXCUugxw/fWdeVMqj0U5m4yH/Rng/0VdTeE2ozoQ489jrCZ9DpoZ1rVSMOqrU/4b1n/IFxTie5uU5vhWbiv3m5RtzJpDlUlrGYh36mQjrCnaAWEriJYCJb4UtJ1E+PIk279blgX1gBAbO8o5r+72ffTLs/OtDK2BJHzLhgGmK0HBTlWmr6JgiAIghCLvDaHcdKQfyHRpArbv+iIDj9dgdKvDyFvXkm2XQtQ7xbss7t6NSMQ0dVEtJiIFsOoTLU0Mic0VNj7dD3FJ+1hJtMrH/V4OnlJW76wx07Qpm64BriTY7xVh9kKdyyOcElOdCe6A8iaE3y+HlGp7rsvmaB4H/e2DeRhzymPTQ1xbzf/lfP4af30b2ccmB6mBAT9IsheZ6PuhBbHUY9P5I0QgeFZv8NkxTasivybFNvxOkcsWV9UYcoGgQ03MuPfjMHbbnJ2ILMjSGpkyLbCBiybtfHv1LELEbUnoreJ6HPrp3ZaMhFdYeX53FqHaacPJ6JPiWgtET1qrd8MtUtE/YnoIyKqIKKb6qaVgiAIwBfzP8ShWe1BBFRXJrDkwB0oun0D8lq0wOKHb8aR8ubZdjFAfREvO6zpYLB+fmWlbwXQTcnX1UoLSw/AzE8ycykzlyLRNEW3MqEq/ISMLGtLJwEIWRkQXmGcZrORUq/4NZoBbxXVlms6m36Pw57sh9WRTAp5JZb5sQenfnv27lfxbYb7F+gHaxDvn+6U5GoFLpW9U5daMOAf+fvSW4PjozWAdxbNJ2m07qWY9iDd3t2N2Ztma3kPpBEU/r5jd9c0Z3cydn0NvY0Vm552si0GvMdGtWG+qBLs+Q+ObetuIdeWbZjZFCzM7s1tGPZLKs1MzpoW750GIgMEgvo4R+07NYJjBLfNE2pG2DpMhyRrL2cBmAJ3zaY9rTnM7h4APwEwo1ZaIwiCoOGDn30XRavORdP8ChzelwciA0e2rMbBnbvwwW2TMbLkFXyypjTbbgaoL+JlDgD7qdUVAF5V0i8nk1EAyq3pZW8BGENE7aw/FmOstFogmapIddDgy1+roiVG/WHE8EsdfAfPJBd9YYP9aHvJp5QFBvNJPUlmIZ0c8XHa73sSX1PUJ/uO2dDrmvxa+W2mbsWbxx6vqyLJ76Y/yqL1y7oY6uZhkVEN+8AprNiy61Xskf1/K0wY7EIr8miV8btqi0XPDgTKWUfwOQLHEtCWj052pT1mmXi/Z0JahK3DVNGuvbQewLVm5oXWTIJn4V3HGbDLzF8x878BHK2V1giCICiseucNHPxdAU75xquorszBR1umodXU3Viy8iSUdp2DvHklKO06B0tWjsDoR97MtrsBsrFV8nMATgdQQERbYD65ug/A34joBwA2ArjEyv46zG2S18LcKvkqAGDmPUR0N4B/W/l+xcz+TQBScUqXmLa5JJV5D/3jjtBqY/roHwFq83FIevpttodQCY8dvdDQeUOeL/5mEIKp6fuoRge8sQY9FPJdZ9OTN6I7I+WwPWgOOpkWqoBRoy7xPXKFhnN9FAUS9yWVgLdPyFet+rLPVLzzaYHASy/VeoN3vi1N2JPuWeeixqjIjazoXyBKyv8BkAF1RYrrG5nrVsiMzti/AObsIn0HqveDuvMeeVomZIiwdZgqUWsyt2jS49oVBEGoNT64/VqMKHoeTdtW4sCOVjAu/BinlHQHAI9QaQVgdHZcTEqdixdm/k7IqbM0eRnAdSF2ZgOYnVLlziPQhkiY4KhJkYgMaVQXLEbOwC1KADhlWRk0KvkM59heDRNPaIT6qAxonQE9goPGVJrOSsNjD7TtsiEF0rwEkWVUEZKq3bBeV9ejRBnViyYEGurs/EWuTUWPqFn1dWo7Ofyc1hapaea94X8u4L4vRiOGKRgOClbNSnTIFjJmTvW9k0FB4/5OufU11H/XsgcRvQOgk+bUL9QDZmaiKEmeHunaJaKrYb46AMXFxZl2SxCERsq6RQvR9sMLMLr/fhz9uin+VXYhzvjNn7PtVlrUl93GjiH8w7B0yqdArKo0I7uk5aKf3dvPhf0vqUwF26uEPy3FJ/Oh9pWIRI5jxe1fbRAL+ivoPLHn6CsUy6bPeCASkw7k+aGJcoTfl5FRIp/NsItuR9bs65dUxJAyIUqdLpXMMc+UME025ZqDgbCxI6m+wCtu/YLFnu5nbl9sBPzSuWm+38XpOUWoKFEizzw3tXFKfMeO2GhbIUTBzGeHnSOiHUTUmZm3+dZhqmyFOYvApiuAD6z0rr50e01mHLvJ/H4SwJMAUFpaKiE3QRCS8uH//DdObPM7NO1SiX1bW+PIOa/jjKu/kW230qa+rHlpYJDySadshMlM4X0sG7OQMn8+xlR6QnhPhDUnLF9U8/2uZHJdiFuHvsFxL0sqLoX1V9I60m23YtxvwrWZXLjEvj6+Mh4bFLQZuAfY/dhpsdtO8EzhUwUG+WyClGhKwFGvHfMLOaIj0BdkKjN1DZi2rYo4MSMs3o8fZobBruNqNMrWLuQ1KmSGsHWYKtq1l9a0sP1ENMraZexyeNdxJrMrCIKQEXZtWI+1t/XFyV0eQSLXwOJFJ6DDz7ahaEjDFS6ARF5SIGxwUMNBQ6bHHJmyl8yONvoRPsJUnx37B5bRA2R9JCQZqXeD+xQ8snwKhsOmOiXNm+J8MW22ZKEiO1uEltYlptqvyhKPcFei7LL+UCv+yFuXru+95ciyyVYUxk1Vdb92upsjYNSNvq03srAlhRlIEJm/F8q6IHJNBDCterfBUMUbg5DwtRPMol0yj3YdJhGVAvgRM/8wydrLqQD+CKA5gDesT5TdTgAWA2gNwCCi6QAGMvP+2m2mIAiNlY8efxDfaPortBtchd2b2uHAN/+MkT84I9tuZQQRL3VOzMURsW0pRuKOACNRRpmRNpPbjxt5cX4qo/d0B8m6p/rJfNLnCFn/orlskd2uGUgHynGIzZjXQL0L1J+p9aG3Mp1NPxRyMhDdsfKoL4V3owZumaiXVPrTGGawg5SGRok4uz3+aW6eOnXKWvHfa9Y3P82aZ2ZLX7LXsABg8q7VCt7dpNgLttjOb/aXKozccJLMHcoszLwb+nWYiwH8UDnWrr208g1Owe52eKeaCYIgpMXBPbux8q6xKB2+CmwA68u6otevV+G4RvSUS8RLUjJ8sWvj5qmN+zFp6EGdOkP+8Z6Cd6gWJii8Y0bd83H1WD+9S2czdfTDQIb18DyFUWJEwMMhqZ+pNqJGmjikZEhynPb5TahTqjznU3BajVx41sQkNP7YwjCOMLIuhisOVL/Jsz4m2HbfneuoInaEkQEy7yFb6Dhrbtz3xniteNfYuBWbNtmw2hyxQ5kgCILQuJk/fSxO6LsYeW0Oo2J/MzRrcRTDRhrYu6Uttvd/BIPvvTjbLmYcES9J0T8NTd9c1ByedG2mYidmJaHNTj41zC9W1C++59VOmiNeSFNWQ7Kn/o7YCPMn2nJgshrBnMyTo7ERGZnw+eXHiThEiA5/H4baAdwNA3yqKFBUuR5RNgHfepOIxodGath33ckceCfIG3Hx1OsTG7o1NYFtkA2AE958UdEY//bJbAcyrGthqDcTGYFfCTWO4rTLOuPoHCanPQRWfv0ZgBHcbQyuOLfeye4INEc8sRLDYdTKGjBBEASh/jN/+lgMH7AIC9dPQJODmzHyxMWgXAP7d7RCq2mfY3CLFtl2sVYQ8ZISuuFQKs+fNdRJFC/N0U1U9IUNGNa2UmG7PkQ+5YZ3fO0O/moSNQmS4vIRTUlfKtfEZkhN7NrVvePE71Wceg0DzntIAlGNNBx3RARr7Cm+JcPfd2xYB4ngvaGrP5lRVmyGvtuFdYWD511RZDhLWygQ3bHFLiPBrvCwzaj3t3mPW5EW5SEGkbtWRnWEGUio9TGBiZU1OLaEEvUiCIJwLHJC38VYWjYYJw2dgyYtjuLAjnyUbRyCE/ouRV4jFS6AiJc0qGkkRveYOZnJFOuJdDFq6B0xtyY8d3BAqvw/bEDqmQUD75N5dTjmFTKprYXRPa33RzhImztF+yE2U/FVFQdAuOBI546zhZF/UyrdIDzUhv0/ZYztlEottOW99uTatI8j3v0YmuwEM5REXV/qp3tx8JqRV9awHVNR9YXHkPVOI+eFk66sATGYNFPAbJ+YALJfUOk5E2is93fMQNQmGYIgCELj5fDBr5HX5jBOHL4UiSaMHesKUPDTz3DCwSPIm1eSbfdqFdkquUbU1cChBk9X1Tk4cW2y7xNlOtSiPn4SGVXR1OUVMlbpFMWVxx6b04H8U200m986NpKNzW2bgfQIe6od3YJwOxqTyTAUsxmRsf3wnU1eXpOL1b60B+0hpjwvXoQrVFWjdl8a3g23QrvAjWjAO7L32VSvt78d9n3lt+P4S8FyzFaEx2fXMWEvpifD1yFuLq9fBGbz42mdIsDI80tpKNYk+iIIgnAs8f4NF4KeLwIR9axpfQAAIABJREFUUHGgORbvvxNd/nsjmjZvhcUP34wj5c2z7WKtIuKlzqnJQCM47Ko5Ef5EDpzDhvvRg/ZUUcej9lgxrp2wXlajHAZHC644V8sZiLMbQXCiChqfYt0BakQijdslUDW5g/Fgu1Xvou3p7AK+wXzUjcEhNVnn1JdDGnBFof+u14qWkDQ7SXldinValVBRyllvUHnHpKlTnPrZmwh/nepPWFPIzA8RWwKG3LVQmhuJnP+AQEhNEARBaJTs2bQZn944FKcMfwu5zY9i+xcFyG16FEc2r8LBnbvwwW2TMbLkFXyypjTbrtYqIl7SpibDcU25lMzFFECeEV5cm5xy0/yRCe/UluRPzaOq00Z3YjY9DF30QLGe1FZ0xMkrYuL6x+qJqEhMOmgiB0Gb4VdBHW5rIy8RxzrLSa+3JnLi9yV44JZ3gh5qXX57DJjTrpT3tGhEkDdS5AoGf3TJtmmQG47xCBrbLtmRGVgvprR+2kLE4yeB2d6JjD3lVSfJFjqCIAhCo2Xhj09G8zePx8DStdixvgBLvr4bRbdvxJKVo1DadQ7y5pWgtOscLFk5AqMfeTPb7tYq9WrNCxHdAHMPfQbwKYCrAHQG8DyADgCWAPg+M1cSUTMAzwIYDmA3gEnMvKEOvExynAzNo+m0Bx4hBWs6kIkT3iDfoMxT2JvGyk+/WlYHxuFVxh+1p9t0s8lej7W2KIU6QjRqZNZkii9uVWpCxPUkCs+kjd4kqzfsvJJRrSlw3VUBofSF+5JGfdM88QydUxQsByi7dkX8Siag9JMjGFg5Vu9wsiIpVhk7my2E1PapztqL9gGAvPPR1Gl53g3KVb9FvQiCIDRG1n30ETD3+ygdtQ0wCPOXjcdp9/8NRdZ5Vai0AjA6K17WLfUm8kJERQB+AqCUmQfD3JX2UgD3A3iYmXsD2AvgB1aRHwDYa6U/bOWrLe+A4DCrBrZ8ZjNFRuzFN+COqYKToULGj+6UqqQ1xZ5gFVqnXzwlR3nCHStXfH/C2qv66LGZQtN17Q6ri0Izkecud8bq1qDffsGkP6oBXxm/WQbA5NVkCX8+cgf32t80f5RDSXJefKkRBqQx5iT5OsiOQjnnwhrkqcCfprEJMqd9UWg2X2pQvZJPyDBg7iSndJgs3BcEQWhcVFVV4bObBqHLZ2NRPHAbtq7phLWdXsBp9/8t265lnXojXixyATQnolwALQBsA3AmgL9b5/8E4Hzr+3nWMazzZ5Fucnh9JGOiRT/lJUiqQ+04RfwvqfT+ZzcybAoRQ7+GxS0ZtJWs49RhX9iT/WgL0WdStWkYmkRNOe30IuVcMvyC0L8oPkpouGm+ipxBsSIONOm6unQuhwkn0jhGuo/Gntp2/0nPveAXMlZhdecwWwTZ9gylvCm+VPXhr5V861K8SswAnHUsps9qXrs2NdpCVt8o+X0vA2KDwc7CJRbpIgiC0IhY+sJfUf5wN/QftgEA4eOt16Hkri/Q/7/GZ9u1ekG9mTbGzFuJaAaATQAOA5gHc5rYPmausrJtAZxIWRGAzVbZKiIqhzm1bFcteIcMqQ3TFiPcXtJqQobNARfVgwRi61TPSDU+YbOd/INyfz576FbT3tXVkboyTz4ETOdN8DWrMblBtS9Tqlznja+B/uulMxtVle6cYzNE9UXNnAurS1fGSQv59VWrtzf58myrrK7fIVbskZXfjdLZ0w4J5ChO590tqlhiQiJhvZDSmV5mixQ16kfOO3WiXtzq2gy2TxAEQWhYlO/ciS33nYnBx28EdTKwdU0hWlzxNr7Zo1e2XatX1Js/eUTUDmY0pQeALgBaAhibAbtXE9FiIlqM6soaWEp9GlOIRwgMQfyPwrUnQkZ6oS6qviYJAQTqjAEbjlW1R3Q9xAj2ni5P4Il5yEfrTsQnypbXppvCIK0tdavheDaT++f0ixJp8EQiYrbdOWbTT79NfySDPOWtNjOgbH7lDODtXb+MOI33+2bZsbeoVj/2lsja6In1Ue8LT59ZNlW7um2ww6Izpl12bIEBNswPDDfNqDYAw+khXY87IoXtxjg+EdiwG2P1ocEwrBuJyJMZrpw3QGSArGtilzUX8cMTybFtCoIgCA2XDx+8B01f6YP+w9fh673NUUYPoPiX61AgwiVAvYm8ADgbwHpm3gkARPQSgG8CaEtEuVb0pSuArVb+rQC6AdhiTTNrA3PhvgdmfhLAkwBAeW0z9BfeP1yvYdxANUf+E2na9thMxUZqddpRE/3zei8hMaPAOb/oiLIZhV8ouU/I45SKZ7umESPbhv0gn5Hi5UqC5wWV0TltL5JGUkJfpJmWg5ZAsaoPE2lhddnJ6vQ6R7vDtWknkSdTuE3vvWlNqrMEQjBiRE7H+KM8zldn+2TFT1tdwl54TwCbr8N0IjOJ4O8W2TeL/VMQBEFoUMyfPhYn9F2MvDaHcaS8Gb7e1wInd9sHo5qweVUndLrlU3yjRYtsu1lvqTeRF5jTxUYRUQtr7cpZAFYAeB/At608VwB41fo+xzqGdf49Zv8z19okRiRES6ou+p/0xozCqFmTZkjBZoh577No8xm1B6XZujLO029fEXftgbsCJm4PhkU/7OiBGomIa0dn016xEIhyxPXN31X+6EG6t5pyWQPvdlGiOkrNkea02yIrER7HZpQZ8vwIDObtSErci+zpGl397O3PYNwkuLLKifp4/GNPdND/gko4h+TYBAhMhvmxy3sugCtg7JgOKHzbY/f3xo4WqWtdRMQIgiA0BOZPH4vhAxZh8ZZz8f7i85GXX4GC7ntxcHdLbO7xd3T/1RfIE+ESSb2JvDDzx0T0dwBLAVQB+A/MiMlrAJ4nonustKetIk8D+DMRrQWwB+bOZHXpsfUz1VFluo+rdc+Pk9hK6mIN4gchIyyvRWVL2fRqcWy6kRiyptrEKxd6zheRcH1T+zk1n/02OUTA6ASQLlNNojthZcIjMd4YV1SdAb8scRC2hsWpIUzQaSKPtoBJhNiMEn+h+f1t1zVU86tFyp7HniieHfwgXzF1Qb8uCuNaAMCWgLHXwZjnVFHt1s8BC65wS/e3SxAEQahLTui7GB+XnYiSNv9Ct9IvYVQm8OXajigo3I9ep52TbfcaBPVGvAAAM98J4E5f8joAIzR5jwC4uC780lMLgwWtSV1iCk9ZyflfBJrRYwzCBrm6yEqY1ZgyzGOvSYy8cVthD+ZzPLUgcES+tMjBfcCm73yUTY3htOOJGkc9giMkcwwt4JRQzztvsNf8q0KA570tkT4DTkzY8LoWLVrsvL5220KFlBvT1AiB+KBbRvHVNOcWdu5Z1Z5VJ5PhsRn2++GKE6vP7UX+imix17f4Y5QeoU3+NEEQBKG+sn/nLrRocxijR80HAKz/rBhtJ7+MggkFyJtXkmXvGg71adpYAyHJ4+WkhMyJSctk1GPudG2mVrvuo5630bVaFS6puGu447hQn1LFGx+ikKPUiBJsoQIh07N/fB0fnDblzxziF8Lb47enrh1X28qahofeP7YQstI47p4TBE80zVOdzy8nKeTm9UTl7GMi6+NvBLuxFDvo4m+rLUzccIljy7brxewEg9kRR9rNHOLMfRQEQRCyyjvTL0HihQEgAozKHCxYPh597l2Jjr37Y/HDN+NIefNsu9hgEPESm7BhbKqDBp+dpKPjqAUAGRy91wC3OtNX765M3kzqw/fkrnLIJ1BxtCBICbsNIeVTMRoyUA+r1edCStUE7Mbw0xm4K1YiixE876SJLVojRItj1/+xzysiRjkMxAoD64x8A331NSl+aepfY6T1LdAXtvDQR0XcndTI8c9vm9RKPN8Y6ntfPDatLdhcsUOe/hEyAxG1J6K3iehz62e7kHxXWHk+J6IrlPThRPQpEa0lokftd5CF2SWiy4houVVmARENrZuWCoJQ2yz609M49Pv2OGPEa8htVol1Zd1QXZmAkdMKB3fuwge3TcbIklfwyZrSbLvaYBDxEotMDg2UufApmY1+Zu7YrDNIGWjZgiU4iA2LtoRNKbOGk1p7UfjtkfLdX3+0Tf1ZzxP4mDaNJO8QVQfoWpuM2C+p9NuM+3HLOUvG3TS/kFAa4tjQCEidy55roxh0pkgpBnRbO2u7IWwamt+nkMb7BYtOWRPgvANGvalccW4t+Lc6yr1zXb8NxZj3hZdeUe5ZH6ZEYtTfBsem+eZL5yaR11RmnFsAvMvMfQC8ax17IKL2MKc5j4Q5tflOReTMAjAFQB/rY2/7H2Z3PYDTmPl4AHfD2iFTEISGy5r5H2LZ9KH4BqajSasKlG9rjd0j30efe1dhycpRKO06B3nzSlDadQ6WrByB0Y+8mW2XGwyx1rxY/0gnw2DmfTX0p55RC2qgRtM7/GXtuSRx89cGroTReZfwPz32ffda0R8F0Q/U/HWk3vroASAlz6L1J1meyHx+ZZcEhrXIPQXIb1wVFAgKFH35ZPYVYcMAJbwZVBu6e0nng7s2xDoObCscYRCavrdFjV1GrcPy3r4H1M0YXM1DjsB1etVSn/bLJE0/7TTLpp3HqY88i/jJ1zlem5bQ0bVbqAnnATjd+v4nAB8A+LkvzzkA3mbmPQBARG8DGEtEHwBozcwLrfRnAZwP4I0wu8y8QLG7EOZrAQRBaIBUVVVh0fWnY8RJ/wGNAHZu7IBdfe/B4J9e7uRRhUorAKOz4GdDJu6C/S+tT9TfyBwAxTX2qF4RFjeoicmIkVS8RI3NsCJ2Xak8lQ3xL0aJsAfhgNcDfw1hNaba22F1xB//u2dZ+b+algiJkqTiWyBdecqf3LNwO3YeQ1FvTjny/ND4plhQgoP+WF9gB7U4gop9PhLAhmtf/anW4zGvOOFM0vILDAMwSH/Xh/nsaZsa6bLyGAywYTi7L6in3e/stsvK5AgbpSFknTDX77jTwthSIfZuY+rifVfIqGLNlU1kTXmTyEvGKWTmbdb37QAKNXmKAGxWjrdYaUXWd396XLs/gCl0BEFoYLz7q1swtNn/w8hv7kV1ZQLLlw9C6UML0SnbjjUy4oqXlcz8jagMRPSfDPjTAEl1sE+RhzUmde2RZj0GDGtE5517qEx98RXRHXsEBnkHhzqbKbsZUX+4b9H1RYm0tODgQFwlnXoMw4xE2E/za3CHetIy+YJKsgfyttBKEuEJxXdBbJuqPc+vhSe//n4lv0phU1no18aTJWy9u34FIoB2fWRvj2xHZ+xTaueaeRIJn98eUUpw34QkpAoRvQNoxxS/UA+YmSnu/uwpoLNLRGfAFC+hD2KJ6GoAVwNAcXEje14oCA2UtQsWoP2Cb+O0XuUwqgifLB2CgXe8gdIr22bbtUZJXPFyUobyNHDiDoXTNBkwG2NSfzKboVlr7n9w2oz5fzVqEVaLWlZ9wq+mu2M1neX4/tk4NpXBvNeP5Jb9g1M10W8zlUhKUnGQzuVSAin2e1jCIzHRFTgRBefpv1JK15mp+KhEOQAgRyfgQtzziAPrhgn4qIm0eNvNwSb4QjUMdzcxJ7Li84ntgmrf2utRNNsy29eErTLkaUhIY50c7PG7JgL/WIWZzw47R0Q7iKgzM28jos4AvtJk2wp3ChhgTvX6wErv6kvfan0PtUtEQwA8BWAcM++O8PtJWGtiSktL5cILQhYp37kTZXdehNJhy5Hb5SiOlOdhdctfYfiM67LtWqMm1oJ9650qIKKLiSjf+n47Eb1ERMPUPMcO/gk1dVWX5/lwvKKRNtNsAwVLeq15hpVJUhUDMWzW9Kl/4A32IT4Rkvjrsxd4H0tIFCUwiNXkc2yGOZcEXRH7Dfbp3rW6OyZuXwII2fEraNRge0F6tD+BqIZf+fp8DHtfjiuOfXZsQeEsnHfNMpsRHt0WzmYRBsgAYDhhHA7k8vplvtdFvevcXzJXePqvQl3+O1T/IKLbiOivRPQcEf01g6bnALjC+n4FgFc1ed4CMIaI2lkL9ccAeMuaFrafiEZZu4xdrpTX2iWiYgAvAfg+M6/JYDsEQcgQ86ePxcHHC1D1l5Y4+HgBPr1hMFq83hOjRi9BxaGm+Pf2H6Pltbsx7HIRLrVNqi+pvJ2Z/5eIRgM4C8ADMHdVGZlxzxotNZxmlvlJS2naDF8k7G9hVCQiWY3/n70zj7OjKvP+77ndSTr7ThKyAtkJZmtCWAQxgAkCAREXVNCw6IAoOo4ijDIqKjDOgPqiI4Ns8zqigwp5I/smgkMggRBCEkgEQhKykUD2rbue94/azjl1art9u++t7ufL59K3qs55znOq6qbOr56z2CIxWRR38JY8ySaHkZhoafnibPE2dcoJilWqq1bQLrf6GN4Dtjs09i5Uoxx+ZCbmAqUuUqlGNChcoNKfYct6H2W8qSJBjaCg+G5XpJ0I0iNzZNhkACVftKhhKbvf5HUNIwoNqOcymIaZwrS6jPeNV/LfgUJCzHx+K9i9HsDviegiAGsAfAIAiKgRwJeY+WJm3kZEPwDwgpfn+/7gfQCXAbgTQFe441ceTLIL4LsA+gP4hTfLXBMzy7ypglAjPHPlbEyf8DwWrjkbneqmYcz26zGh8U3AAdasOBQjvvsqZnbqXG03Owx5xUuz9/ejAG5l5j8T0XUV9qkAtKTBkND/JVc5GURQpFGeRl5hFbVufeMfsz9J1MTl9btAZfUnk00GmONXKbc13NP2xc3LkGozIU9avaMZ9MJM7aDbI8u3DNfW76qlbMcFoEzBFHuvRByNkddxPyUlsV20+NtO7E/EXJfFj82431m74EG9GHDARh67Xfe7L2A8KaL2xWO3Uxgzw2EnnLLa/NGwF4ms/JCMonAEEZ0HYDcAMPMDlTDqdduaZdm/CMDFyvbtAG6PSTcph92LVbuCINQWU8Yuwt9WnYbRXZ/G0B6/A7oDm9/qj179duPwH6yqtnsdjrzrvKwnol8B+CSAB4ioSxk2CoytSVKBN5+xJtK6hMT2g2mBW9kbQRT5qF1adN8Z0XfcqpvxLsfbjPOnLCia22qPWnbFYxu1/pcyewHZ/Aww7GlnMtK6z1NIjl+EkdCPJUTvIQTnWFvnhsM/Nk/9hn0gAC1ORce+2Fa38ZJzaCKwTeGGKibChSpDJ4PuYEpESltvBtDWcgkXvSQQOQi6nPkecBCfgSuiSJs8oANPlvwXAN0ADAQwoMq+CILQDtny9lo09N6L48Y8jGETNqB5fx2eXfUp9Lr0RTT06mAjJmqEvJGXT8BdbOsnzPy+N+DwnyrvVq1RyYZBOX2AMnZgqoib+Y34g5kTrRjdf9IbvC17k2xruyfXTC8vSWDk6U6Wlo48gxEfcxRiO5e2CEWar2Q7U0be1K5fFvwxPSU1G+nfk0za7hf2/leKUYNJP69A4BgGg3uzZBy3vZ6JvUF8WebZJH+MFuvJoO5T8mgxPEO5RXJRVN11PFb5a6QQ0cxqOyMIQvuhqakJT33lYzhp5hOgevfl0XOrP4XjvnMbTiLCU1fPQ+OwruhRbUc7ILmiJsy8h5n/yMyrvO0NzPxIpZwhoj5EdC8RrSSiFUR0LBH1I6JHiWiV97evl5aI6GdEtJqIlvoTB1SeSr/RpOSWVS70PvhtC2nfzf/UWIyaXG2W+WOyw6ab2uUmais+bhHaVMuw5Yq1YIm8mLW12U2ymaV7W1zNlJf8qaj1VvME22YUweq/GRZAIDC0xr53+8aWBXszWmuO+7bVyAFF92vTElPUni+GkyZK0PwkaJdZmzHN/+tNL+2wXh9W1RaZq6qEhkndVkRQOBDfv8tVv/0oi34l/agMmY57oR122JswoEOv8nKO8v2sqnkhCEK74onL52DnzSNw8gmPg5tL2Lq2DwgODu5j7H53K566eh6OGXkflrwuQ9OqQSbxQkQvViJNBn4K4CFmHg9gMoAVAK4C8DgzjwHwuLcNAHMAjPE+l8KdOKAVKLMfT5I9W08oaxHZG+7R/CnpsxvKnCu2Ow+0ZlckXdhsi/qb9QzElWHLrzZogway/yo/oQx/bEOiTdWXDKdSFXeaP1EdETTW0+rtL1JpigDtY+QL+zfpJyC4PdWAofGJ7FP9o8iuwF6065py3LCpCo3I9aHQlnkuYn8WxjkAwV/KJcDhcPpmX7C4t4mbM2LfEFrEBGIK0zO8VTRDL5k5EDahPfaO+fbC9KFEUi+S5cboOAwioiOI6HAAh1bbGUEQis2TN/wAO356CE46/ml0G7ATS16aiuaPrcEh31qPxStmonHYfDQ8MhKNw+Zj8YoZOOHmh6rtcocka7exCUS0NOE4AejdEkeIqDeAEwF8HgCY+QCAA0Q0F+Fc+nfBnUf/WwDmArib3eWpn/OiNkOU1YsrTBn9ZbJSKZNaVyPVXwfBEuGVwluk0mxMmqIh2Oc3qJV9ZPz133qbNm2N1cxuemmzzVCmtrTtXXX8qYbzXrKktmUgDiwN/aiP8XbVY/4ilVkXqAxkmxGNMMWFw9ltAroYMM9bUG9GcIGM9n+ALrTCDf/e8tv3jhuUiF/bxbhBg5iFEp1i/7u3g5sdbyYxi2OqYf/e8Ew6iNaHyYuacDMApUtZMF2bXksCKZNJUDAhgHuvuL+c3BM5tC/+GYA/L+m/VNEPQRAKzGPf+RrG1/8JHzxiC9gB3n+nF7ZN+zWmf/70II0qVHogYSVZodXJKl7GZ0jTnJ4kkcMAbAFwBxFNBrAYwFcBDFIEyUYAg7zvQwGsVfKv8/a1knjxMZuLeZuylrRxLdCWCCbNZisILlsxxl7tzFgavHECRX2Lbtq0ZkjxjZD1TGZvBdoiIOUS1NNv/FbwcqlTNyebJcu3mFQpfuZy3xMuamTHqg9SylIn21KCaK55UvYjrIMqicx7US+OQpvMURETnAzWplcOkhHgDsBX85EiOrxpkT3xGJ5b1n83frQoOGaNLXUomPltuC+zBEEQcrPisSfhPPBlfGj6WwCANSuHof70X2DkBbPQv7quCQlkEi/MvKa1HYHryzQAVzDzQiL6KcIuYr4fTJRvTlAiuhRutzKgvmuFXA08Qnnv4Mt9bx/36rclJEmKfDlDL/21QqKXKi5KwwDYixaYx32b2t4Mp9F2OO5MUvD/5NsrzqbfSE6MGMXtN3aob9KpJXP5qdEHJWJUKtmSpJ9QZqgLyGtRE7JdWJs7SsM++KIUrY41ySLiyNwgRKZKNtfJCd3z403+1Q/DTlqPLU8s+KKCgWAisOj9Gt5JblczfY490sI6HESJQvnEgdjS8mmRJO/EB9G69itgiKg7M+8moh7MvCsl7TwAbzDzU23jnSAIRWX544+i11+/iMNHvIv6xmZs39gTy3efjRN+8B/Vdk3IQN7ZxlqTdQDWMfNCb/teuOJlk98dzJvdbLN3fD2A4Ur+Yd4+DWa+FcCtAEANfWrgKV+O+Ii85m2BLRMzJpFRXCW0LFURozbpyvVWjcQAhDpLY83mdVpXLd8vHUMk5SAS5chYYWtJfkPbaHhnJSm54/Vn0qMc0RhXUmRM22d21YoTXEnRH8MoKzbNRSpNf7LobzViFBUHrCc0jqv3caR7n2GT/J3qLAmaWVWtuXe2W0/vd0LwxsCEIjOYTtkY1E8Iu5NV/J1G7dCXiL4AYDWAtM7lCwBMbX2XBEEoCs9cORtTxi5CQ++92Le9K15aORV8sBnHHL0Y9WObsHtrNyzbfzmmf/1fpBtYgaiZNVqYeSOAtUQ0zts1C8ByAPMBXOjtuxDA/d73+QAu8GYdmwlge+uNd7HRClEQ6yv5pHf9WW1m8TN/FxRbalI+aV211NrFpYl2H4O1j7/ZsM16ZfRac2RPXJ7E46wM9E4t07AZ43ywbkgeEiIgQWM+5lzahIJNHKrZfR/j7otMt5iqVD3Rop5Lzbeknwf0e1HdF0SMYKzyouhWX3uEUkNZW8VIT3CjhmCAyQlDP2x30Y8quR9lrRcYgo3JO58Mdc2XwGYwhVp+cVsgZsEdB3k4ER1iHiSiTt7fIwAcYOaH29Y9QRBqlWeunI3pE57HonVnYdsJr2Lbxp6YefTfcPwHF+LAnk5Y8uIk9PzyZkz/h3+ptqtCTmop8gIAVwD4DRF1BvAGgC/AFVi/J6KLAKyBu9YMADwA4HS4b+T2eGnbgAyveROxxAiyvo7OQ9mNmewZVeVryxUXw4h7gx5ng21pYtxsSXQna9QlszCyvBBPEnJB0ZW83JZbSNtFCQlTXFHPVqZrGhMRsaZh41qHeiASBVLFlS8MbAVFd3vdG2N6ovrDUPzz5AuGknl/KOqI4QqQoAuhEjkLzrdSMX/8SklzWo2wuDOSAXAnYAgL9OrKMRVuNzwPYB6A4cy82XL8R0R0M4Dr4I67/GxbOicIQu0yZewiPPfmmdi/v4T63x+LoeN3wGkmHNhdj66Xrsf0zl2q7aJQJqniJU+f45bCzEsA2CbNnmVJywhnmWkDKtVAIOvXZDKKmIq4mL31rEdFwgZdltxxb/ejJaTtSRcE+WqUPVWqTaXgtLSaj1a1ZkmX5EeGCkdtxa/THjTg82hvrwxTOJDx1y4sdCOsbwb5wyiE4VMOcatGn4LuX4qTZjdAVkSH7hFDnQHMj9iUStEuZLqPhHChV7V2hqT2hZAxxsj8/bUnmHmF9zVutstecGee/DFEuAiC4NHU1ISG3ntx3Oj7UN+tCU3767B8yWj0/PSvMGz5LNSLcCk0WbqN9SWiL6NDzwpXyTebSv+VcvPGbleCrI6R0mhivSGpEBd1UXsQmY1Y8rrzqDbNhmpceTD2x6Wx+ZaU2lZ2aq6UyxPUgaP51WPmflsxtgZ9lk9SHdQ1YUwHAhtGIzpsckd9DLIrhWmD6L39cevSJBvVfdTOh2fDrLwmWhTf1TVmyN/WyjP7v3ldvyj8NQRllgAH5I5j8cvVHGbjo1gl/xdGehkMOMGc0G63svYpXaIQUWciUmdeeQpAX2ZeCmBVdbwSBKFW2LNrFx7+0sew8+YRIALqujZh1Ssjse9bpBaZAAAgAElEQVQjL+OoG1/GW/9zK/Ztr/TkTUJbk0W8JPY5bt8kNX3LNRnXEsuUOX639VCFfU8oPE5qqCICiL5BV3vzmzZjPyktNXXYRJrn9pzx6fOc0SwNylR7psKISaKd35yOkmlcOc3BGTFES1z5Sf4F4sC06Tf01TpksBUIHw7t5RGRml+kiBbfphLxYSJFxPjy2iyCAr8CwaEIU3YI7Cjz5rEuoFixA1/w+PX0xRaHv7bARybEx8zaD0T0VbhT4a8mohVE9GVm/i0z/xAAmPk/q+uhIAjVYu/O3Xjs0tno9IchOOXEh9Gt7268s2ogDu6qx0aaibpOPfHU1fNwzMj7sOR1WwcfoUhkGfOS1ue4HZPQf6cSJlVaIj5i3fSb8HkWqczfbUz9G3HB4qKPmsdRMtoax5qtGP2i2vPL1Lu2pREpKWJLG4sRk8u2P+6y28RBFs9sXqqNYn9HkC/Bfjhag4IdphjybUbG8WQ4sUFeRM+Jw94bFMMuKxvqddWurx/E9BIwewvYI3ovaK4qijpIYxagnACn2XF/PmQ9HIiJIKrC6sTHoUPknVjHAULJ7i8yyYqA46Be7iKVCOy79Q4vJnknwWnHK1V60+a/CHfdrwnMvJmIBgL4HhF9n5m/W10PBUGoFu9t2IDXvn8OJo57Eyd/aBecJsK61wfjkK8+h+F9B+KZK2ejcex8NDzyOzQO64rFK2Zoi00KxSRVvGToc9xBiGvUZ2/sW9MnZs1rO45WeCvLDtibtFgP3yVHLuL2qY3BqOCw2MxwGk0hkxYdsOdMtlupq+M3UBl6FMIsI+sd4Xhr5vj28viZdJ3Adh/Lhj2hwoh0QdPKz6DeggiFsrS9GdEhJb2W2SgzulYMBUIhuvaOG4UpsRmPUeyqBRMrERd3gUoKlJF/Irw0Jf3c+z8MCna0X9Gi8CTcNcAGAPgbEe2A+zx6BcCXiOgmZn6vmg4KgtC2bN+8DYu/cz6On/G/OPqDTTiwuxNeXDoTk//5Xozs0TdIpwqVHujQ4x/aFblmGyOiUcz8Viv5UgAq0Ww18sW+HjYTmM38GB9S7aUdzF4v7e18sE3Ktr1hZWuMM6CtFaKKGNOy7SVzbCSGo2nUxrwumthqKOmMB36SJcKTcCqTojeRtV2yat2YQsxzq77FJzNxDH67Onz7H7UV2ExqTydU3J8S2bZIY5I5I2ARey7VaIxZb//eCu4HrU5KTkLYfcsQMexnVMUiOVBHpKjlMnO4rgvBm/UskLAwb0brQpWBzfYrYpj5PgD3eVPifw1u17EPAJgMoB+AJ4ioFzMfUUU3BUFoA95eugzN95yDgUPfw0kn7cWB3Z2wZuWhGPjVv+Lo/oOr7Z7QRuSdKvmPcN+ABRDRTGZ+rnIuFYVoM6gmSXxV34I6UNR0VNrpDbDUUiy+6jY9q4mt43RsCz+2TMbZu2pltckxBbXkDrOWo3bfyhmN8fNFuk0plyIxOpJ0Xgyj5gKVCSYVkZBuM87HiE5R/lKQiSP3Nzve8ZK+3/3iK5zk+1/1i5UbIRAyDG/gvtmvzRcuFsXWfrkcwO8BLIEbdZkA4BVm/pA3vb4gCO0Ac2HJJa83YsxXbsVrN1yAxqlL0WXSfjTtq8Pi5bMw7Tv34PAu3artstDGZFqkkog+QUTXA+hJRBOItHeOt7aOa+2VvA1v831+a3QVUW1mtZ0yrS709mOc3sjT5nK8T5Y80ffW0TL9xSTjmpeM7GfbZtOWL5NN45KXtUBlmumITbZ8s7oTpDHrwY7eZUuzweEnFvW4J46D66OIicAfbUNxzNtHRh7N8aAY+9UwffWHxKtlBzOYMZQ1JBkgb50WW/l+MgpnJCMKzyaRP/YlEhqDfqd6HgXzJrd/9cLMqwAcA+BeAA1wu46d4x07UMmyiKgfET1KRKu8v31j0l3opVlFRBcq+6cT0StEtJqIfkbe1HFxdoloLhEtJaIlRLSIiKR3i9AhUReW3HfaGixcdQpmTH0G/f46Ecef9AIcp4SlSyaCP7keM66bj3oRLh2STOIFwLNwV7vvC+Df4c728iIRLQCwt7Wcq11sraY8eRNMZialNRtp5VXAZkJRapHm/jQRQQinqs1CWkM+zY6ZPRQHdsNxL/XTbCaRxWakjLyXx9IujwgOi03bNTS/J9o08mj3QUq0K7gMakCBPVGUBYoRSRabWjTFdvOSuTuQDFHfyVVZjiGFo6JFtwe4UyAH84X596IfJWOGw+GileZilwRfCLV/8QK4IoWZ/8zMP2Lmn7fiWJerADzOzGMAPO5taxBRPwDXwhVUMwBcq4icXwK4BMAY7zM7xe7jACYz8xS4E+Tc1hqVEoRaZ8rYRVi45mz0O/F8vPKds3Dc+EdQ14lB9YznXzsD3b60CVNvfAEN3XtW21WhimTqNsbM6wHcTUR/Z+ZnAYCI+gMYBWBl67lXa9gaCC1sNKRmz9l5qA3bMEYPG+h98HX89piqlrO5mr3F3pKqh2+74+uQt5BIwzVrxkpccls0wlZEnpNG2X4B1qIpmiYIksTYtV36uFMTREP8DYvNqJggzyZ73bMs6YLoSLQgd5eqqtyB98yqgCE3ulNS7PlfDbEUxDIpFCu+DVamHIu8k2C0uCulEGEugA953++Cu57Mt4w0HwHwKDNvAwAiehTAbCJ6CkAvvzs1Ed0N4GwAD8bZNRaA7o7Kh9cFoRA09N6LIzY+hSFbfwc6Edj1bncsWT8LR497AMd+73fVdk+oEbJGXgAAvnDxvm9l5sXMvLvybtUilVIF5ivgMvJp+2oB3be4TmiEPB63rHuc+cY/zVLy+/LwiH8ok02t21G8n8FbdtNmxlNgi3SkN9xt2/ryiaogCPZn8Clyl5KunzS7ZM+T6KjvBis2Mv6W1EhL5PqoykixaY5Jcg/5J0JJSPZfqONVUr0fTYvRTpihXXMJSr87XdDPzpgUQKgIg5h5g/d9I4BBljRDAaxVttd5+4Z63839iXaJ6BwiWgngz3CjL4LQIWhubsaTX5yFTdeNAAAcOn4TmvbVY/HLx6LXFZuwv6mnLCwpaOQdsN8BaYVQRtldPGLyVaXHiBpvoQQVHHZ3MfGHR9ijMUmVsjfUjKZkpgZ7VtuBLc5u0xLwsNpM9DPvtSW9/rYy4/eRttMaNTEjGqT9SXJLt2HYSZs8wWaLfLHgR03I4i/0fRFxBuNcUyiMSoqPDAqiG2yrsyZQ1IvgLyipHPdFURDtCcWHTeaQao85tOnAnUpZG9AvZIWIHgNgm57oGnWDmZlaIbRl2mXmPwH4ExGdCOAHAE6x5SOiSwFcCgAjRoyotFuC0Ga8985mvHDtRWgcsxgnnrQdzMD2jb3RvdduPPfmuWj8xo34yzUX4ZiR97nrs1TbYaFmqDnxQkR1ABYBWM/MZxDRYQDuAdAfwGIAn2PmA0TUBcDdAKYD2Argk60zjXNaEzQvltezyqGUHXZydjNKpjwj5tt/87s5JkJN05xQal5v1MCA0lMng73o221bijqLjSy+x13yYByIKQpsdhJOhn9OtdXmLRW3mbD65ok0M9ASEaEJfqu2zOsPTxwwQhGi3SumuLH4qy7e6I8TUaMkwTlB8jlU7flCiBBO3ewaCEezKBOBAV60SvPDK9QVuxReY/9E+N/hGAtUsndYF/ysVNDVKcGk4dlnsBAiMLNVHAAAEW0ioiHMvIGIhgCwLdC8HmEXMAAYBrcb2Hrvu7p/vfc91S4zP01EhxPRAGZ+13L8VngT5TQ2NopqFQrHskf/gl5Pz8PgIzZj1skOmvbW462Vh6Jp5nUY95lPysKSQio1J17grqK8AkAvb/sGADcx8z1E9B8ALoI7GPIiAO8x82gi+pSX7pOt41Jc09w/lqf1YElfqcZHrIhx4Da7sxrJ4BA7cFBnjRr4pL35V/MGjT9jf0vJruts19Vij/PYzAiHdvOscZKEv0hlOVMiJ6V3uHwfbXeWPzuZuWZK1iKCyIuXiUmxaREyST9lUhNDEQ+OEwxtsS1Q6WZhlDimTCj3tDezGHsqJ5wSOdrH0I3+EPSVkzyx5FU4nKlMqDDzAVwI4Hrv7/2WNA8D+JEySP80AN9m5m1EtMNbl2YhgAsA/DzJLhGNBvB3LxozDUAXuC/lBKHd8OAVF+Cwzi9gzJHvoH5CE5wmwouvzMTUa+/DEQ3hAHxZWFJII9eYl9aGiIYB+Ci8mVa86SU/DHdqTMAd4Hi2932utw3v+Cx/OsrWhZVPOcS8+rWajCuHlE+Ki+Fr3wQbKfZiUN+Um2/W2fvPlt7Mq/71v/tDls14SNzClzaiPnlv5pVPOBg7ctIy2U+2mR0/e+y0yOXc2RSeS31K6PA4qRsZ/dR8NI3mrbdXcXWKaevdGmNXO/WmqvT9NARFqk9KWi8GokVn7LO+kXsfKDdDOAAfYHJCB1V/mNyPX0lSa4RI9EwV+Qx9YL9QUa4HcCoRrYLbfet6ACCiRiK6DQC8gfo/APCC9/m+P3gfwGVwn2OrAfwd7mD9WLsAzgWwjIiWALgFbk8CubhC4dm/bz8WXD4P714/FKfO/APGTH8b723ujaXvfxn1n9uJo3/8OOobZOYwIR+1Fnm5GcA3Afh3cn8A7zNzk7etDnwMBksycxMRbffSR8LsrUfeqEtLygEqqzXj4gfZ62PWXrdoypN06+oq8GZOvznobmR7ptvKYqWBrEYQKKO/STbVMRJ5/LItUhksXljBS85+LyOruEq/l5nhLyCv+RhEjFIuj21cC/vplWiD4x0oZag7Rb4guIS+r2YkJqq3/DuWdTuKWFDzBTb9Oim+6z550lHJr0VRWO0eRkYXMsOmGRYKO47lEvRCNph5K4BZlv2LAFysbN8O4PaYdJNy2L0Bbu8BQSgk5sKSLy4/Cof2WI8hI7ZizvH74DQRdm7ugVV1F2HGVT+yDjYThKzUjHghojMAbGbmxUT0oQraDQY3or6os1WYDetKCqYybVL8IpW2ZnD+uE6Yz7cZiI6MedMCGE6kYeinCHNmOTtqY55VewmBsTSbkQZxGZEc2z4/yKT5qXlGVv9sItX3y4/GwBefcRfI1wZWBWgco/D6BGNjbHUzbMXZD3yErdubvfEfijCLsDVEXEndp3blCoMviqhn5S97oj0UMsykBWHCAfm6nA9mh+sga7wIglCb+AtLLlxzNpzm6Rj1zs04bubzoBLgNBNeeXUqRn/5bvQdcjhmVNtZoV1QM+IFwPEAziKi0+GuntwLwE8B9CGiei/6og58XA9gOIB1RFQPoDcsfYTVwY3U0KeCryhbocEQMZkkD/LYzOKr+kY3X93SGrlx1uLymV6ZNrN0pkg7c5pNNo8mkxxxKs+/wGac4Cnnzo3pMmX3kyzf9O24qJPZkM/ak8x2DrTghyrgyJLHFrGCHsnRAhaK0CJvZ5w9/1rodVciNEYZvk2HnMS1jNTB+H4v13Bckm7X7VLG3jgXP58irtUZzmSdF0EQqsSUsYvw0kvjMHn0g+jZ73eg/sDe7Q2oq29C/efewZSG7tV2UWhn1MyYF2b+NjMPY+ZRAD4F4Alm/gyAJwF83Et2IcKBk/7AR3jHn2ibPsJmDCGviLG4GBuWMN+2ZoSQYLNyqEWE3zn4KHMixY4mIWRxN8lCvE/50XNb/aLs9hOjH3FpW3DJrTss9rRdWsEZ7BrHLDGJ+F+HUXlG9Pqr3bCIwza5303L9NIsN1YAGtfNkwLhXUqR5EHZQVQliIZQIDgC4RBEW8gdu+MLJD8i5dfN6FsYDNPzxIz78bqbebMEBONsNFXnjqkhbZ8gCELb8ciPf4yN141AQ++9OObEpeg5aAcO7OqCxesuAM5diU7dmtBJhIvQCtRS5CWObwG4h4iuA/ASgF97+38N4L+IaDWAbXAFTytRyYaB+Xo3Cxm7drVx+0VtfJrNSlujVs1XQhZ387Xi4yIGWWJJ5tiBpPRZO9rFdnVSMM9TREtkuKa2eicKJIt/cWm0/QQtqpGWxy/DjIJEzkmaILSILz9/8PbF9CnGYFxbX+tSZnE0Kg6VCIhhM7imXt+8kqqEVLMRZ1RZGdoPXgIoh0pGeEfGvQiC0Ba88/qbWHrDFZg0dAVOPmITSp0Y7ABvrhyOwV+ajx5Dx2IGgKeunofGYV3Ro9oOC+2SmhQvzPwU3PnywcxvANFuksy8D8B5bepYReD4llWWvJH3x0aLqc3Qx7wkj4BR04V7bSKGrKnNku0NNX9vcredJOIlV7yP8TbNCQhi7XGCzQzKy1bvOL+y7ovcVpS8PxrVSChHizyEeSjHrexHNZgs55gMYR1j0L8+ql5RI1L+fjbqHu2i5UdADMXpXVgHADGBSn4k0na2HKN2HERlWP11+QtlegOC3AkdzHn9BEEQKstjN/0S/VbdiqOOXYVTZzGcphLWvTkEmzsdi4ObN2H6hBew8Jbr0fi1G7Hopm/KwpJCq1KT4qX2yPLuPo+5BHuJxSQcjLypb1s1ExcoMKMAkXEXyH92bQ01Wxn5+0SmNwHz6M60iEQmU0mqydgdnNu40EsqUbVlXq/M4ifhmM3PpHtE3dBOhy98YjR8sDvmZGuixc+v2lR8UWeEI/amRVZkiFsEGWKJQOEAG7Djfin5IkabbcysN4XiSi1b+8beRAmUaWY2QRCEPKxb+QbeveVjGDNhHU4asA+lQYwDuzth/duDMeIbT+Gw3oNxmJdWFpYU2hIRL5mJ69WflzyipYxyghaQ2hTKs0hlxjLZAXuLVKptQ1vD0zbOhS1/YW2kZXQnZp8f3clmNzzKyv9VHMdMmc3XJFkUCDjKLw5U28E1YNfPUp2yPyGqweoRNmx5G0Fj3vQxS1RIEQLmfeE43mxiFrtqvUixEeRnLTkAhONNKJo+4jcpMQtPY6jTHfs+Oc0OUIJ12uqgu6F3o7Hiq3s8DAP5UzE7DoPZ0aM1/olS9rn3A4XjZwhgpjCPsoCl46g1FQRBSMec3njJ64049t/+jIcvPx8jOi/HERPXY8ix+8EMvPX6MNQd+20cdv7nMdpiSxaWFNoSES+5iGv6lSlmUrOVYbvFIih7mWrUxP6+PtkLmwBg5W/YViyvYcbG3+y1yp6qEvGt4Pyx3n2qpajRgzhhpKT2vUgWUGxETlqK1/UrbODHlJ+m+ZWud9q0HaTfW2r61IiM4hODgrmboyLGT8SRMUFhEIZ1J+EKN3/2MH+tF7A7t5g7ZTK7okkrS1kHRp2SWRAEIQfq9MaN592I//3BZfjg5Iex/z8H4iMn7gcAvL+xF17ddALGXf4LjP7MsCp7LAghIl5yUanoi8VcrNmkjjsWH3K52LI62KIrQZeX4P9KAuPtv5rH1pb0RwGUoI6oyd6/36ydGeHQz2S81aQznmgz4fQmRS8ia7uUe5mUfJGFNK2RmHjh6gcGIotUeipT69qUdIHMcuN8NF1JEy/+hinSDEHIZvrg3mLNJ12guXeob0db00b1X/EoOEfkaKWG9fJssitg/EhfONtYfF2DqKAXkiFlryAIQhamjF2EZ1d/FLu3N4F/OwEnTdmPuoZmcJcmvL+hF9b2/gdM+fp30b/ajgqCBREvZVPJd+95y81YZqqLtgQZbcckM0VM1hm8gswxeiyM8CiNu5RTEdecyxqRyBWvUmxGF0FMthnrZxl+JJUDhAIhWm9VHsb76QtNLYfaVSup7nHn2jAYrBXD4exf5uQHSeIv6SSnRqEsglFdW0UT3Ep3rkg28vsXJt3/nk2vsoEwgrJIpVa+GUtUy2vrf4cEQSgie3bsxrNXfgwnz9qLmSMfQtd+e8AM7N/ZBcu2noMPHHov+v/jBhEtQk0jwzxrHluLMEd3EfU1eyzldD+Jt2lGVpJS5wkuMLyZmzKkzdqUY3Z7A5HlPDPsZybtTDkcrg4fKS/NJiFyyYN1PipAYDpiM76RHadJzHoww12PxfKvCgHpvZzUk+MV6kA/l5ovKT8N7d5ie90p5t7X1piBJ5rVu0QRF/DrDS/SQuHMYZbL6e4P1nTxP/5+JUrESgGKcAltUqDERLoIghDHvr37MP/Sz+Kly6ah+fbD8eFTnnH/nalrxiuvzcS2KQ+j+5e2Ycd7ddi3vWu13RWEVCTyUhYtaSrEvE+vdOujLHu2zlvZirHlUN/S26yqeVNe2utepjTky6l62ObWpVdrNArjzlVQbFxUK6+AsahH8+6LCpi4eExCNCfBJhnpzABB7HX3xYUSjckEIT5CY9gMuoJFEiIaTVGiIKQaC9Jz0EWNvYiRra6m+vIH7ZOqhBSHmRmOV/lSScuq2BTpIgiCTnNzMx743o0YvOmPmDR9NU4/6QCIgN3buuH15Udg3756jB/zFt4/OBKjDxmPp66eJ9MbC4VBxEtm0mIHZdpJzZ6z81CL2zH5DYQ5Ehr8FK1JeknZVUqiIMhFimjJYdScQSspqyYbKnHJU/IGRRit4cRshEyLVKYJFj+NWnRsuUYUJbajIxn7Y869TZox9IH2Ed9s/gUiRl2fxV+RhYNoWckfw6I4QKEJxQ//viPPZjQS5nano8i4JTCLfhEEAc3NzXjkxlswctOvMHrK25gz1gGNB/bv7Iyta/ti+4R/xtjzv4ReXnqZ3lgoKiJe2pzI6998+dzMyr6UFnwrYn0DrewpWY6miYw4m2nECaOkhrUd2xvw5IZ2YsPbbFTb8nGMzYwiRr0L1L95BB1ZCvMbyKQn1FNZbr+4LnGmKACUyIry3eYjGzsZipBKyAfVPvRzFVlEVLWn7DfLds0aUUp/8UjvKPljWBBKGgrSWGtoFVbqEd9GGN3x+7bJIpWC0FGwTW+8feApmHzgFvTssxenDtsFGslwmgnr3xiE+g/9CId+8JPoRoRBhi2Z3lgoKiJeEmkFNdCiV6QxeSsRJgjI2m0sbCYbbUjDkh7JUK2r41fiGm7xPsZ7lNVKVruavTytxJRTGSewrImykhTFSC1CVwG2LlV5BJF5PIwv6D8D8ydh7WJo6YoW6VJWivobCEOLwIncs94O9vMp55JBAJmLUpqZ1bK8bWXgDLPXTcwXMV5BpAgfxQoCKWTWx0/v9XUk0ifGEAShfaJOb7xr7WAcid/jmKnPgkp/BdUBzkHC31cfjobjvoIRp83DSNviVILQDhDxkkiWuEFekzEt2qTXxqk247Ko75tbn9guPYYH5hmIa+PnPdtxZdj8saO+7bZ/K8VFSXL45hN0OPIazfFRkfSCgivtjbuI2EyKasTs8O8c7XgZlddmd/PysBO9M7V7wvDXvLaq3UDEOIBDejoz2qIZJcOuH8gwRBE7TvAvpXqPq3GUoF5eojC6o1ZEORFK1zBttjEogt8zGtaTdZted7fgmguC0G55b8s2TB2/EOtWD8KRfR5D35FbQSWg+UAduKkOr279LKZ85ecYV8q6ILUgFBcRLy0ma6TChxI3W0xed8oux4ED9x/JuHc7aYJEffOtNv4q6X7W4SP68eSmYFabmeFoQ7ylOA5A/orvOaMxSdfN4eSpoPNAnogBIbLwYy6NZFyQwKZFyGjpjQ31uCb6GIHSJDKvEQVWSqx3/TIjkv7gfBAHUyK7+72OZdpN4KbRBumzG/0JRalVXgqC0E54/o8PYMP9d2Fcv1dx2KS1qOvZhMOnrsXBvZ3w7vq+WL/7SIy7/E40PDYaU6/8RbXdFYQ2o2ZiikQ0nIieJKLlRPQqEX3V29+PiB4lolXe377efiKinxHRaiJaSkTTWt9LNj6tbTKunEiHl3ibsVDMJzt+DrMovxe+2RM/KSLDlu/6sGX3jTTl6N9vNiQDm0p1/cYoa6myEZxmstvM6pu6HTstcjmCwfOH4YqOSARFEzXJBagRBd9HNk+XekNkddH3kcMppq2exLinil9zDIztXEZdI+X/ShW8a+rFQPR7M+Y2cc9ReCOQd4KZOLJYpe+f+5e8bmkpN44mxhgc+YUIlSLuuWNJd6GXZhURXajsn05Er3jPp5+RN51cml0iOpqImojo461bQ6EWaTp4EAuu+yme/PyH8P6/DcG0vefhjI8swJij38SB/fVwmggvvjITXeZtw+BvrcP07z+MRT+9RqY3FjocNSNeADQB+EdmnghgJoDLiWgigKsAPM7MYwA87m0DwBwAY7zPpQB+2fYut1XDwW8tmQIjQ4s21sUWCjCK5tYt2sVQokSKaRCaNlsanbA1auNMZjnjcYIjdZYtP78lXWAzv6YMyrHZjIiY8GiqTZsmznUuFcGkiVfDqMNu5CjNJU1ym0aVvKaPpll/9RbTTqAlKMwXiBj2Ijy26w54M4w5ABzog/n1MJHqGzN5XcKUjxKMCWM89tcFQkWJe+4EEFE/ANcCOAbADADXKmLklwAuQfiMmp1ml4jqANwA4JHWqJBQXZ65cjZ2/WIAmn7THbt+MQDPXOneEmtXvIl7L7oUq/9pHPi/+2H2yKtx4mkvoNuAndi/swuWvnYcnNNfRc/LtuL5l07ApFEv4S/XXIxdW94Npjde8npjlWsnCG1LzYgXZt7AzC9633cCWAFgKIC5AO7ykt0F4Gzv+1wAd7PLcwD6ENGQNna7DMppZJgxjko2VMq1SbGN1DJiRQmlhDb9tmJWO3E1UqMcfmM+fP+uW896ZtSIRLxAyB8U06IcLSSoXaw9vXlt5jVTsnJAa8wn3BiUVA/1OBkLVCo2tatku7Es+/zro5/8lN+UVsmoQTJvTj+VH2VRhVDwVY3xmAW5g/f9LmWB2LOsARMumYn0iI1QDnHPHZWPAHiUmbcx83sAHgUw23sO9WLm55iZAdwN/bkVZ/cKAH8AsLmiNRGqjj/QftG6s7DnlDfx7JJj0Tjpb9h3Wx8c8uxUnDPrNzhs6jqAGBvWHIK1Pa5Dp89uQ/cvbcPU7z2KTn1GAXBnB1u8YgYah81HwyMj0ThsvkxvLHRIanLMCxGNAjAVwEIAg5h5g3doIxDM9jcUwFol28u3droAACAASURBVDpv3wZlH4joUriRGaC+kqHVchsLKf1fMpeRoTVLkS8plNdCzhkLiqRNq2WkmZen6llseoKjFFN/W8M9bV/ehTSD/AmOl71IJVk3DXtk+aZvx0Vz/GhKnI/aeaEUe9AFjG+THQB1Rp64n5KSP0gSqTwAOLE/EXXaZlV4uN85esE9HeSQE+ax3CiB3UCUsL7wpZLHjcQwHHaCcUYUOXl+xEgiLxUm7rmjEvcMGup9N/fH2iWioQDOAXAygKMrUQGhdpgydhFeeH4ixo96HPS7I/Hh4/ah1NkBczP2bW/Aa5uOxxGf+R66j2rE8BRbMr2xINSgeCGiHnDfPl3JzDtIeaPIzEyU7ynNzLcCuBUAqKFPC5/wttZSXhFja9EkpU1KkEcIVZ6oaIk/vf67ZTPUp7bF7GeXjW17Iz+uQZw0WN1sCPtjFNJEXGYpaCk71Ze0S57VJ1Pxkb4ZJKGYRDa7Fp/irlucIZtbcb6bIsbmpWkjVgBSNF94d0VXXoksWmkUENyX2v3CwR/286jdvozKUuAsh/cfAETGx7giRkvjeR+KrDb60bcjiOgxAIMth65RN8p57mTBsHszgG8xs0MpUTT1hdyIESMq7ZZQAV5+7Dms/s2tOHbkE+g9YBca+u7F8bNeAgA4TYS1a4Zj3yGnYmyPX6PHZVvxgSr7KwhFo6bECxF1gitcfsPMf/R2byKiIcy8wQvH+yH19YD2kmKYt681PKu8rVwmM7ZoK+JmfiO2NSbiZJ7a2ExscGeMAmURJlnOXpZ1MrSX9in2zONpfkZsxhRikxi27SwyW7cV0/w1bleboEjDH9NTUrOR/j3JpCYeoNwZDNQpldXOd4J/NoHDihYJZj7z09g618ae4FCxsKdg1LVd7FnVu0A9wYYoMo66iiiaRsgGM58Sd4yI4p47KusBfEjZHgbgKW//MGO//2yKs9sI4B5PuAwAcDoRNTHzfRa/gxdyjY2NcuFrgOfvexzr/ngHZoz6GwYMew/jS4xJpx4E4EaNnYMlvPXGCHQ/5Woc+sFP43Aq4amr52HEsK7oUWXfBaGI1MyYF282ll8DWMHM/64cmg/gQu/7hQDuV/Zf4M06NhPAdiUcX0nPasik+Zxywq9t/uI1LNCd6FX/z29Cmx6rzbToEAlWctr/81MnvfE3RUOW6ACnpDIb3bYyIjYzdB3z27VxNs33vdZyYIhCNWJg+Gfb5+63FKTWVTFAlFxW0pgZdZwM1PyKATI+QPRc+mWr3Qi1oSxmfRXbMGwSFGFVCu9NtT6sqi2yzKOnhVWMkwQoA/FtcR5vYL+hWIkMe2o+ZnAwuCr7DHxCZuKeOyoPAziNiPp6A/VPA/Cw9xzaQUQzvefaBdCfWxG7zHwYM49i5lEA7gVwmU24CG2LbZB9c3Mznr57Pu773Cfx9jVH4MDtvTB56zmYO/tPGDJ+E+q7HcDmzX2xfP1s7Jp6P+o+sxPPLzkew4duwKqHHsfud7fJQHtBaCG1FHk5HsDnALxCREu8fVcDuB7A74noIgBrAHzCO/YAgNMBrAawB8AXWsetMvvxJNkzW3A+kV05yoy8ki/XX3v3oSy5bKWajWRbOkdJHftCuwxfzBfo2XPGlx8nVKxlZDiVaoM7VYyl3DLBO3h/HIrpeIw7qng0QxZsfIlENBL8jisvuAdiTqb/88hzL1iHtNjSW4QNEEaH/FNAUCYLADTBQl5/QH+Pen3crof+fjLGsLCbF+F2kJVIsRdGbtSxMTbZ4/Ymq9S/TYKC9blDRI0AvsTMFzPzNiL6AYAXvDzfZ+Zt3vfLANwJoCuAB71PrF2h9vAH2T/31lnYu+d4DFh1K2Yc+yyc3/TGTIdQN8d9cjnNhM1r++P9rsdjzKf+CZ0HT8FwIq1byAk3P4RnrpyNxrHz0fDI79A4rKsMtBeEFkBciWmMCgI19GEM+1DW1Nn2Uyk+aYSY5rSZP1ghN81wHSKr+0Vsek20UqeMLtZnKNdLWtcpViCEL9IZnevCBJb2dPC3e70aeYmmC7aJUW8sImzzuARGl07RcmzUldxPmMj+uygB6NKJEv3zqU+4PGE+Rqc6Ql1d2Gi2p3O/1NfHTxWt7u7cCagrlUKbceKFgE71JX2Hmc7b6NoFIKrT/bT4XCoB9XV2J1VfSgR0bUB0MLrxHQDq6xh1CQtH++k71x1EQwO0iJDqp7rdpb4JVLJ35yIlT0OXfe59VDLr4IkNCkVMQ5emQHxo9sgTJQQADrp3241OndS8XvyMwn0AUFdy0LnL/vAe9o/59SFf+jN6jf7rYmaWV7kdiMbGRl60aFG13Wg3NDc14dGf3YbdLz2Fj37wIex8twf6DN0OBlDXyf2tMQOb3+6P93udgjGf/Abq+09QoqSCIFQKIop9ptVS5KUgmI3avJGKuFfNtsMtiPpoNlvvH1a/ew2gesnB/1UtoDVOYWksKrnNgdjl9OnPf6WylxF7ycogqKc60DshbR5YsZme1yJcbCky+JndwTDqwewKGasQTRFsavc6Dv7n/vHzar8mrQIcuRf1bU+OOL5YMRIEMzMwiFk7Foolx9jhd1tzoyrB4H3t3LIuDjWRx16lO87LJ0HIwn9//B8wfvdr6N2wH9v3dcHK7uNw/r3RZeD2792HJ399L3q+dAt6d9uF7l0Pot+g93HK4J2gOW6avt3eg9NcwtaNfbCj35kY/OGL0P25E3Hot9/GoW1cL0EQQkS8lEVLWm3ldMtSm1058qYmbVnr08wd1oy872xNTEp6f5vhDmxUIxW6QDByZTiNtsPJZ5KQ1hi02fTffcc1vFNtGDuCsRg5L3dSQb6IKVFURGaFGdoMasG6KSXDZswptEaA/FPu7XC8tn8po3ORCBEhMlOYdj4RHf7u31vqDGLRrm0ciApXyESvjxpvcevKYHVcGqCIG7fibtcwUsrjWFEY/gL03wAZtRKEjsp/f/wfcNwhz6D3tB3o2W0bdu7ph34vbsH/PedS9D3+WOx76VEcN/ZvaOh2AHV1Dj7cbzfqZnkRFYew671u2LmlBzZsG4pRQ9/EorfPxIk/vBtDAAwB8NTV89Aog+wFoeqIeCmLlrx3L7c1qjbeo7EOK6mBmxbUI6aFFRUcYZOu3JrrkRiyrsdi0zJJzTnz1IR5TWmVw08jypE1MmEtyW8kx401SSEuebDgJZnRDD3GlVRc5LbicHxG4oVOEneGUcfvRUWhYDCjI/YNe/lqxCgaxbGIbE3ghfexuq6Nr0NUm4GQULp3+X9CWcPKX1/AKJLKC0WV/G5qypgX1VftVEu3FUHAzIHPou/UzXjpjVl4f80+jBvyGkYf+wY+0fwWiH6L0kd9oQLs2NoTb68dhf0HG9DpA+dizDlXok9dAwCgL9wxL0dPWOAKlq/diEU3fRPHjLzPHatSxToKgiDipQW0QmMh7ZV8QI6Gtfq6O5HyumXZLNsiKzZiG6NGGSVju1xbcfb1TOnnIbVxz7rgiiuTjH1Jl6qsoWkxDmiREwsZtEBgPmKPYf1XhWwZkoyWwk3Vz0TRotpQhBIZ+4LgBxtRDkv0KBROFBwgIz3BixoSwOSkRrZ8YUvaBQ/FkS9a3EUq3UiLEptRIkQWnwShgDxz5WxMGbsIDb33Yt/2rljyemPiYPYNf1+HRfc+jL2vPo9xPZ/DkEO3Ye/Orhg+cwNAjBOOvB80yU3LDkD1Dt58cwycQ47GgGPOQr8PzEa/Uif0S/BJBtkLQu0i4iU3LW0mxLTgrGbTmskJx8p2M3tG9c1vqogxGpRmmqQX9tZGcoJP5cAR9VCBbjgxziSdq7J6FSZhud3sd2B0b4tEjC1PjJCKvfURts/V6ZDj7rlgf4x4iKx47wuTmAuileNvky9jzEpyuFeJGGkmI477ky+wMuCXI3/9SVWCuUHU+vlKSBAKij+r18I1Z6PxPC/CMeE+/PWK07BnwsXY8+zvMG7gSuza2RUD+u3CoJHvYmCfvZg9mFAaHv4OnWb3N7Jrcw8cONgJ7w+Yi8M/ejHuv+5ezD3mZoz5zpIEL+zIavaCUJuIeMlMlvhBTjuZsiZ17bK0dKvQjjEbc1YX/EYowgZruqv6G2VNTmQ4jWpzMNtpyS5Ystg0x15ktpclQpGWJENeveFOkWwRoUAWAWApKnLNDNFqacPHu2u5JOYvQm3Q2wRMvK/eneuLA8WG5hvpZbhp1bsrFBqqgHMnICC3S5jlftXPvXqv6wJGswmgBNLGhmVZYFUQKk3eaImK4zhYt2otVj3zImaOXYg3lh+KPZvWY+k/nYWxozagrnMTZh79LLj5OdR9tDnIxw5wcF89Du7pjLUbh6O59wQ0DJuEgdM/iu4jJuO9X43AtlcGYUm3szD7oq/hvmtvwpQ9D2LHzj6JURZBEIqFiJdMVPpVeFJrLS0vkOuVfquhv4GOiyaYzSrz/bL5Zj6TEEo5Zmso24i2w+OjLkkN7bgyHI6fJUvLxzE2k3RrmFVLQpbvWXwlyxWxzlBmijFLo9zWlFZFayRyAF1IZfZbM6onjitPy85hHYPzTVFfOGLfjI6EERRfgpS8i8rkyhJiBNMys/VMWe45oiA9BT65w/XZYffeKjFkiUohKy0RHKYda7Tkq6eh33k34PU/P4i9G7egft9WDKx/C+NHv42d73dDfb2DPgN2oueQHRi4pxMGd25GqXcTxh/zFsbjrcC+0+wK9DVvj8I+7oPm+r4Yc/630XXYNNTXdQYAjLX41WfOTairvwJHPfv/sOmSR3BUr/0YePx69Dz152WeMUEQahERL4m0ghpoURePmMhLS16/txhbs9fFfUtsvD02vtvyZYlTZBElqZERa87k9JU+o6k2MyixSLQkp6ORmIsiKABkGsORbl8Xs+ZYk0gdDBs2Had1KVMjJCYJY3+0e5EQ6aYWnAtSoiNMYLLd1xSIpUBwKFMns+MJG1/EsGfTPN9KRIgMn1wRE46PcbuoyTKVQjpxguOZK2fjhJsfAjNj1/s7sfGNd7Dx9Tfx/pp12L9rH/Zt2Yj+uxfhYFNnNHEXNNB2zDptITasHohum5bhnR+diBnjNqJ5fx1mTvtfNL/6YYw/6gBwlF7+IfAiJ/vr3Zm9djdgx7v9MezQt7BlQ3/sGXYODv/Ip1E34Ej89btXoHHYfIz+56W56lga9Qn0PBXoceiNwI5XgF7jQEf+HKVRshaoILQnRLwkkuHVd0tMqljNZywz1k2/1eYASFjhL2KsvLomxYXMd8x+w5ERLTEtssGU3sHLt5lVyMSUpH0LxjOk5LLtj/M3sJsQdUjar9oOGtLKDjNCEn9tlKvAYVq1UxQAbarkVMcMfzTh6p1HPzpl3gOc6m9o15+MixlwSL/2VjcVNaVdF7Wyiipxmh3350PWwyBf1FD0HmElDOTLfMcB3N+kIkKgTh4QdmMjUHSq5+DkMIj97mT6lMyCYDJl7CIsXHM2aMNq8G8n4qhenbFnWzfMmPIsDtzZC017O4EO1GFYpyYc3mc/nCEloMQoTbT/6zV80kYMn7QRgHsPNu2rB9U72PpeL3Tdsx9bdgwCHToDPUdOgNOlPwZNnYW6HkNQ7y3CPND7+KJq9Wvbcejph2PRd69o0axepVGfAESsCEK7RsRLZuIa9Xkb+0b6Sr8ytbrTCu9l2YHjCSJ9Efn4Ll9Jb+3Vxl9UcKR3i0mP1eQ5C8nlpXTeyw0hbMzHRQjy4nhr5viRmDw2EqMrrHeragmq6Ai2Y3xILE/NT+7bXTWKoiTxIifKTrLfr6Rk8KMtMCIhqrcMoMT2iKB+XRkgVhaodCMppCkf98SwG7rUsgYi1BA6rfIbF9oVDb33ovG8G7Hr19PQbcBudHV2o/lgHUqdHDhNJTjE2H2wCw7u7Y5ezk7s2NkDu3kImqkruhx4B3vrh6HX+Jlo6DsAPVb/C5atPQZH/9P/ATr3Bbr0xzPXXITGYfMx9Ko1AJB5jInM6iUIQl5EvOSiEpEYI5/ZTo5ETmwHUsrO7GZiMzUV9e1zuO2/X9a71STlDd7wM7QuNF7bzVISkEWNxMVR4s9kPpGktYEVgWD+zeJbJGoCRLpW5UY9l2yImEhkI7kAv10d2FSiM5EKp5/GiI9AsIA96nLUVRO5kQiFko70aIxeb45WwQjV+KNZgvPA0AbNB8WboSljoUrt/vGuCXt5iNRfgxk7gnaevZEvuQS+0LHZt70rFt30TZz0vVeBUieg1CUQHD0uexedAW3xxV4Jtp6Z/xCmT3gef7n+x+4aKN+/qEXREpnVSxCEPJTSk9QuRDSbiF4jotVEdFXblm52qGkrcrZoE11sQR3MLjcRa3rsRN0T67XFFYbawcbNHRehyIoa3VF9awnB4o/qvpgoSkRUxRRudinLgy0LsysQyr3qjGheW72t7voRC7KcA8Oow27kKG1tG82OumFx1OZnKOAo3CT9o05FHKm7A5i9tYKsxAA53kcrTiucNR/J6xKmqRR3TEugiczK+UoKgpDIktcbcczI+/CXa7+K3dt24S/XuIJjyeuNuW2dcPNDWLxiBhqHzUfDIyPROGy+REsEQWgzCht5IaI6ALcAOBXAOgAvENF8Zl5eXc/SyNvNLEv8oKWoNrP6Fz9I2HxvnCcCkZQmyZ5NjKQ10OPewpeDGjlJ6laVKShmBucs3arKIWgWc+iL3v2IjG+xLoXnTo1y+Dttw6vU9nXCjaMKCC0ap+QxgiJRx2JEo+64+z+KGyui+gI/rRrKMWz6YUJyu4WphdqqS/4EABQa0Abm+33qIiov9MYzZPdfEAwq3T1LoiWCIFSLwooXADMArGbmNwCAiO4BMBdAG4iXct/ZJ8QdtN1ZA2KJcYwMrUWTljXc4xq8DCSuD5IUkbE19m1v5FsSRfEbyVnrb2sfm/uyRA2s+ROcT7MZzaAX1tJzGRfNMRvpcQLNFHWxIlTx22/bs23OCasq0PMHfyw2tbCJeW8qecN705tBzLhPgnox4HhdueLuZ63+3kYQVVH74nlGmRkOO+GUzsaPjcyTLwgJiOAQBKE9UGTxMhTAWmV7HYBjWrfIVmghVNpki+1lNxAVLfGta/XldJ6S1IZilrZ72dUPlEPlugKmRS+sZArNZLAbUQ32YnK9uI+JaCTVM06UkXIsYlYTGNEEsZEhipal6veouFLGZ7F+LkhxThukrxTgflUjN2FIK3Tdi7CUDB+hRFfcDcXXcFG+oFBmr3shhecsZrIBQRAEQWjPFFm8ZIKILgVwqbe5C3+//7Vq+hPDAADvVtuJvDTpm7F12NcGvlSAQl4DA6lD9amm/yOrVK5QJRYvXvwuEa0xdhftNyT+ti7ib+tSNH+B4vgc+0wrsnhZD2C4sj3M26fBzLcCuLWtnCoHIlrEzPlHTdYQRa9D0f0HpA61QNH9F4oFMw809xXtHhR/Wxfxt3Upmr9AMX02KfJsYy8AGENEhxFRZwCfAjC/yj4JgiAIgiAIgtBKFDbywsxNRPRlAA/DHcp7OzO/WmW3BEEQBEEQBEFoJQorXgCAmR8A8EC1/agANd2tLSNFr0PR/QekDrVA0f0Xik/R7kHxt3URf1uXovkLFNNnDeLc868KgiAIgiAIgiC0PUUe8yIIgiAIgiAIQgdCxEsbQ0TDiehJIlpORK8S0Ve9/f2I6FEiWuX97VttX5MgojoieomIFnjbhxHRQiJaTUS/8yZRqFmIqA8R3UtEK4loBREdW6RrQERf8+6fZUT0WyJqqPVrQES3E9FmIlqm7LOec3L5mVeXpUQ0rXqeh8TU4V+9+2gpEf2JiPoox77t1eE1IvpIdbwWOgJENNu7z1YT0VXV9sekqM++oj3rivZsq/VnWdGeWx3lGSXipe1pAvCPzDwRwEwAlxPRRABXAXicmccAeNzbrmW+CmCFsn0DgJuYeTSA9wBcVBWvsvNTAA8x83gAk+HWpRDXgIiGAvgKgEZmngR3wopPofavwZ0AZhv74s75HABjvM+lAH7ZRj6mcSeidXgUwCRm/gCA1wF8GwC83/WnABzp5fkFEdW1natCR8G7r26B+7uZCODT3v1XSxT12Ve0Z11hnm0FeZbdiWI9t+5EB3hGiXhpY5h5AzO/6H3fCfcflqEA5gK4y0t2F4Czq+NhOkQ0DMBHAdzmbROADwO410tS6/73BnAigF8DADMfYOb3UaBrAHeyja5EVA+gG4ANqPFrwMxPA9hm7I4753MB3M0uzwHoQ0RD2sbTeGx1YOZHmNlfs/U5uGtOAW4d7mHm/cz8JoDVAGa0mbNCR2IGgNXM/AYzHwBwD9z7r2Yo4rOvaM+6gj7bavpZVrTnVkd5Rol4qSJENArAVAALAQxi5g3eoY0ABlXJrSzcDOCbABxvuz+A95Ufxzq4D6Va5TAAWwDc4XUHuI2IuqMg14CZ1wP4CYC34f5Dvx3AYhTrGvjEnfOhANYq6YpSn3kAHvS+F7UOQvEo1L1WoGdf0Z51hXq2FfhZVuTnVrt4Rol4qRJE1APAHwBcycw71GPsTgFXk9PAEdEZADYz8+Jq+9IC6gFMA/BLZp4KYDeMMHqNX4O+cN+YHAbgUADdEQ0TF45aPudZIKJr4HaN+U21fRGEWqUoz76CPusK9WxrD8+yWjqfabSnZ5SIlypARJ3g/uP9G2b+o7d7kx9e9P5urpZ/KRwP4Cwiegtu14QPw+1j28cL+wJuSHJ9ddzLxDoA65h5obd9L9x/8ItyDU4B8CYzb2HmgwD+CPe6FOka+MSd8/UAhivparo+RPR5AGcA+AyH888Xqg5CoSnEvVawZ18Rn3VFe7YV9VlWuOdWe3tGiXhpY7w+s78GsIKZ/105NB/Ahd73CwHc39a+ZYGZv83Mw5h5FNyBXk8w82cAPAng416ymvUfAJh5I4C1RDTO2zULwHIU5BrADbHPJKJu3v3k+1+Ya6AQd87nA7jAm71lJoDtSpi+piCi2XC7lpzFzHuUQ/MBfIqIuhDRYXAHcT5fDR+Fds8LAMZ4szR1hvtv8/wq+6RRtGdfEZ91BXy2FfVZVqjnVrt8RjGzfNrwA+AEuCHGpQCWeJ/T4falfRzAKgCPAehXbV8z1OVDABZ43w+He9OvBvA/ALpU278U36cAWORdh/sA9C3SNQDwPQArASwD8F8AutT6NQDwW7j9mg/CfUN4Udw5B0BwZ0/6O4BX4M5GU6t1WA2337D/e/4PJf01Xh1eAzCn2v7Lp/1+vOfI6979dk21/bH4V9hnX5GedUV7ttX6s6xoz62O8owiz3lBEARBEARBEISaRrqNCYIgCIIgCIJQCES8CIIgCIIgCIJQCES8CIIgCIIgCIJQCES8CIIgCIIgCIJQCES8CIIgCIIgCIJQCES8CIIgCIIgCIJQCES8CIIgCIIgCIJQCES8CEIKRDSRiD5PRMOJqGe1/REEQRCEcpFnmlB0RLwIQjqdAFwB4BwAu8yDRDSKiPYS0ZJKF0xEXYloCREdIKIBlbYvCIIgdDjkmSYUGhEvgpDOcAB3AFgNIO4t1d+ZeUqlC2bmvZ7ddyptWxAEQeiQyDNNKDQiXgTBg4ie8N4ILSGifUT0CQBg5gUA7mXmB5h5RwY7o4hoJRHdSUSvE9FviOgUInqWiFYR0Yw86QRBEAQhL/JME9orIl4EwYOZP+y9EfoVgPkA/qAc25jT3GgA/wZgvPc5H8AJAL4B4Ooy0gmCIAhCZuSZJrRX6qvtgCDUEkR0AYA5AM5l5uYWmHqTmV/xbL4K4HFmZiJ6BcCoMtIJgiAIQi7kmSa0R0S8CIIHEZ0H4DMA5jLzwRaa2698d5RtB/rvLms6QRAEQciMPNOE9orcSIIAgIjOAHAZgDOYeV+1/REEQRCEcpFnmtCekTEvguByF4BhAJ71BjdeVG2HBEEQBKFM5JkmtFuImavtgyAUGiIaBWABM09qxTLeAtDIzO+2VhmCIAiCIM80odaRyIsgtJxmAL1bc0EvuIuKOZW2LwiCIAgG8kwTahqJvAiCIAiCIAiCUAgk8iIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiEQ8SIIgiAIgiAIQiGor1bBRNQVwEMAPszMzZbjPwHwADM/0ebOCUKFWbx48SH19fW3AZgEeWkgVBYHwLKmpqaLp0+fvrnaznRU4p5pRHQngAXMfC8R3QPgO8y8qkpuCkJFkGea0IqkPtOqJl4AzAPwR5tw8fg5gP8EIOJFKDz19fW3DR48eMLAgQPfK5VKXG1/hPaD4zi0ZcuWiRs3brwNwFnV9qcDk/ZMA4BfAvgmgEvaxiVBaB3kmSa0FlmeadVUy58BcD8AENG3iOgVInqZiK4HAGZeA6A/EQ2uoo+CUCkmDRw4cIf8Iy9UmlKpxAMHDtwO9w2oUD0+A+B+cvk/RPQaET0G4BAlzV8BnEJE1XxxKAiVQJ5pQquQ5ZlWFfFCRJ0BHM7MbxHRHABzARzDzJMB3KgkfRHA8dXwURAqTEn+kRdaC+/ekq4bVUJ9pgE4B8A4ABMBXADgOD8dMzsAaIUNMAAAIABJREFUVgOYXAU3BaGSyDNNaDXSnmnVetgNAPC+9/0UAHcw8x4AYOZtSrrNAA5tY98EQRAEIQ/qM+1EAL9l5mZmfgfRrs/yXBMEQWgB1RIvewE0ZEjX4KUVBEEQhFol6zMNkOeaIAhCi6iKeGHm9wDUEVEDgEcBfIGIugEAEfVTko4FsKwKLgpCu+S8884b1a9fv8ljxow5srXs1NXVTR8/fvzE0aNHHzlu3LiJ11577aDm5qQxzMUiqX4LFizo2bNnzynjx4+fOH78+InHHXfcWAD4+te/fmjXrl2nrl+/Phjr0K1bt6n+97fffrv+jDPOOHz48OGTjjzyyAknnXTS6KVLl3YBgKVLl3Y56aSTRo8cOXLSxIkTJ5x++umHr127VsZM1BDGM+1pAJ8kojoiGgLgZCO5PNcEoULIM63lFPGZVs0+0o8AOIGZHwIwH8AiIloC4BsAQESdAIwGsKh6LgpC+2LevHnvzp8/P3Wa1gULFvQ899xzR5Vjp0uXLs7KlSuXr169+tUnnnji9UcffbT3N77xjXbTTSatfo2NjbtWrly5fOXKlcv/9re/ve7v79OnT9N11103yLTnOA7OOuus0SeeeOLOtWvXLnv11VdXXH/99evfeeedTnv27KEzzzxzzBe/+MUta9asWbZ8+fIVl1122ZaNGzeKeKk9HgFwAoA/AVgFYDmAuwH8r5+AiAYB2MvMG6vioSC0M+SZ1nKK+Eyrpni5BcCFAMDM1zPzRGaewsxXe8fPAHAvMzdVzUNBaGfMmTNn18CBA1v8m8pqZ+jQoU233XbbW3fcccchjuO0tNiaI0/9Pv3pT2+dP39+v02bNtWp+xcsWNCzvr6ev/nNb27x9x177LF7Z8+evevWW2/tN23atF3nn3/+dv/YGWecsfPoo4/eV/HKCC3lFgAXssuXmXkcM5/KzKcz871emvMB/KqKPgpCu0KeaZWlKM+0qr29Y+YXiehJIqqLmRe/HsC/tbVfgtDazJs3b/iyZcu6VdLmpEmT9tx+++1rK2mzUkycOPFAc3Mz1q9fXz98+PCKvoyYMWPGuM9+9rPvfuUrX9m6f/9++uAHPzj285///JbLLrts286dO0uzZs0ac8kll2y+5JJL3tu6dWvdnDlzRl9++eWbLrzwwvc3bNhQP3fu3COuvPLKjeeff/72t99+u37EiBG5/VPrBwCLFi3qMX78+IkAMHfu3G033HDDRgDo0aNH86c//el3r7/++kE33XTTO37+pUuXdp08efIem+1ly5Z1nTZtmvWYUFtkeKYB7qD+/2pLvwShtZFnWuWQZ1o2qtr1gJlvTzj2P23piyAIwAc+8IHxBw4cKO3Zs6e0ffv2ev8frB/+8Ifrzj333B3V9q8INDY27nryySdX245dddVVmydPnjzxu9/9rnQbaockPdO843e0lS+CIMgzrRLU4jNN+k0LQhtTq2+TAGDp0qUrATfse8cdd/T/wx/+8FZLbS5fvrxzXV0dhg4dWvEuoM8///xr/vcuXbqwut2zZ09H3e7fv3+zuj1kyJAmdbucN1SAXr+XX345Me2AAQOazznnnG3/+q//GixceNRRR+297777+trSH3nkkfuefvrpHuX4JQiC0BbIM61yyDMtG7KomSAIrcY777xTf8kll4z8whe+sLlUan//3JRTv2uuuWbTXXfdNbC5uZkA4Mwzz9x54MAB+slPfjLAT7Nw4cKuDz30UI9LLrlk6+LFi3vcc889vf1jDz74YI8XXngh67S8giAIQoWQZ1qUajzT2t+ZFwQhljPPPPOwE044Yfybb77ZZdCgQR+46aabBqTnymdn//79JX/axZNPPnnsrFmzdvzkJz95J8lekWhp/YYMGdI0Z86c9w4cOEAAUCqVMH/+/L8/8cQTvYYPHz5p9OjRR37rW98aOnTo0IM9evTg+++/f/Utt9xyyMiRIycdccQRR95yyy2HDB48WCYyEQShwyPPtJZTxGcaMXPeegqCkJOXX375rcmTJ79bbT+E9svLL788YPLkyaOq7YcgCO0feaYJrU3SM00iL4IgCIIgCIIgFAIRL4IgCIIgCIIgFAIRL4IgCIIgCIIgFAIRL4LQNjiO41C1nRDaJ9691f6WexYEoVaRZ5rQaqQ900S8CELbsGzLli295R97odI4jkNbtmzpDWBZtX0RBKHDIM80oVXI8kyTRSoFoQ1oamq6eOPGjbdt3LhxEuSlgVBZHADLmpqaLq62I4IgdAzkmSa0IqnPtA43VTIR3Q7gDACbmXlSC22dDOAmZdd4AJ9i5vtaYlcQBEEQBEEQhCgdUbycCGAXgLtbKl4Mu/0ArAYwjJn3VMquIAiCIAiCIAguHS7Ux8xPA9im7iOiI4joIfr/7N13fFRV+vjxz5OEhNAChITepSMgIoIFVpEFdRUUQVARFFH3h1hQUdYG6Fd0ZcXOIthwEcQOLiI2sC2hiKhIh9A7acT0eX5/3JsxCZk0MpmEPO/X675m7r3nnPtMxDlz7j1FZK2IfCci7UtQ9DXAZ9ZwMcYYY4wxxj8qXePFh1eB8ap6NnAf8EoJyhgOzC/VqIwxxhhjjDFelX7AvojUAM4D3hPxTpoR5p67GpiaT7Z9qjogRxkNgTOBz/0brTHGGGOMMZVXpW+84Dx9ilfVbnlPqOqHwIdFKGMY8JGqZpR2cMYYY4wxxhhHpe82pqqJwE4RGQogjq7FLGYE1mXMGGOMMcYYv6p0jRcRmQ/8D2gnIntFZAxwPTBGRNYDG4BBxSivBdAUWFH60RpjjDHGGGOyVbqpko0xxhhjjDEVU6V78mKMMcYYY4ypmCp040VE7hGRDSLym4jMF5GqgY7JGGOMMcYY4x8VttuYiDQGvgc6qmqKiCwElqjqm77y1KtXT1u0aFFGERpjTNlZu3btUVWNCnQcpuxYnWaMOV0VVKdV9KmSQ4BwEckAqgH7C0rcokUL1qxZUyaBGWNMWRKRXYGOoTwQkYHA80AwMEdVn8pzPgyYC5wNHAOuVdVY99wkYAyQBdypqp8XVKaItAQWAJHAWmCkqqb7uoaIRALvA+cAb6rqHTniOht4EwgHlgB3aSF3F61OM8acrgqq0ypstzFV3QdMB3YDB4AEVV0W2KiMMcYEiogEAy8DlwIdgREi0jFPsjFAnKqeAcwAnnbzdgSGA52AgcArIhJcSJlPAzPcsuLcsn1eA0gFHgHuyyf8mcBYoI27DSzp38EYY05nFbbxIiJ1cKY0bgk0AqqLyA35pLtVRNaIyJojR46UdZjGGGPKTk9gm6ruUNV0nKcieae+HwS85b5/H+gnIuIeX6Cqaaq6E9jmlpdvmW6ei90ycMscXNA1VDVZVb/HacR4iUhDoJaqrnSftszNUZYxxpgcKmzjBbgE2KmqR9yV7T8EzsubSFVfVdUeqtojKqpk3cFXrlzJxo0bTy1aY4wx/tYY2JNjf697LN80qpoJJOB0+/KV19fxSCDeLSPvtXxdo6C49xYStzHGGCp242U30EtEqrl3wPoBfmlh3HnnnYwbN867P2PGDD7++GN/XMoYY4zx6VR7E7z00kvcc889fojMGGPKRoVtvKhqDM7j+J+AX3E+y6v+uNbcuXOZPn26d/+ll17is88+8+4PGDCAWbNmefeTk5P9EYYxxpiC7QOa5thv4h7LN42IhAAROIPqfeX1dfwYUNstI++1fF2joLibFBI3cOq9CWJjY9mwYUOx8xljTHlRYRsvAKr6mKq2V9XOqjpSVdP8cZ327dvTvXt37/62bduYMWMGAOnp6YSEhBAU5Pwpk5OTiYiI8J7PzMxk6dKlxMXF+SM0Y4wxf1oNtBGRliISijMAf1GeNIuAUe77a4Cv3XEmi4DhIhLmziLWBljlq0w3zzduGbhlflLINfKlqgeARBHp5fYkuDFHWaVq+vTpLFtmc9sYYyquCt14CRQRoVq1agCEhoby3//+l7FjxwJOY2XKlCmcf/75AGzatIlLL72UJUuWAJCUlMSSJUvIzMzMv3BjjDEl4o4vuQP4HKcb8UJV3SAiU0XkSjfZa0CkiGwDJgAPunk3AAuB34GlwDhVzfJVplvWA8AEt6xIt2yf1wAQkVjgWWC0iOzNMXPZ/wPm4EwUsB348/G+McYYrwq7SGVJ9OjRQ8t6TvyUlBRiYmLo1KkTUVFRvPXWW4wePZoffviB8847D4/H431qY4wxJSUia1W1R6DjMGWnJHXaDz/8wLRp05g5cyZNmzYtPIMxxgRAQXVaRV+kstwLDw/nL3/5i3d/xIgRREdH07t3bwAmT57M8uXL+eqrr6hSpUqAojTGGFMZpKens2/fPk6cOBHoUIwxpkTsln8ZCw0N5dJLL8Xp1gzNmzenc+fO3obLnDlz+N///hfIEI0xxpymLrroItatW0eHDh0CHYoxxpSINV4CbMyYMbzyyisAZGRk8PDDD/PWW295z9vCmsYYY4wxxjis8VKOVKlShe3btzN16lQAtmzZQsOGDXn33XcDHJkxxpjTxaOPPsq1114b6DCMMaZErPFSzlSvXp3o6GgAatWqxT/+8Q8uvPBCAFasWMGdd97J8ePHAxmiMcaYCqxatWpUr1490GEYY0yJ2ID9cqxBgwbepzAAv/76Kx988AHPPPMMAGvWrCEiIoI2bdoEKkRjjDEVzIMPPlh4ImOMKafsyUsFcscdd7Bz507CwsIAmDBhQq5H/5s3byYjIyNQ4RljjKlArL4wxlRE1nipYEJDQ73v586dy8yZMwHweDz07dvXu1gmOAtiGmOMMXmNHDmSgQMHBjoMY4wptoB3GxORF4qQLFFVH/Z7MBVMixYtaNGiBeA0Xv79739Tv359AI4dO0bDhg15+eWXGTt2LNmLkWZP0WyMMeWR1Qllo0+fPsTFxQU6DGOMKbaAN16AQcCjhaR5ELCKqgAhISEMHjzYu+/xeJg0aRK9evUCYPXq1QwfPpyFCxfSo4ctwm2MKbesTigDOZ/SG2NMRVIeGi8zVPWtghKISJ2yCuZ0ERUVxZQpU7z7IkLnzp1p1aoVAO+//z7z589nzpw51Kljf15jTLlhdUIZycrKYt26dXZDyxhToZSHMS8/FJZAVZ8ri0BOZ+eccw6LFi2ibt26ACQkJLB7924iIiIAWLhwIQsWLPB2LzPGmACxOqGM/POf/+Tcc89l9+7dgQ7FGGOKrDw0Xl4Vka0i8riIdAx0MJXFmDFjWL16NUFBzj+B2bNnM3PmTO+YmISEhECGZ4ypvKxOKCM33HAD8+fPp1GjRoEOxRhjiizg3cZU9SwRaQcMB94XkQxgPrBAVWMDGlwl8vnnn3P06FEATpw4QYsWLZg0aRITJ04McGTGmIpORLoXdF5Vf8rx3uqEMtK0aVOaNm0a6DCMMaZYysOTF1R1s6pOUdWOwI1ABPCViBTafcCUjqCgIKKjowGnH/Rdd91F3759AdizZw+PP/44x44dC2SIxpiK61/u9jIQA7wKzHbfv5w3sdUJZUdVmTVrFm+++WagQzHGmCIp1ScvIvIi4HPQhKreWUj+ICAaqA9UBw6XZnymaCIiIpg8ebJ3/6uvvmLKlCmMHDmSyMhIkpKSqF69urfLmTHGFERVLwIQkQ+B7qr6q7vfGZjsK5/VCf4nInzyySeICKNGjbLp9I0x5V5p//pcA6wFqgLdga3u1g0I9ZVJRC4UkVeAvcB9wHdAO1W9qpTjMyUwevRo9uzZ411T5s477+Scc87B4/EENjBjTEXTLrvhAqCqvwEd8iayOqFszZ8/n08//dQaLsaYCqFUn7xkT28pIn8HLlDVTHf/3ziVz0lEZA+wC1gATFZVu7NWDjVs2ND7/tJLL6VLly7eJy9PPfUUl1xyiU23aYwpzC8iMgf4j7t/PfBLzgRWJ5S97Fkn4+Pj2bFjB927FzhEyRhjAspfA/brALWA4+5+DfdYfi5Q1V1+isP4wbBhw7zvjx8/zrRp0/B4PPTo0QNVJTk5mRo1agQwQmNMOXUT8HfgLnf/W2BmnjRWJwTIDTfcwPr169m2bRthYWGBDscYY/Llr0ELTwHrRORNEXkL+Al40kfamworTEQml2JsphTVrVuXffv2cccddwDwzTff0Lp1a37++ecAR2aMKW9UNRX4N/Cgql6lqjPcYzmdUp0gIgNFZLOIbBORB/M5HyYi77rnY0SkRY5zk9zjm0VkQGFlikhLt4xtbpmhp3CNe0Rkg4j8JiLzRaRqYX+H0vb000/z3nvvWcPFGFOu+eXJi6q+ISKfAee6hx5Q1YM+kt8iIokFFCc4U2ZOLsUQTSnK+ZQlOjqaiy++mPbt2wPOk5k6depYX2pjDCJyJfAMzhjIliLSDZiqqlfmSFbiOkFEgnFmL+uPM15mtYgsUtXfcyQbA8Sp6hkiMhx4GrjWXVNmONAJaAR8KSJt3Ty+ynwamKGqC9zu0WNwniQV9xoNgDuBjqqaIiIL3XRvFvgHLWWdOnXyvl+6dCnnnnsuder46jRhjDGB4ZcnL+L8Ur0E6KqqnwChItLTR/LZQM0Cthpumvyu005Efs6xJYrI3aX8cUwxdO7cmfnz51O1alWysrK46KKLGDNmTKDDMsaUD48BPYF4AFX9GWiZJ02J6wS37G2qukNV03HGzQzKk2YQ8Jb7/n2gn1tnDcJZSyZNVXcC29zy8i3TzXOxWwZumYNLeA1wbiaGi0gIUA3Y7+Mz+t2xY8cYOnQoDz540oMrY4wJOH+NeXkF8OB8sU8FkoAPgHPyJlTVKSW9iKpuxpnJLPuO2z7go5KWZ0qXqjJ27FjvImhZWVkcOHCAJk2aBDgyY0yAZKhqQp4nsbmm1z+VOgFoDOzJsb+XP3sAnJRGVTNFJAGIdI+vzJO3sfs+vzIjgfjsiWnypC/WNVT1fyIyHdgNpADLVHVZMT53qYqMjGTp0qXeJzHx8fHUqlXLpsc3xpQL/vomOldVxwGpAKoaRwFTJZeSfsB2G+hZfoSEhHDHHXcwaJBz4/PNN9+kTZs2bNiwIcCRGWMCZIOIXAcEi0gbd22wHwMdVKCJSB2cpzItcbqTVReRG3ykvVVE1ojImiNHjvgtpvPPP5/atWsDMGrUKPr164eqz2XcjDGniSNHjvD++++TlJQU6FB88lfjJcN9EqIAIhKF8yTGn4YD8/18DXMKLrnkEh588EE6duwIwO+//05GRkaAozLGlKHxOOM90nC+rxOB0uzquw9ommO/iXss3zRuF60I4FgBeX0dPwbUdsvIe63iXuMSYKeqHlHVDOBD4Lz8PqCqvqqqPVS1R1RUlM8/RGlRVa699lpGjBiBiKCqfPnll2RmZhae2RhT4SxatIgRI0awfv36QIfik78aLy/gdN+KFpH/A77H92xjiEiwiNxT0ou5M7xcCbyXz7kyuUtlCte8eXMee+wxRIQ//viDiy++mJtvvjnQYRljyoiq/qGqD6nqOe4P8IfymW3sVOqE1UAbdxawUJybWovypFkEjHLfXwN8rc4jhUXAcHemsJZAG2CVrzLdPN+4ZeCW+UkJr7Eb6CUi1dyxMf2AjSX4/KVORLjuuuu49dZbAVi5ciX9+/fn7bffBrCnMcacZsaMGUNMTAwXXHBBoEPxyS+NF1WdB0wEpgEHgMGqelLDIkf6LGDEKVzyUuAnVT2UT9llepfKFE14eDhz5szh7rudm65JSUmsXr06wFEZY/xJRBaLyKI829siclfOqYFLWie440/uAD7H+fG/UFU3iMhUd6YzgNeASBHZBkwAHnTzbgAWAr8DS4Fxqprlq0y3rAeACW5ZkW7ZJblGDM7A/p+AX3Hq5leL+/nLQs+ePfnoo48YMmQIAAsXLuT888/nwIEDAY7MGHOqjh07BkD37t1RVVatWlUub1CIP4ISkbr5HE5yH4f7yjMDqAK8CyRnH1fVn4pwvQXA56r6RkHpevTooWvWrCmsOBMATzzxBI8++ijbtm2jVatWgQ7HmApHRNaqao9Ax1EQEXkeiOLPLr7X4nQdU6CWqo7MkbbEdUJlUR7qtA8++IBZs2axdOlSgoKC+PLLL4mKiqJr164BjcsYUzyHDx+mUaNGvPTSS9x+++288847XH/99fzvf/+jV69eZR5PQXWavxovsTj9euNw5uSvDRwEDgFjVXVtPnm+yacoVdWLC7lWdZxH7q1UNaGgtOXhi97kLykpiSVLlnDttdcCzhoDvXr18g4YNcYUrII0Xlar6jn5HRORDaraKcfxEtUJlUl5rNO6dOlCzZo1+eGHHwCnW5mt82VM+Xfs2DFmzZrFVVddRYcOHUhMTOSTTz7hiiuuCMhvsUA0XmYD76vq5+7+X4EhwBvA86qad+rKMlEev+jNyeLj42ncuDE33HADs2bNCnQ4xlQIFaTxshEYoKq73f1mOE/NO4jIOlU9K7ARVizlsU47fvw4hw8fpn379iQnJ3PeeecxdepU76yTxhhTFAXVaf4asN8ru+EC4M5X31tVVwJh+WUQkQgReTZ7cL2I/EtEIvwUnynHateuzQ8//MDDDz8MOI8y9+8P2HptxpjScy/wvYh8IyLLge+A+9wn6G/lTGh1QsVUt25d2rdvDzhTrkZFRREZGend/+233wIZnjHGh99//52UlJRcx06cOMF//vMfdu/eHaCo8uevxssBEXlARJq720TgkDt9sq8pk1/HWcxymLsl4jypMZVQt27dvItb3nnnnfTo0eOk/6mMMRWLqi7BmWHrbuAuoJ2q/ldVk1X1uTzJrU6o4Fq0aMGXX37pnbXo5ZdfpkuXLuzbl3f2amNMIGVlZXHOOecwadKkXMcPHTrEyJEjWbJkSYAiy5+/Gi/X4cxf/7G7NXOPBeNUQvlpraqPqeoOd5sC2Mhtw9SpU3nuuecIDw8HsEaMMRVbG6Ad0BUYJiI3+khndcJpZvz48bz77rs0btwYgMmTJzN79uwAR1V55Bwm8Mknn9ChQwfvHfVPP/2UPn36sGuXs873/v37y93dduM/Ho+HuXPncuONub+OW7Vqxbp16xg7dmyAIsufv6ZKPqqq41X1LHe7w118K11Vt/nIliIi3kmlReR8wH6lGtq2bcuwYU6bd/ny5bRs2ZKffrIJh4ypaETkMeBFd7sI+CfOGl35sTrhNBMZGcnQoUMB54f0jz/+yKpVq7zn3377bfvB7Cc///wz7dq189adkZGRdOzYkbCwP3vyBwUFkb2kxNy5c2nevDlHjx4FIC4ujqysrLIP3JSJKlWqMGTIELp3757ruIjQrVs3goODAxRZ/kIKT1J8IhKFs85LJyDn3P0FzRJzOzA3R5/mOP5c5MsYAKKjo+nTpw/t2rULdCjGmOK7BueJyzpVvUlE6gP/8ZHW6oTTmIiwbNkyUlOdNUr37dvHjTfeyPTp07n33ntJS0vjww8/ZODAgdSpUyfA0VZMqkpSUhK1atWiZcuWNG3alLS0NAAuuOCCXIsQ/u1vf+Nvf/ubd3/YsGE0bNiQevXqAXD33XezevVqNmzYYLPHnYY2btyIx+OhU6dOJ53bu3cvs2fP5uabb6Z58+YBiO5k/uo2Ng/YBLQEpgCxOKsU50tEgnD6PncFugBd3Cc2v/gpPlNBdezYkYULF1K9enUyMzO5+uqrWbZsWaDDMsYUTYqqeoBMEakFHMaZVj8XqxMqj6pVnfubjRs3Ztu2bYwc6Sz18+OPP3Ldddfx448/ArBjxw6efvppDh48GLBYK5pRo0ZxxRVXoKpERETw1Vdf0bt37yLlbdWqFaNG/Xmv4JprrmH8+PHehsvVV1/N9OnT/RK3KXuPP/54rsZrTklJSTzxxBOsXXvSKicB46/GS6SqvgZkqOoKVb0Z8PnUxa3MJrrvE1U10U9xmdPIoUOH2Lx5M3FxcYEOxRhTNGtEpDYwG1iLs6L8//ImsjqhcmrdujXR0dEA9OnTh1WrVnHhhRcCsHLlSh588EGSkpIAWLx4MX/961+9jZkjR46wd+/ecrkaeKAMGDCAK664Ao/H1zxJRXfFFVfw97//HYDMzEyqVKni7UqUlZXFuHHjKG/Tdpuie+SRR3j99dfzPde+fXuOHz/O1VdfXcZR+eavxkuG+3pARC4XkbOAuoXk+VJE7hORpiJSN3vzU3zmNNC4cWPWrVvnXdhy0aJFLF++PLBBGWPyJc4t22mqGq+q/wb6A6NU9SYfWaxOqMSCg4M555xzqFWrFgDXXXcdR48e5YwzzgAgPT2d+Ph4b5eyWbNm0bRpU283tPnz53Pbbbd5GzObNm0iJiYmAJ+k7KSmpnLHHXfw0UcfAXD99ddz3333lfp4hZCQEN59913uueceALZt28a8efPYsWMHAEePHmXu3LkkJto9h4qiQ4cOXHTRRfmeExEiIsrXLPX+arw84fZTvhe4D5gD3FNInmuBccC3OHfk1gLWjDcFCg0NBZy+vU8++SQPPfSQ3XkzphxS53/MJTn2YwvpBmZ1gsklMjLS221pyJAhrFq1yjvgfNCgQbz++uveWSl37tzJd999500/Y8YMrrzyz7kh7r77bnr16uXdf/7555k4caJ3f/HixSxYsMC7/+OPP/Ldd99597ds2cK2bX/OP3Ts2DESEhJK8+MWW1BQEDExMfz6669let127dpx5MgRBg8eDMCSJUsYNWqUtzETFxdns4SWY0lJSSxatMg7OUN+Vq1axYgRI4iPjy/DyAqgqqW64UyHfE8x8wQB55d2LHm3s88+W83p68SJE7p3715VVU1KStKYmJgAR2RM2QHWqJ+/Q091w1mI8pwipCuTOqGib1anFd3WrVt1xYoV3v3Zs2frpEmTvPvjx4/XgQMHevcvv/xyzfn37d+/v/bu3du736dPH+3bt693v1evXtq/f3/vfo8ePXTw4MHe/SFDhujEiRO9+59//rlu2rTplD9XVlaWvv766/rHH3+oqmoCUYHXAAAgAElEQVRqauopl3mqPB6Prl27Vj0ej6qq3n///RoZGemN0ZQvP/zwgwL66aef+kyzbNkybdq0qa5fv77M4iqoTiv12cZUNUtERgAzipHHIyIvAWeVdjym8qhevTrVq1cHYNq0afzzn/9k27Zt5WZ2DGMM5wLXi8guIBkQnIcyXXImsjrBlLYzzjjD2+UM4JZbbsl1/oUXXsi1v2DBAjIyMrz7M2fOzLX/5JNPZje0Abjvvvu8PQEARo8e7e3yBlC/fn3q1nV6Paoq119/PYMGDWLOnDkAvPHGG/Tr149mzZoV63OtW7eOm2++mYyMDG699dZcUx8HiojkmnJ30KBBNG7c2PtU7I477qBp06Y88MADgQrR5NCtWzdWrlxZ4Cyul1xySbmaxlxy/s9XaoWKzACqAO/iVFAAqKrPxTlEZDrOwM0P1R9BAT169FAbUFY5JCYmsnTpUu/6MMePH/dWHMacjkRkrar2CHQcBRGRfO8kqOqufNL6vU6o6KxOq5hUlY0bNxISEkLbtm05cuQI0dHRPPnkk0yaNImsrCwOHjzoXcwzr8OHD7Nq1Srv7FDLly+nb9++FWIKY1Vl6NChtGzZkmeeeQZwFsjs379/uWh4mfKjoDrNX42Xb/I5rFrAOi8ikgRUB7JwFiLLviNXy1ee4rIv+srp999/59xzz+X111/3LpBmzOmmIjReANyFJ9uo6hvummA1VHVnPun8XidUdFannT527NhBzZo1iYqK4uuvv6Zfv3588cUXXHLJJWzfvp2YmBiGDx9OUFAQf//735k3bx779++nRo0agQ69RFQVEeGXX36ha9euPP/889x5552BDqtSWrFiBenp6fTv37/AdG+99Rbz58/ns88+K5OGckF1ml8WqVTV/KcsKDhPTX/EYkyDBg244YYb6Nu3b6BDMaZSE5HHgB5AO+ANnCf0/wHOz5vW6gRTmbRq1cr7vk2bNkybNs07ocA333zD2LFj6d27Ny1btuSee+7h7rvvrrANF8D74/fMM89k2bJl9OzZE4DvvvuOX375hVtvvZUqVaoEMsRK4+mnn+bQoUOFNl4yMzPJzMzkjz/+8HbRDxR/PXmpDzwJNFLVS0WkI9BbnbVffOUR4Hqgpao+LiJNgYaquqq04rK7VEZVeeCBB7jpppvo0KFDoMMxptRUhCcvIvIzzjiWn1T1LPfYL3nHvLjH/V4nVHRWp1UOCQkJHDhwgBYtWngX9TxdjR8/nk8++YQtW7ac9p+1vDh06BAJCQm0bds20KHkUlCd5q+pkt8EPgcauftbgLsLyfMK0Bu4zt0/Abzsj+BM5bVnzx7eeustlixZUnhiY0xpS3fHryiAiBR0+87qBGOAiIgI2rdvXyl+zL/wwgvExMRQtWpVsrKymDBhQq4pqU3pq1+/frlruBTGX42Xeqq6EPAAqGomTr/lgpyrquOAVDdPHBBacBZjiqdZs2b89ttvTJgwAXD6GWdmZgY4KmMqjYUiMguoLSJjgS+B2T7SWp1gTCUjIjRs2BCAjRs3MmfOHFatsoet/nLixAleeeUVtm/fXqT048aN4+qrr/ZzVIXzV+MlWUQi+fPuWi+gsNWbMkQkOEeeKNzGjzGlKSoqChEhOTmZvn37cvPNNwc6JGMqBVWdDrwPfIAz7uVRVX3RR/IS1QkiMlBENovINhF5MJ/zYSLyrns+RkRa5Dg3yT2+WUQGFFamiLR0y9jmlhl6CteoLSLvi8gmEdkoIr0L+6zGnM46d+7Mtm3bGDFiBABffvklmzZtCnBUp5cdO3Ywbtw41q1bV6T0zZs3p02bNn6OqnB+GbAP3AssAlqLyA9AFHBNIXleAD4CokXk/9z0D/spPmOoXr0606ZNo2PHjoEOxZhKQUQmAO+q6hdFSF7sOsFt7LwM9Af2AqtFZJGq/p4j2RggTlXPEJHhwNPAte7YzOFAJ5wuz1+KSHZfCl9lPg3MUNUFIvJvt+yZxb2GqmYBzwNLVfUatxFUrQh/I2NOa9HR0QBkZWVxxx13EB0dzbfffhvgqE4fnTt3Zt++fbnWJCrIxIkT/RxR0fhrtrG1ItIX586aAJtVNaOQPPNEZC3Qz80zWFU3+iM+Y7LdcMMN3vdPPfUU1apVY/z48RVivnxjKqCawDIROY6zDth7qnoov4QlrBN6AttUdQeAiCwABgE5Gy+DgMnu+/eBl9zJAQYBC1Q1DdgpItvc8sivTBHZCFzMn2Ny3nLLnVnca4jI70AfYLT72dOB9EI+qzGVRnBwMMuXLyc52Vk6MD09naysLO/Cl6ZkgoKCaNSoUeEJ88jMzCQkxF/PPwrnl25jIvILMBFIVdXfCmu4ZFPVTar6sqq+ZA0XU5Y8Hg8xMTHWt9YYP1LVKaraCRgHNARWiMiXBaQvbp3QGNiTY3+veyzfNO54zAQgsoC8vo5HAvFuGXmvVdxrtASOAG+IyDoRmVPIZAbGVDoNGjSgdevWAEyYMIHzzjvP25gxJbN06VJee83nRMAnUVU6dOjAvffe68eoCuevZtMVwLU4gzM9OHfYFqrqbj9dz5hTEhQUxAcffEBGRgYiwv79+0lOTi4XfTuNOQ0dBg4Cx4DoAMdSHoQA3YHxqhojIs8DDwKP5E0oIrcCt4IzAYkxldFll11GgwYNAr7eSEX39ttvExMTw5gxY4qUXkQYPnx4wJea8MuTF1Xdpar/VNWzcR6pdwFOWkHZmPIkKCiIsLAwAP7+97/zl7/8hdTU1ABHZczpQ0T+n4gsB77CeRIxNr81Xk7BPqBpjv0m7rF804hICBCB04jyldfX8WM4s6aF5DlekmvsBfaqaox7/H2cxsxJVPVVVe2hqj2ioqLy/SMYc7q77LLLePhhZwjcli1b+OSTTwIcUcU0d+5cYmJiCk+Yw2OPPcawYcP8FFHR+Gu2MUSkuYhMBBYA7XG6kRUlzyXu+3ARKXCFZZudxfjLCy+8wGuvveadV98fi7kaUwk1Be5W1U6qOjnPQPqTFLdOAFYDbdxZwEJxBscvypNmETDKfX8N8LW79swiYLg7U1hLoA2wyleZbp5v+HMymlHAJyW5hqoeBPaISDs3Tz9yj9MxxvgwefJkbrvtNk6cOBHoUCqc4OBgIiMji53vxIkTAe2y568xLzE4s8QEA0NVtaeq/quQPGNx7jbNcg81AT4u5FLZs7O0B7oCNk7GlIrmzZszcOBAAD7++GMGDhxIXFxcgKMypmJT1Umq+rOIRItIs+wtv7QlqRPc8SV34CySvBGnu/IGEZkqIle6yV4DIt3B8hNwumehqhuAhTiNhqXAOFXN8lWmW9YDwAS3rEi37GJfw80zHpjnjhntBjxZ0Gc1xjjmzJnDV199RY0aNQC72VhUGRkZTJo0qdhjfXft2kVERATz58/3U2SF89eYlxtVdXMx84zDmdklBkBVt4qIz77QIhKBzc5iykBSUhJ//PGHzWpizCkSkSuAZ3GmCT4MNMdpEHTKJ3mx6oRsqroEWJLn2KM53qcCQ33k/T/g/4pSpnt8B3/OSJbzeEmu8TPQI788xhjfqlWrRqdOzlfIzJkzWblyJXPmzKFKlSoBjqx8O3ToENOnT6d169b07HnS15hPzZo1Y8qUKcXKU9r8NVXyZhG5HKdCqprj+NQCsqWpanr2FLVuP+GCms85Z2fpCqwF7lJVm3rClKqRI0dy/fXXExQURGpqKosXL+aaa66x6ZSNKb4ngF7Al6p6lohcBNzgI21x6wRjTCV3/Phx4uPjrX4ugiZNmpCamkpWVlbhiXMQEe94o0DxV7exf+PMNjYeZ37+oTh32AqyQkT+AYSLSH/gPWBxAemzZ2eZqapnAcm4j+bzxHKriKwRkTVHjhwp/ocxBmcwP8Crr77KsGHD+OWXXwIckTEVUoaqHgOCRCRIVb/B99OG4tYJxphK7qGHHuLDDz8kJCSExMREjh8/HuiQyrXg4GBCQ0OLnS8zM5P169eTnh6YDk/+GrB/nqreiLPC8BSgN9C2kDwP4jxJ+RW4DViiqg8VkL5Is7PYzCymNI0bN46lS5fStWtXAGJjYwMbkDEVS7yI1AC+xRnf8TzOjaf8FLdOMMYYgoODUVWGDx9Ov379yMzMLDxTJbRo0SL+8Y9/4PF4SpS3W7durFu3zg+RFc5fjZcU9/UPEWkEZOAsSFaQ8ao6W1WHquo1qjpbRO7yldhmZzGBEBwczIABAwDYvn07HTt25LnnngtwVMZUGIOAP4B7cAasb8dZFyw/xaoTjDEmm4hw//33c//99wd0JfjybOXKlbzxxhveniXF0adPH+bNm8cZZ5zhh8gKJ/6YlUFEHgFexGlQvIzTT3l2zkGT+eT5SVW75zm2zu0S5itPN2AOEArsAG5SVZ9TQvXo0UPXrFlTrM9ijC8ZGRk888wzjB49mkaNGpGZmWlfkiZgRGStqlaYAd8i8jdV/bSA88WuEyobq9OMKZrvvvuOatWqcfbZZwc6lHLF4/GUqPFSFgqq0/zSeMlz8TCgqqom+Dg/AmchywuA73Kcqgl4VLVfacViX/TGn4YNG0ZkZCQzZ84MdCimEqqAjZeTGifu8TKrEyo6q9OMKZzH46F79+6EhYWxcuVKG8xfSvbv38/69eu59NJL/VJ+QXVaWdwmflFVby3g/I/AAaAekHMtmCTARkWbCsHj8dC2bVtq1ixsDT1jjMvXLwirE4wxpSYoKIj//ve/eDwea7i4VJXRo0czYsQI75p2xTVnzhwmT55MQkJCmf/2KYvGS4F3AlV1F7ALZ1C/MRVSUFAQTzzxhHf/xx9/ZO7cuUyfPt27cJYxJpfb8jtodYIxprQ1btwYcH6033fffXTu3JmbbropwFEFTnx8PCtWrKB375J/zY4aNYrLLrssIGvglUXj5XBREolIEn/O4R8KVAGSVbWWvwIzxl9iYmL48ssvbaVfY3IQkWrAvUAzVR0rIm2AdvmNfbE6wRhT2jIyMvjtt98qfd1cp06dU54ttXnz5jRvXtgqKP7h11E6IlJNVYv0PEpVa6pqLbdiCgeGAK/4Mz5j/OWee+7hl19+oWbNmmRlZTFjxgySk239VFPpvQGk8edTlX04C1eexOoEY0xpCw0NZfHixUyfPh2Aw4cPl2iqYOP4/vvv+eijj8r8uv5apPI8Efkd2OTudxWRIlc66vgYGOCP+IwpC9WqVQOcWU4mTJjAp5/6nFjJmMqitar+E2f6fFT1D3yPffGyOsEYU1pCQ0MJCgoiOTmZPn36cPvttwc6pDL39ttvc+WVV/L4449z++23M336dI4dO1bscp577jnuu+8+P0RYMH91G5uBU8ksAlDV9SLSp6AMInJ1jt0gnLEyqX6Kz5gy85e//IWff/6ZLl26APDzzz/Trl27gPQTNSbA0kUkHLc7mIi0xnkScxKrE4wx/lStWjVuv/12unc/adLD09amTZv48MMPefHFFzl48CCLFy+mbt26HD9+nCeeeIK5c+dy5ZVXFrm8Z599NiATFfltzIuq7skzq0NWIVlyLlSWCcTiLGhmTIXXtWtXAJKTkxkwYAAXX3wx8+fPD3BUxpS5x3AWp2wqIvOA84HRPtJanWCM8RsR4e677/buz5s3j/bt21f4tWA8Hg/Hjx/n0KFDHDp0iA0bNrB69WpWrlzJ1q1bAejVqxcPPfQQQ4cOpX79+mzYsIFRo0YxePBg5s2bx4gRI4p0rWbNmvnzo/jkr8bLHhE5D1ARqQLcBWwsKIOqVt5pH0ylUb16debNm0fDhg0BSExMJDg4mOrVqwc4MmP8T1W/EJGfgF443cXuUtWjPtJanWBMDqpKRkYGaWlppKenExISQmhoKGFhYeV2oUFfVDXXBs6snYV9DlUlMzOT1NRUUlJSSE1N9b4/ceIESUlJnDhx4qT3aWlpua7n8Xhy7WdkZLBgwQIiIyPp379/rvN50+YkIgQFBSEi3i3nfknOpaenk5qaSlpaWoFbQWnyatCgAT179mT8+PFcddVVNGnSJNf5Tp068e2333LZZZcxcuRIwsPDGTx4cJH+W86ePZvatWszdOjQIqUvDX5ZpFJE6gHPA5fgVFDLcCqpkzrUiciL/DmjzElU9c7SissW9DLlzQMPPMDbb7/N5s2bbY0Yc0oqwiKVInIV8HX2osUiUhv4izueJTtNmdUJFV1J67SUlBTCw8NJS0tjw4YNxMbGsmvXLo4dO0ZCQgKJiYkkJiaSkZFBZmYmmZmZud5nZZ3ckcLXb4n8jpdl2vIWV/b7wl4BMjMzc/0gTU9P93nd4OBgwsLCvI2Z7Ndq1apRp06dXFvt2rWpVasWtWrVIjQ0lOTkZBITEzl69CiHDx/m8OHDHDlyxPuanp7u83MU9BkL+jv5EhQUREhIiHerUqUKISEhuRosxR1gn/23KazRoKqICCEhIagqQUFBBAcH50qbvWV/Nl8NnIIaP4WdCw0NpWrVqoSFheW7FeVcvXr1iI6Opn79+pxxxhk0btzYG3dGRgb9+/dn/PjxDBkyJNffKikpif79+/PTTz/x/vvvF6kL2TnnnEOTJk1KfeB+mS9S6d5Ju76Iya01YSqtwYMHU69ePW/D5bvvvuPcc88lNDQ0wJEZ4xePqaq3hlPVeBF5DPg4RxqrE/zouuuuY/ny5fTo0YNly5bluksbFBRErVq1iIiIoGbNmoSGhnp/PIaEhBAeHk6VKlW8P/by8rUAYKDTlre4st8X9pr9ozu/LTQ0lKysLG+jJudrzvfJycnExcWxbds24uLiOH78OCkpKfnGHRoaSlRUFNHR0URHR9OuXTvq1atH1apVC/wchZ0r6H3OLSsry9tAztlgzsjI8P77q1q1KlWrVs33fc2aNalRo4Z3y97PbrgUlapy+eWX4/F4+Oyzz067hS0TExNR1XxvQtSsWZOlS5cyYMAAhgwZwiuvvMItt9xS4N/giy++ICIiIt9z2U/KqlSpUmrxg58aLyLSEhgPtMh5DVU9qQmnqm/lyVvDPX7CH7EZU5707t3bu0jU/v376devHxMmTOCpp54KcGTG+EV+fUJy1UNWJ/jXmWeeyfz58/nqq6/4f//v/3HeeefRunVrmjdvTp06dU67H2rmZOnp6SQlJZGUlER6enquH/v2399pVA0fPpz09PTT8u8RGRnJihUrfJ6vXbs2y5YtY+jQodx6660sWrSIJ598kjPPPNNn+qysLGJjY/n999+928aNG9m4cSPPPvssY8eOLdXP4K8xLx8DrwGLgSI93xORzsDbQF1nV44AN6rqBj/FaEy50rBhQxYvXkynTp0A2LJlC6tXr2b48OEEBwcHODpjSsUaEXkWeNndHweszS+h1Qn+cddddxEaGsrIkSOJjo4OdDgmAEJDQ4mMjCQyMjLQoZRbN954o/f98uXL2bhxI7fffvtp2ZjJT0REBEuXLuXZZ59l6tSpdOnShU6dOtGzZ08aNmyIx+MhKSmJ3bt3exstOZ/kNGrUiI4dO3LzzTd7f9OUJn+NeYlR1XOLmedH4CFV/cbd/wvwpKqeV1px2ZgXU5FMnDiRV155hZ07dxIVFRXocEw5V0HGvFQHHsEZDwnwBfCEqp60gmtZ1AkVndVpxvjf6NGjiYmJ4aeffjotljh44IEHiI2N5d133y1S+uPHj/Pmm2+ydOlSfvvtNw4ePEhISAjVq1enWbNmNG3alLVr19KtWzcee+wx2rdvT+3atU85zoLqNH81Xq4D2uAM1Pd2qFXVnwrIs15VuxZ27FTYF72pSDweD7///judO3cGnMZMv379GDDA1ukzJ6sIjZfiKGmdICIDcSaMCQbmqOpTec6HAXOBs4FjwLWqGuuemwSMwZna/05V/bygMt0u0guASJwnSCNVNb0k13DPBeOM+dmnqn8r7G9kdZox/ufxeDh8+DANGjQgMzOT/fv3B2yK4NIwbdo09uzZwyuvFHnt+EJlT3ZQmsp8wD5wJjASuJg/u42pu+/LDhF5BKebAMANwA4/xWdMuRcUFORtuCQkJPDhhx9Su3Ztb+PFH18WxviTiEQBE4FOgHcUsKrmVzcUu05wf/y/DPQH9gKrRWSRqv6eI9kYIE5VzxCR4cDTwLUi0hEY7sbWCPhSRNq6eXyV+TQwQ1UXiMi/3bJnFvcaqprd3yJ7WYFaBX1OY0zZCQoKokGDBgA8/vjjvPDCC/z22280btw4wJGVzKRJk0q9zLL+LeKvicGHAq1Uta+qXuRuBTVcAG4GooAP3a2ee8yYSi8iIoKNGzcyYcIEAL7++mv69u3Lnj17AhyZMcUyD9gEtASm4Cw8udpH2pLUCT2Bbaq6Q1XTcZ6K5F3YchCQPSnA+0A/cWreQcACVU1T1Z3ANre8fMt081zsloFb5uASXgMRaQJcDswp5DMaYwJk9OjRTJo0qcI2XPwlNTWVyy67jFmzZpXJ9fzVePkNKFaHN1WNU9U7VbU7cA7wqKrG+SU6YyqgKlWqeKesTEhIIC0tzTsW5sQJm4jJVAiRqvoakKGqK1T1Znw8kS9hndAYyNmi3+seyzeNqmYCCTjdvnzl9XU8Eoh3y8h7reJeA+A5nKdSxVvEwhhTZlq2bMnEiRMB2LlzJ9deey1Hj+a7zm659MMPP9CyZUtKu7tp1apV8Xg8ZTa5kL8aL7WBTSLyuYgsyt4KyiAi74hILXdA56/A7yJyv5/iM6ZCu+qqq1i5cqX3C+PCCy/kzjtt7T5T7mW4rwdE5HIROQtnNrGTVKY6QUT+BhxW1XxnXsuT9lYRWSMia44cOVIG0Rlj8vPzzz+zYsUKEhISAh1KkYWHh9O7d29vN7jStHTpUm655ZZSLzc//mq8PAZcBTwJ/CvHVpCOqpqI89j9M5xuBSP9FJ8xFV52H9PMzEyGDRvGBRdcADir5y5fvrzYKxsbUwaeEJEI4F7gPpwuUvf4SFuSOmEf0DTHfhP3WL5pRCQEiMAZVO8rr6/jx4Dabhl5r1Xca5wPXCkisTjd0i4Wkf/k9wFV9VVV7aGqPWwWQmMC56qrrmL79u20bt0acJ5qlPd6t3v37rzzzjs0adLEb9fIyMgoPNEp8kvjxe0OcNJWSLYqIlIFp6JapKoZOIP8jTEFCA0NZdKkSQwbNgyA9957j4suuqjARaiMCQRV/VRVE1T1N3cs5Nmq6uupfEnqhNVAGxFpKSKhOIPj85a/CBjlvr8G+FqdXxyLgOEiEubOItYGWOWrTDfPN24ZuGV+UpJrqOokVW2iqi3c8r9W1RsK+azGmACrXr064Kwyf8EFFxR5+uFASU9P91vZGRkZtGvXjqlTp/rtGtlKtfEiIt+7r0kikphjSxKRxEKyz8IZvFkd+FZEmgOF5THG5HH11Vczb948+vbtC8D8+fN55513yv0dIXP6E5FWIrJYRI6KyGER+UREWvlIXuw6wR1fcgfwOc6sXQtVdYOITBWRK91krwGRIrINmAA86ObdACwEfgeWAuNUNctXmW5ZDwAT3LIi3bKLfY3C/3LGmPLs4osv5tVXX2XIkCGBDsUnj8dD/fr1efzxx/1SfpUqVRg0aBDdunXzS/k5leo6LyKyTlXPKsXyQnIMhjxlNie+qYwGDBhAWloay5cvB2yK5dNVRVjnRURW4kw7PN89NBwYX9RFjUu7TqjorE4zpvxJSkrixhtv5Mknn6RDhw6BDscrJSWFadOmceGFF9K/f/9Ah1Ooguq00u42VuKWkIhEisgLIvKTiKwVkedx+gkbY07BZ599xnvvvQdAYmIiZ555Jv/9738DHJWppKqp6tuqmulu/yHHei85WZ1gjKmIdu/ezerVq9m9e3egQ8klPDycqVOn+r3hkpyczMGDB/16jdJepDJaRCb4OqmqzxaQdwHwLZD9zO164F3gkoIu6A5wTMJZrTizvN95NKasBQUFeadUPnLkCFFRUdSvXx+AuLg4RITatYs1s7kxJfWZiDyI832vwLXAEhGpC6Cqx3OkLVGdYIwxgdSpUye2bt1KeHg44NSzderUCXBUsG/fPho0aODX6Yw9Hg+tW7dm4MCBvPnmm367Tmk3XoKBGkBJ+qQ0VNWcHfGeEJFri5j3IlWtOBNtGxMgrVu35ptvvvHuT5s2jdmzZxMbG0tEhN3UNn43zH291X3NriuG4zRmco5/OZU6wRhjAia74fLDDz9w2WWX8f777we8q9bll19O06ZNWbx4sd+uERQUxDPPPMMZZ5zht2tA6TdeDqhqSacZWCYiw3EGM4IzQ8vnpROWMSY/119/PU2bNvU2XN555x0uuOACmjVrFuDIzOlERM4B9qhqS3d/FM4TlVhgcp4nLtmsTjDGVGidOnViyJAhnHVWqQ0HL7FJkyZRs2ZNv19n5Ej/r3IS8AH7IpKEc8dNcGaVyV5dOAg4oaq1Csm/E4hzy5ilqq/6SmuDG43xLSEhgcaNG3PTTTfx4osvAja4vyIpzwP2ReQn4BJVPS4ifXC6hI0HugEdVPWaHGlPqU6oTKxOM6bi8Hg8xMbG0qqVrwkWTx9bt25lw4YNDB48uMRllOWA/X7FzaCqNVW1lvsapKoh7hZUxErqAlXtDlwKjHMrRi9bjdiYoomIiGDjxo089NBDgLN6cPv27Vm7ttBFv40pTHCOpyvXAq+q6geq+giQq39BKdQJxhhT7jz88MP06NGD/fv3l/m1v//+e78Pos/p6aefZvTo0X5bsLJUu435ePRfZCJSB2fRLu/sM6r6bSHX3Oe+HhaRj4CeOIM8s8+/CrwKzl2qU4nPmNNd06Z/Lv6dlpZGkyZNaNGiBQA//vgje/bsYciQIYSElHaPU3OaC84xzXE//hzzAgXUQyWpE4wxpjwaO3YsUVFRNGzYsEyv6/F4GDp0KBdeeCELFy4sPEMpePjhh5kyZQpVqlTxS/nl5heIiNwC3AU0AX4GegH/Ay4uIE91IEhVk9z3fwX8v7SnMYJ8wV8AABe/SURBVJXAueeey1dffeXdnzNnDkuXLvUuwnXs2DHq1q1r3cpMUcwHVojIUSAF+A5ARM4AEvLLUJI6wRhjyquWLVtyzz33AE79Wbt2bb/O/JVNRFi6dGmZ1tXZNz39pbS7jZ2Ku4BzgF2qehFwFhBfSJ76wPcish5YBfxXVZf6N0xjKqfZs2fz3XffERISgqpy0UUXlcnAPFPxqer/AfcCb+J09c1+Ch6EM/YlPyWpE4wxplw7fPgwXbt25YknniiT64kIXbt2pUuXLmVyvWwbN25k1KhRxMXFlXrZ5anxkqqqqQAiEqaqm4B2BWVQ1R2q2tXdOrkVpDHGD4KDg2ndujXgPIYeN24c11zjjLNOT0/nuuuuIyYmJpAhmnJMVVeq6keqmpzj2BZV/clHlmLXCcYYU95FRUUxZswYrrjiCr9fy+Px8Mgjj7Bx40a/XyuvlJQUdu7c6ZexNuWm2xiwV0RqAx8DX4hIHLArwDEZY/IRHBzMbbfd5t3funUr33zzDTfeeCPgPBLft29fmd/pMacVqxOMMacdEWHKlCnefX/O6rl161aeeeYZOnbsSIcOHfxyDV+6d+/Ot9/6Z4hiuWm8qOpV7tvJIvINEAFYFzBjKoBOnTqxZ88e7xfwG2+8wf3338/27dtp1aoVcXFx1KhRw2+D98zpx+oEY8zpbvLkycTFxfH888/7pfx27dqxZ88eatSo4ZfyA6XcNF5yUtUVgY7BGFM8OWcgu+mmm2jSpIl3PvsHH3yQTz/9lL179yIibN26laioKGrXrh2ocE0FYnWCMeZ0FB8fT1JSEh6Ph6Cg0h3JkZaWRlhYGFFRUaVabnlQLhsvxpiKLTIykuHDh3v3r776arp16+Z9MnPLLbeQkpLCqlWrAFi+fDnNmzenZcuWAYnXGGOMKWvPPvtsqTdawOmKdvXVV9OgQQNee+21Ui8/0KzxYozxuwEDBuTaf+KJJ0hJSQGcL9kRI0ZwySWX8PbbbwPw+uuv06tXLzp27FjmsRpjjDFlIbvhEhsby7p167jqqqsKyVE0Ho+H3r17U6dOnVIpr7yxxosxpsxdeOGFufa/+OIL75d4YmIit9xyC1OmTKFjx45kZGTw6KOPct1113HmmWcGIlxjjDHGbx544AGWL1/OwIEDCQ8PP+XygoODefjhh0shsvLJGi+FmD59Oi+99BINGjSgfv36Bb6ebgOiiiolJYXdu3eza9cudu/eTXx8PGlpad4tNTW10Pf5nUtPT6dq1arUrl2bOnXqULt27ZO2/I5nH6tWrZotoOhKT08nISGBxMREEhISvJuv/T/++IOwsDDCw8OpWrUq4eHhJX4fERFR4JexiNC5c2fvfq1atdi/f7+3MbN161b+9a9/cdZZZ3HmmWeye/duHnroIR544IFc+Soqj8dDVlYWf/zxBwcOHKBq1ap+X+DLGGNM+fHss8/i8XhOueGSlZXFbbfdxq233krPnj1LKbryxxovhWjTpg19+vTh0KFDxMbGEhMTw+HDh/lzjbU/VatWrdBGTrNmzWjUqFGF+VGtqsTFxbFr165cW3ZjZdeuXRw5csRn/rCwMKpWrUpYWJjP97Vq1cp1PPtcaGgoqampxMfHExcXR3x8PJs3byY+Pp74+HiSk5N9XhecAeQ5GzQtW7akXbt2tG/fnvbt29O2bdsK3eBMTk5m69atbNmyhS1btrBz507i4+PzbYykpqYWWl54eDgRERHexkZaWhopKSmkpqaSkpJCSkoK6enpJYo1OjqaFi1a+NzyfmE3aNDA+75jx44kJCR4/5+JjY3liy++4N577wXg66+/ZsqUKbzxxhu0atXKLwMfffF4POzZs4fw8HCio6NJT09n4cKFdO3alQ4dOhAbG8sjjzxC9+7dadSoEdu2bWPWrFm0b9+e8PBwdu/ezW+//UZISAiZmZkA3Hjjjbz11ltlEr8xxpjAa9y4sfd9fHx8iSezOXjwIF988QW9evU6rRsvkt+P8NNVjx49dM2aNadcTlZWFkePHuXgwYMcOnSowNejR4+elL9u3bp07do119axY0fCwsJOObbi8ng8HDhwgNjY2HwbJrt37+bEiRO58oSHh9OsWTOaN2/u3bL3mzVrRt26dalatSpVqlTxayMt+2lCdmMmZyMn77Hjx4+zfft2du7cicfj8ZbRpEkT2rdvn6tR065dO5o0aVIuGpgZGRnExsZ6Gyhbtmxh8+bNbNmyhX379uVK26hRI+rWrUtERAS1atXyNkSKul+UaYw9Hk+uxkxR3mc3fmNjY73/zvI2gurXr++zYdO8efOTGjfZ31siwmeffcbUqVNZtmwZNWvW5IUXXmDGjBn8/PPPREREcPz4cWrUqEFoaGiJ/husX7+e8PBw2rZti6py/fXX89e//pXLLruMNWvWcPnll3PuuefSokULDh48yIoVK6hWrRopKSn53uQQEerWrUuLFi2oU6cOR44coVu3bnTp0oV69erRuXNnunfvXuw4RWStqvYo0Yc0FVJp1WnGmPLhkUce4e2332bDhg1Ur169yPmOHj1KnTp1CA4OJjExkVq1avkxyrJRUJ1mjRc/y8jI4MiRI97GzI4dO1i/fj3r16/n119/9Q5aDgkJoX379ic1aurXr3/KMSQkJLBjxw527tx50mtsbCxpaWm50kdGRvpsnDRv3px69eqVix/2JZGWlsa2bdvYtGkTmzdvZtOmTd73iYmJ3nTVq1enXbt2JzVq2rZtWyr9UXNSVQ4cOJCrgZK9bd++3XtHHqBOnTreOLJf27ZtyxlnnEG1atVKNS5/8Xg8HDx40PvvL++2a9cuMjIycuXJbty0bNmS1q1b06pVK1q3bk3r1q1p1KhRrictS5Ys4eOPP+bVV18F+P/t3X9wFPd5x/H3g/ghIFjYIlIBCUsYDIN+xHKDQyj1gB1inHpCMuPG/JjguHRsT2iTeOpxcTwubsczTaat03TaOvWYBCe1TWPs1tiNQwlmpm6MMXYgwmABkvglAjZgjEshAcTTP/Yr5XRIiJPudLvS5zVzo9vd7+0+99VpHz373d1j2bJlPPfcc7z33nuYGTt37uSKK66grKwMgNdffx2AmTNnArBo0SKuvfZaHnnkESAaBZo5cybz58+nvr6elStX0tra2qGoHzFiBOPGjaO0tJSRI0dSVlZGeXk5JSUllJaWdvhZVFSUk78fFS8RM5sHfBcoAJ5092+lLR8G/BD4XeA4cIe77wvLHgSWAq3A19x93aXWaWaVwGqgGHgb+LK7n810G2ZWHtqXAg484e7dfvGDiheR/uW1115jw4YNLF++nMLCwst6zaFDh6irq+P+++/ngQceyHGEfUfFSxC3HX1rayuNjY3txUzbo6Wlpb1NaWnpRQXNlClTOhwlP3v2LPv37++yQDlx4kSH7Y4ePZqJEydSWVnZ/rPtCPeECRMSfSpVT7k7R44cuaigaWhoYP/+/R2O9JeVlbUXCmbW/o9o2/P06Us9P3/+PM3NzR3+ES4sLGTy5MnthUlqoVJcXNw3HZJHqaOB+/bt61DkNDc3c+DAAVpbW9vbDxs2rNOipu2zvWnTJnbv3s29994LwNy5czl27Bhbt24FYPr06RQXF/PKK69w8OBB7rrrLgYNGsSYMWOor6+noaGhfbSusLCQqqoqamtrqa2tpaamhpqaGkpKSvq+o9KoeAEzKwB2A3OBFmALsNDdd6a0+SpQ6+73mtkC4IvufoeZTQOeBW4AxgE/A64NL+t0nWb2Y+AFd19tZt8Dfunuj/dgGyXAWHf/hZmNIiqEvpAad2filtNEJHvcvcsDXadOnWLbtm3MmjULd+fhhx9m4cKFVFVV9XGUuaPiJUjKjv748ePU19d3KGh27NjRfqrN0KFDqaqqYtSoUezdu5eWlpYOp6cMHTqUioqK9n/eUouUysrKfnvrvFw5c+YMe/bsaS9o9uzZw9mzZ3H39gfQo+eDBg2isrKyQ6FSXl7eZ9dsJNG5c+c4cOAATU1NNDc309TU1OF5+mmO48eP71DYFBQUUFRURF1dHdu3b2fjxo00NTWxe/duTp482f66iooKampq2guV2tpaJk2a1OHLOONExQuY2aeBR9z9ljD9IIC7/3VKm3WhzSYzGwwcAT4OLE9t29YuvOyidQLfAo4Cv+Pu51O3nek23H1T2vt4EfhHd19/qfeblJwmIpnZvHkzy5cvZ8WKFcyePZtTp06xZcsWbrzxRgoKCrjnnnt45plnOHz4cL894HypnBbPLDzAFRcXM2fOHObMmdM+79y5c+zatatDQXP69Glmz5590ShK+mk00jvDhw9v/+dV8m/IkCHtoyvp3J2jR492WtSsW7eOw4cPX/SaUaNGUVNTw8KFC9t/z9XV1RQVFfXF25HsGg8cTJluAT7VVZtQdJwkOu1rPPBG2mvbrqLtbJ3FwIfufr6T9j3ZBgBmVgHUAZu7e7Mi0j8NGjSIwYMHM2nSJABeeuklFi1aRGNjI9dccw333XcfS5Ysyei6mP5ExUtCDBkyhOrqaqqrq1m8eHG+wxGJJTOjpKSEkpISZsyYcdHy06dPs3fvXpqamnB3amtrufrqq1XsSyyY2ceA54FvuPtHXbS5G7gbYMKECX0YnYj0lenTp7N+/W8HXuvq6li/fj1jx44FYOrUqfkKLRZUvIjIgDFixAiqqqr61XnB0sEhoDxluizM66xNSzilq4joovpLvbaz+ceB0WY2OIy+pLbPeBtmNoSocHna3V/o6g26+xPAExCdNtZVOxHpP9puHCQRHW4UEZH+Ygsw2cwqzWwosABYm9ZmLXBneH478KpHF6KtBRaY2bBwF7HJwJtdrTO8ZmNYB2GdL/ZkGxZdlbsSeNfdH8tab4iI9EMaeRERkX4hXF/yJ8A6otsaf9/dd5jZXwFvuftaoiLhR2bWCHxAVIwQ2v0Y2AmcB5a5eytAZ+sMm/xzYLWZPQpsDesm022Y2Szgy8B2M9sW1vFNd/9JLvpJRCTJdLcxEZF+QHcbG3iU00Skv9KtkgMzOwrsT5s9BjiWh3B6SvHmluLNvaTFnJR4r3b3j+c7COk7XeS0y5GUz3Rnkhw7JDt+xZ4fSY4deh5/lzltQBUvnTGzt5J0tFLx5pbizb2kxZy0eEW6k+TPdJJjh2THr9jzI8mxQ27i1wX7IiIiIiKSCCpeREREREQkEVS8hPvlJ4jizS3Fm3tJizlp8Yp0J8mf6STHDsmOX7HnR5JjhxzEP+CveRERERERkWTQyIuIiIiIiCTCgC1ezGyeme0ys0YzW57veNKZWbmZbTSznWa2w8y+HuZfZWbrzWxP+HllvmNNZWYFZrbVzF4O05Vmtjn087+Fb6iODTMbbWZrzKzBzN41s0/HuY/N7L7weXjHzJ41s8I49bGZfd/M3jezd1LmddqfFvmHEHe9mV0fk3j/Jnwe6s3s381sdMqyB0O8u8zslr6OV6S3+lvui8N+JN3l5kEzGxamG8PyijzHfdn5MG79nklujEO/ZytXmtmdof0eM7szj7FnnDd7sy8akMWLmRUA/wTcCkwDFprZtPxGdZHzwJ+5+zRgBrAsxLgc2ODuk4ENYTpOvg68mzL9beA77j4JOAEszUtUXfsu8FN3nwp8gij2WPaxmY0HvgZ80t2rib7tewHx6uNVwLy0eV31563A5PC4G3i8j2JMtYqL410PVLt7LbAbeBAg/P0tAKrCa/457EtEEqGf5r447EfSXW4eXAqcCPO/E9rlUyb5MDb93oPcGId+X0Uvc6WZXQWsAD4F3ACssL452LqKXubN3u6LBmTxQvRLbnT3Znc/C6wG5uc5pg7c/bC7/yI8/1+inch4ojifCs2eAr6QnwgvZmZlwB8AT4ZpA24C1oQmcYu3CLgRWAng7mfd/UNi3MfAYGC4mQ0GRgCHiVEfu/t/Ax+kze6qP+cDP/TIG8BoMxvbN5FGOovX3f/L3c+HyTeAsvB8PrDa3X/j7nuBRqJ9iUhS9Mfcl/f9SKoM82Dqe1oD3Bza97ke5MNY9TuZ5ca893uWcuUtwHp3/8DdTxAVEOlFRZ/E3oO82at90UAtXsYDB1OmW8K8WApDmnXAZqDU3Q+HRUeA0jyF1Zm/Bx4ALoTpYuDDlA903Pq5EjgK/CAM8T9pZiOJaR+7+yHgb4EDRDvmk8DbxLuPoev+TMLf4R8Br4TnSYhX5FIS9Rm+zNwXt/eUSR5sjz0sPxna50Om+TA2/d6D3Binfk+VaV/H5neQ5nLyZq9iH6jFS2KY2ceA54FvuPtHqcs8ulVcLG4XZ2a3Ae+7+9v5jiUDg4HrgcfdvQ74P9JOEYtZH19JdGSiEhgHjKQPjrJkU5z6sztm9hDRKSxP5zsWkYEmKbkvVULzYJtE5cNU/SE3potrX3enr/LmQC1eDgHlKdNlYV6smNkQop330+7+Qpj9XtvQbPj5fr7iS/N7wOfNbB/R8N9NROfPjg7DuBC/fm4BWtx9c5heQ7TzjmsffwbY6+5H3f0c8AJRv8e5j6Hr/ozt36GZfQW4DVjsv72ffGzjFblMifgMZ5j74vSeMs2D7bGH5UXA8b4MOEWm+TBO/Z5pboxTv6fKtK/j9DvING/2KvaBWrxsASaHO1EMJbqYaG2eY+ognH+5EnjX3R9LWbQWaLujxJ3Ai30dW2fc/UF3L3P3CqL+fNXdFwMbgdtDs9jEC+DuR4CDZjYlzLoZ2ElM+5hoSHyGmY0In4+2eGPbx0FX/bkWWBLupDIDOJkyZJ43ZjaP6LSPz7v76ZRFa4EFFt2pppLo4sk38xGjSA/1x9wXm/1ID/Jg6nu6PbTPy9H2HuTD2PQ7mefG2PR7mkz7eh3wWTO7Mow+fTbM63M9yJu92xe5+4B8AJ8juiNCE/BQvuPpJL5ZREOG9cC28Pgc0XmZG4A9wM+Aq/IdayexzwZeDs8nhg9qI/AcMCzf8aXFeh3wVujn/wCujHMfA38JNADvAD8ChsWpj4Fnic45Pkd0JG9pV/0JGNHdRpqA7UR3iolDvI1E5+K2/d19L6X9QyHeXcCt+f486KFHpo/+lvvisB/p4n10mweBwjDdGJZPzHPMl50P49bvmeTGOPR7tnIl0fUljeFxVx5jzzhv9mZfZGEFIiIiIiIisTZQTxsTEREREZGEUfEiIiIiIiKJoOJFREREREQSQcWLiIiIiIgkgooXERERERFJBBUvIiIiIiKSCCpeREREREQkEVS8iHTDzKaZ2VfMrNzMRuU7HhERkVxQvpMkUPEi0r0hwJ8CXwROpS80swozO2Nm27K9YTMbbmbbzOysmY3J9vpFRGRgMrMyM7sjbXav853yluSaiheR7pUDPwAaga6ORDW5+3XZ3rC7nwnr/VW21y0iIgPazcD1afN6ne+UtyTXVLyIBGb2ajhatM3Mfm1mXwJw95eBNe7+E3f/6DLWU2FmDWa2ysx2m9nTZvYZM/u5me0xsxsyaSciIpJNZjYLeAy4PeS8idCjfDfSzP7TzH5pZu90MpIjknUqXkQCd78pHC36F2At8HzKsiMZrm4S8HfA1PBYBMwC7ge+2YN2IiIiWeHu/wNsAea7+3Xu3pyyLJN8Nw/4lbt/wt2rgZ9mOVSRi6h4EUlhZkuAW4HF7t7ai1Xtdfft7n4B2AFscHcHtgMVPWgnIiKSTVOAhl6uYzsw18y+bWa/7+4nsxCXyCWpeBEJzOwPgcXAl9z9XC9X95uU5xdSpi8Ag3vQTkREJCvChfQn3f18b9bj7ruJrpvZDjxqZn+RjfhELkX/HIkAZnYb8FXgNnf/db7jERERyaEKsnBBvZmNAz5w9381sw+BP+7tOkW6o5EXkchTQBnw83Dx4tJ8ByQiIpIjDcCYcJH9zF6spwZ4M9w6eQXwaFaiE7kEi06vF5GeMrMK4OVwsWKutrEP+KS7H8vVNkRERC4lk3ynvCW5opEXkd5rBYpy+SWVRF8cdiHb6xcREclAt/lOeUtyTSMvIiIiIiKSCBp5ERERERGRRFDxIiIiIiIiiaDiRUREREREEkHFi4iIiIiIJIKKFxERERERSQQVLyIiIiIikggqXkREREREJBFUvIiIiIiISCKoeBERERERkUT4fx6bPTdA6oENAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot negative current collector potential\n", + "var = \"Negative current collector potential [V]\"\n", + "comsol_var_fun = comsol_solution[var]\n", + "pybamm_var_fun = solutions[\"1+1D DFN\"][var]\n", + "\n", + "pybamm_bar_var_fun = potentials[var]\n", + "plot(\n", + " t_plot,\n", + " z_plot,\n", + " t_slices,\n", + " \"$\\phi^*_{\\mathrm{s,cn}}$\",\n", + " \"[V]\",\n", + " comsol_var_fun,\n", + " pybamm_var_fun,\n", + " pybamm_bar_var_fun,\n", + " param,\n", + " cmap=\"cividis\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot positive current collector potential\n", + "var = \"Positive current collector potential [V]\"\n", + "comsol_var = comsol_solution[var]\n", + "V_comsol = comsol_solution[\"Terminal voltage [V]\"]\n", + "\n", + "\n", + "def comsol_var_fun(t, z):\n", + " return comsol_var(t=t, z=z) - V_comsol(t=t)\n", + "\n", + "\n", + "pybamm_var = solutions[\"1+1D DFN\"][var]\n", + "V = solutions[\"1+1D DFN\"][\"Terminal voltage [V]\"]\n", + "\n", + "\n", + "def pybamm_var_fun(t, z):\n", + " return pybamm_var(t=t, z=z) - V(t=t)\n", + "\n", + "\n", + "pybamm_bar_var = potentials[var]\n", + "\n", + "\n", + "def pybamm_bar_var_fun(t, z):\n", + " return pybamm_bar_var(t=t, z=z) - V_av_dim(t)\n", + "\n", + "\n", + "plot(\n", + " t_plot,\n", + " z_plot,\n", + " t_slices,\n", + " \"$\\phi^*_{\\mathrm{s,cp}} - V^*$\",\n", + " \"[V]\",\n", + " comsol_var_fun,\n", + " pybamm_var_fun,\n", + " pybamm_bar_var_fun,\n", + " param,\n", + " cmap=\"viridis\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot through-cell current\n", + "var = \"Current collector current density [A.m-2]\"\n", + "comsol_var_fun = comsol_solution[var]\n", + "pybamm_var_fun = solutions[\"1+1D DFN\"][var]\n", + "\n", + "I_av = solutions[\"Average DFN\"][var]\n", + "\n", + "\n", + "def pybamm_bar_var_fun(t, z):\n", + " return np.transpose(np.repeat(I_av(t)[:, np.newaxis], len(z), axis=1))\n", + "\n", + "\n", + "plot(\n", + " t_plot,\n", + " z_plot,\n", + " t_slices,\n", + " \"$\\mathcal{I}^*$\",\n", + " \"[A/m${}^2$]\",\n", + " comsol_var_fun,\n", + " pybamm_var_fun,\n", + " pybamm_bar_var_fun,\n", + " param,\n", + " cmap=\"plasma\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot temperature\n", + "T_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.T_ref)\n", + "var = \"X-averaged cell temperature [K]\"\n", + "comsol_var = comsol_solution[var]\n", + "\n", + "\n", + "def comsol_var_fun(t, z):\n", + " return comsol_var(t=t, z=z) - T_ref\n", + "\n", + "\n", + "pybamm_var = solutions[\"1+1D DFN\"][var]\n", + "\n", + "\n", + "def pybamm_var_fun(t, z):\n", + " return pybamm_var(t=t, z=z) - T_ref\n", + "\n", + "\n", + "T_av = solutions[\"Average DFN\"][var]\n", + "\n", + "\n", + "def pybamm_bar_var_fun(t, z):\n", + " return np.transpose(np.repeat(T_av(t)[:, np.newaxis], len(z), axis=1)) - T_ref\n", + "\n", + "\n", + "plot(\n", + " t_plot,\n", + " z_plot,\n", + " t_slices,\n", + " \"$\\\\bar{T}^* - \\\\bar{T}_0^*$\",\n", + " \"[K]\",\n", + " comsol_var_fun,\n", + " pybamm_var_fun,\n", + " pybamm_bar_var_fun,\n", + " param,\n", + " cmap=\"inferno\",\n", + ")" + ] + } + ], + "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": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/old.py b/old.py new file mode 100644 index 0000000000..8a6330cd2e --- /dev/null +++ b/old.py @@ -0,0 +1,257 @@ +import pybamm +import sys +import pickle +import matplotlib.pyplot as plt +import shared +import numpy as np + +pybamm.set_logging_level("INFO") + +# increase recursion limit for large expression trees +sys.setrecursionlimit(100000) + + +"-----------------------------------------------------------------------------" +"Load comsol data" + +comsol_results_path = pybamm.get_parameters_filepath( + "input/comsol_results/comsol_1plus1D_3C.pickle" +) +comsol_variables = pickle.load(open(comsol_results_path, "rb")) + +"-----------------------------------------------------------------------------" +"Set up and solve pybamm simulation" + +# load current collector and DFN models +cc_model = pybamm.current_collector.EffectiveResistance1D() +dfn_av = pybamm.lithium_ion.DFN({"thermal": "x-lumped"}, name="Average DFN") +dfn = pybamm.lithium_ion.DFN( + {"current collector": "potential pair", "dimensionality": 1, "thermal": "x-lumped"}, + name="1+1D DFN", +) +models = {"Current collector": cc_model, "Average DFN": dfn_av, "1+1D DFN": dfn} + +# parameters +param = dfn.default_parameter_values +I_1C = param["Cell capacity [A.h]"] # 1C current is cell capacity multipled by 1 hour +param.update( + { + "Current function [A]": I_1C * 3, + "Negative electrode diffusivity [m2.s-1]": 3.9 * 10 ** (-14), + "Positive electrode diffusivity [m2.s-1]": 10 ** (-13), + "Negative current collector surface heat transfer coefficient [W.m-2.K-1]": 10, + "Positive current collector surface heat transfer coefficient [W.m-2.K-1]": 10, + "Negative tab heat transfer coefficient [W.m-2.K-1]": 10, + "Positive tab heat transfer coefficient [W.m-2.K-1]": 10, + "Edge heat transfer coefficient [W.m-2.K-1]": 10, + } +) + + +# process model and geometry, and discretise +meshes = {} +for name, model in models.items(): + param.process_model(model) + geometry = model.default_geometry + param.process_geometry(geometry) + + # set mesh + var = pybamm.standard_spatial_vars + submesh_types = model.default_submesh_types + # set npts + var = pybamm.standard_spatial_vars + npts = 16 + var_pts = { + var.x_n: npts, + var.x_s: npts, + var.x_p: npts, + var.r_n: npts, + var.r_p: npts, + var.z: npts, + } + meshes[name] = pybamm.Mesh(geometry, submesh_types, var_pts) + disc = pybamm.Discretisation(meshes[name], model.default_spatial_methods) + disc.process_model(model, check_model=False) + +# solve model at comsol times +t_eval = comsol_variables["time"] + +solutions = {} +for name, model in models.items(): + if name == "Current collector": + solver = pybamm.CasadiAlgebraicSolver(tol=1e-6) + solutions[name] = solver.solve(model) + else: + # solver + solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-6, root_tol=1e-6, mode="fast") + solutions[name] = solver.solve(model, t_eval) + +"-----------------------------------------------------------------------------" +"Make Comsol 'model' for comparison using mesh and times from 1+1D solution" + +mesh = meshes["1+1D DFN"] +comsol_model = shared.make_comsol_model(comsol_variables, mesh, param, thermal=True) +comsol_solution = pybamm.Solution(solutions["1+1D DFN"].t, solutions["1+1D DFN"].y) +comsol_solution.model = comsol_model + +"-----------------------------------------------------------------------------" +"Make plots" +t_plot = comsol_model.t +z_plot = comsol_model.z_interp +t_slices = np.array([600, 1200, 1800, 2400, 3000]) / 3 + +# get processed potentials from DFNCC +R_cc = param.process_symbol( + cc_model.variables["Effective current collector resistance"] +).evaluate(t=solutions["Current collector"].t, y=solutions["Current collector"].y)[0][0] + +V_av_1D = solutions["Average DFN"]["Terminal voltage"] +I_av = solutions["Average DFN"]["Total current density"] + + +def V_av(t): + "Include effect of current collector resistance" + return V_av_1D(t) - I_av(t) * R_cc + + +potentials = cc_model.get_processed_potentials( + solutions["Current collector"], param, V_av, I_av +) + +# plot negative current collector potential +var = "Negative current collector potential [V]" +comsol_var_fun = comsol_solution[var] +pybamm_var_fun = solutions["1+1D DFN"][var] + +pybamm_bar_var_fun = potentials[var] +shared.plot_tz_var( + t_plot, + z_plot, + t_slices, + "$\phi^*_{\mathrm{s,cn}}$", + "[V]", + comsol_var_fun, + pybamm_var_fun, + pybamm_bar_var_fun, + param, + cmap="cividis", +) + +# plot positive current collector potential +var = "Positive current collector potential [V]" +comsol_var = comsol_solution[var] +V_comsol = comsol_solution["Terminal voltage [V]"] + + +def comsol_var_fun(t, z): + return comsol_var(t=t, z=z) - V_comsol(t=t) + + +pybamm_var = solutions["1+1D DFN"][var] +V = solutions["1+1D DFN"]["Terminal voltage [V]"] + + +def pybamm_var_fun(t, z): + return pybamm_var(t=t, z=z) - V(t=t) + + +pybamm_bar_var = potentials[var] + +pot_scale = param.evaluate(pybamm.standard_parameters_lithium_ion.potential_scale) +U_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.U_p_ref) - param.evaluate( + pybamm.standard_parameters_lithium_ion.U_n_ref +) + + +def V_av_dim(t): + return U_ref + V_av(t) * pot_scale + + +def pybamm_bar_var_fun(t, z): + return pybamm_bar_var(t=t, z=z) - V_av_dim(t) + + +shared.plot_tz_var( + t_plot, + z_plot, + t_slices, + "$\phi^*_{\mathrm{s,cp}} - V^*$", + "[V]", + comsol_var_fun, + pybamm_var_fun, + pybamm_bar_var_fun, + param, + cmap="viridis", +) + + +# plot through-cell current +var = "Current collector current density [A.m-2]" +comsol_var_fun = comsol_solution[var] +pybamm_var_fun = solutions["1+1D DFN"][var] + +I_av = solutions["Average DFN"][var] + + +def pybamm_bar_var_fun(t, z): + if t.shape[0] == 1: + return np.repeat(I_av(t)[:, np.newaxis], len(z), axis=0) + else: + return np.transpose(np.repeat(I_av(t)[:, np.newaxis], len(z), axis=1)) + + +shared.plot_tz_var( + t_plot, + z_plot, + t_slices, + "$\mathcal{I}^*$", + "[A/m${}^2$]", + comsol_var_fun, + pybamm_var_fun, + pybamm_bar_var_fun, + param, + cmap="plasma", +) + +# plot temperature +T_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.T_ref) +var = "X-averaged cell temperature [K]" +comsol_var = comsol_solution[var] + + +def comsol_var_fun(t, z): + return comsol_var(t=t, z=z) - T_ref + + +pybamm_var = solutions["1+1D DFN"][var] + + +def pybamm_var_fun(t, z): + return pybamm_var(t=t, z=z) - T_ref + + +T_av = solutions["Average DFN"][var] + + +def pybamm_bar_var_fun(t, z): + if t.shape[0] == 1: + return np.repeat(T_av(t)[:, np.newaxis], len(z), axis=0) - T_ref + else: + return np.transpose(np.repeat(T_av(t)[:, np.newaxis], len(z), axis=1)) - T_ref + + +shared.plot_tz_var( + t_plot, + z_plot, + t_slices, + "$\\bar{T}^* - \\bar{T}_0^*$", + "[K]", + comsol_var_fun, + pybamm_var_fun, + pybamm_bar_var_fun, + param, + cmap="inferno", +) + + +plt.show() diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py index 3ca269e8fc..fe63efd631 100644 --- a/pybamm/models/full_battery_models/base_battery_model.py +++ b/pybamm/models/full_battery_models/base_battery_model.py @@ -235,9 +235,7 @@ def options(self, extra_options): "Unknown thermal model '{}'".format(options["thermal"]) ) if options["dimensionality"] == 0: - if options["current collector"] not in [ - "uniform", - ]: + if options["current collector"] not in ["uniform"]: raise pybamm.OptionError( "current collector model must be uniform in 0D model" ) @@ -252,8 +250,8 @@ def options(self, extra_options): if options["thermal"] == "x-lumped" and options["dimensionality"] == 1: warnings.warn( - "1+1D Thermal models are only valid if both tabs are" - + "placed at the top of the cell." + "1+1D Thermal models are only valid if both tabs are " + "placed at the top of the cell." ) self._options = options @@ -526,9 +524,7 @@ def set_thermal_submodel(self): def set_current_collector_submodel(self): - if self.options["current collector"] in [ - "uniform", - ]: + if self.options["current collector"] in ["uniform"]: submodel = pybamm.current_collector.Uniform(self.param) elif self.options["current collector"] == "potential pair": if self.options["dimensionality"] == 1: From b4b9d1b2efd80b3ed79a5df11ab8af9aca5b7954 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Mon, 18 May 2020 17:42:18 +0100 Subject: [PATCH 3/9] #997 add notebook --- old.py | 257 --------------------------------------------------------- 1 file changed, 257 deletions(-) delete mode 100644 old.py diff --git a/old.py b/old.py deleted file mode 100644 index 8a6330cd2e..0000000000 --- a/old.py +++ /dev/null @@ -1,257 +0,0 @@ -import pybamm -import sys -import pickle -import matplotlib.pyplot as plt -import shared -import numpy as np - -pybamm.set_logging_level("INFO") - -# increase recursion limit for large expression trees -sys.setrecursionlimit(100000) - - -"-----------------------------------------------------------------------------" -"Load comsol data" - -comsol_results_path = pybamm.get_parameters_filepath( - "input/comsol_results/comsol_1plus1D_3C.pickle" -) -comsol_variables = pickle.load(open(comsol_results_path, "rb")) - -"-----------------------------------------------------------------------------" -"Set up and solve pybamm simulation" - -# load current collector and DFN models -cc_model = pybamm.current_collector.EffectiveResistance1D() -dfn_av = pybamm.lithium_ion.DFN({"thermal": "x-lumped"}, name="Average DFN") -dfn = pybamm.lithium_ion.DFN( - {"current collector": "potential pair", "dimensionality": 1, "thermal": "x-lumped"}, - name="1+1D DFN", -) -models = {"Current collector": cc_model, "Average DFN": dfn_av, "1+1D DFN": dfn} - -# parameters -param = dfn.default_parameter_values -I_1C = param["Cell capacity [A.h]"] # 1C current is cell capacity multipled by 1 hour -param.update( - { - "Current function [A]": I_1C * 3, - "Negative electrode diffusivity [m2.s-1]": 3.9 * 10 ** (-14), - "Positive electrode diffusivity [m2.s-1]": 10 ** (-13), - "Negative current collector surface heat transfer coefficient [W.m-2.K-1]": 10, - "Positive current collector surface heat transfer coefficient [W.m-2.K-1]": 10, - "Negative tab heat transfer coefficient [W.m-2.K-1]": 10, - "Positive tab heat transfer coefficient [W.m-2.K-1]": 10, - "Edge heat transfer coefficient [W.m-2.K-1]": 10, - } -) - - -# process model and geometry, and discretise -meshes = {} -for name, model in models.items(): - param.process_model(model) - geometry = model.default_geometry - param.process_geometry(geometry) - - # set mesh - var = pybamm.standard_spatial_vars - submesh_types = model.default_submesh_types - # set npts - var = pybamm.standard_spatial_vars - npts = 16 - var_pts = { - var.x_n: npts, - var.x_s: npts, - var.x_p: npts, - var.r_n: npts, - var.r_p: npts, - var.z: npts, - } - meshes[name] = pybamm.Mesh(geometry, submesh_types, var_pts) - disc = pybamm.Discretisation(meshes[name], model.default_spatial_methods) - disc.process_model(model, check_model=False) - -# solve model at comsol times -t_eval = comsol_variables["time"] - -solutions = {} -for name, model in models.items(): - if name == "Current collector": - solver = pybamm.CasadiAlgebraicSolver(tol=1e-6) - solutions[name] = solver.solve(model) - else: - # solver - solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-6, root_tol=1e-6, mode="fast") - solutions[name] = solver.solve(model, t_eval) - -"-----------------------------------------------------------------------------" -"Make Comsol 'model' for comparison using mesh and times from 1+1D solution" - -mesh = meshes["1+1D DFN"] -comsol_model = shared.make_comsol_model(comsol_variables, mesh, param, thermal=True) -comsol_solution = pybamm.Solution(solutions["1+1D DFN"].t, solutions["1+1D DFN"].y) -comsol_solution.model = comsol_model - -"-----------------------------------------------------------------------------" -"Make plots" -t_plot = comsol_model.t -z_plot = comsol_model.z_interp -t_slices = np.array([600, 1200, 1800, 2400, 3000]) / 3 - -# get processed potentials from DFNCC -R_cc = param.process_symbol( - cc_model.variables["Effective current collector resistance"] -).evaluate(t=solutions["Current collector"].t, y=solutions["Current collector"].y)[0][0] - -V_av_1D = solutions["Average DFN"]["Terminal voltage"] -I_av = solutions["Average DFN"]["Total current density"] - - -def V_av(t): - "Include effect of current collector resistance" - return V_av_1D(t) - I_av(t) * R_cc - - -potentials = cc_model.get_processed_potentials( - solutions["Current collector"], param, V_av, I_av -) - -# plot negative current collector potential -var = "Negative current collector potential [V]" -comsol_var_fun = comsol_solution[var] -pybamm_var_fun = solutions["1+1D DFN"][var] - -pybamm_bar_var_fun = potentials[var] -shared.plot_tz_var( - t_plot, - z_plot, - t_slices, - "$\phi^*_{\mathrm{s,cn}}$", - "[V]", - comsol_var_fun, - pybamm_var_fun, - pybamm_bar_var_fun, - param, - cmap="cividis", -) - -# plot positive current collector potential -var = "Positive current collector potential [V]" -comsol_var = comsol_solution[var] -V_comsol = comsol_solution["Terminal voltage [V]"] - - -def comsol_var_fun(t, z): - return comsol_var(t=t, z=z) - V_comsol(t=t) - - -pybamm_var = solutions["1+1D DFN"][var] -V = solutions["1+1D DFN"]["Terminal voltage [V]"] - - -def pybamm_var_fun(t, z): - return pybamm_var(t=t, z=z) - V(t=t) - - -pybamm_bar_var = potentials[var] - -pot_scale = param.evaluate(pybamm.standard_parameters_lithium_ion.potential_scale) -U_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.U_p_ref) - param.evaluate( - pybamm.standard_parameters_lithium_ion.U_n_ref -) - - -def V_av_dim(t): - return U_ref + V_av(t) * pot_scale - - -def pybamm_bar_var_fun(t, z): - return pybamm_bar_var(t=t, z=z) - V_av_dim(t) - - -shared.plot_tz_var( - t_plot, - z_plot, - t_slices, - "$\phi^*_{\mathrm{s,cp}} - V^*$", - "[V]", - comsol_var_fun, - pybamm_var_fun, - pybamm_bar_var_fun, - param, - cmap="viridis", -) - - -# plot through-cell current -var = "Current collector current density [A.m-2]" -comsol_var_fun = comsol_solution[var] -pybamm_var_fun = solutions["1+1D DFN"][var] - -I_av = solutions["Average DFN"][var] - - -def pybamm_bar_var_fun(t, z): - if t.shape[0] == 1: - return np.repeat(I_av(t)[:, np.newaxis], len(z), axis=0) - else: - return np.transpose(np.repeat(I_av(t)[:, np.newaxis], len(z), axis=1)) - - -shared.plot_tz_var( - t_plot, - z_plot, - t_slices, - "$\mathcal{I}^*$", - "[A/m${}^2$]", - comsol_var_fun, - pybamm_var_fun, - pybamm_bar_var_fun, - param, - cmap="plasma", -) - -# plot temperature -T_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.T_ref) -var = "X-averaged cell temperature [K]" -comsol_var = comsol_solution[var] - - -def comsol_var_fun(t, z): - return comsol_var(t=t, z=z) - T_ref - - -pybamm_var = solutions["1+1D DFN"][var] - - -def pybamm_var_fun(t, z): - return pybamm_var(t=t, z=z) - T_ref - - -T_av = solutions["Average DFN"][var] - - -def pybamm_bar_var_fun(t, z): - if t.shape[0] == 1: - return np.repeat(T_av(t)[:, np.newaxis], len(z), axis=0) - T_ref - else: - return np.transpose(np.repeat(T_av(t)[:, np.newaxis], len(z), axis=1)) - T_ref - - -shared.plot_tz_var( - t_plot, - z_plot, - t_slices, - "$\\bar{T}^* - \\bar{T}_0^*$", - "[K]", - comsol_var_fun, - pybamm_var_fun, - pybamm_bar_var_fun, - param, - cmap="inferno", -) - - -plt.show() From 8df1d5bc84882ce33d47d0fb62c4bece390b7915 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Tue, 19 May 2020 14:07:35 +0100 Subject: [PATCH 4/9] #997 refactor effective curr coll models --- .../notebooks/models/pouch_cell_model.ipynb | 152 ++++----- .../anodes/graphite_Chen2020/README.md | 7 - .../graphite_LGM50_diffusivity_Chen2020.py | 33 -- ...olyte_exchange_current_density_Chen2020.py | 39 --- pybamm/models/base_model.py | 4 +- .../full_battery_models/base_battery_model.py | 3 +- .../effective_resistance_current_collector.py | 294 ++++++++---------- pybamm/solvers/processed_variable.py | 37 ++- test.py | 13 + .../test_effective_current_collector.py | 18 +- .../test_solvers/test_processed_variable.py | 4 +- 11 files changed, 245 insertions(+), 359 deletions(-) delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py delete mode 100644 input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py create mode 100644 test.py diff --git a/examples/notebooks/models/pouch_cell_model.ipynb b/examples/notebooks/models/pouch_cell_model.ipynb index 74507b1b8f..d6db44bd0d 100644 --- a/examples/notebooks/models/pouch_cell_model.ipynb +++ b/examples/notebooks/models/pouch_cell_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -19,7 +19,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -31,18 +31,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 14, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:253: 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" - ] - } - ], + "outputs": [], "source": [ "cc_model = pybamm.current_collector.EffectiveResistance1D()\n", "dfn_av = pybamm.lithium_ion.DFN({\"thermal\": \"x-lumped\"}, name=\"Average DFN\")\n", @@ -55,7 +46,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -77,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -108,7 +99,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -125,30 +116,14 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ - "R_cc = param.process_symbol(\n", - " cc_model.variables[\"Effective current collector resistance\"]\n", - ").evaluate(t=solutions[\"Current collector\"].t, y=solutions[\"Current collector\"].y)[0][0]\n", - "pot_scale = param.evaluate(pybamm.standard_parameters_lithium_ion.potential_scale)\n", - "U_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.U_p_ref) - param.evaluate(\n", - " pybamm.standard_parameters_lithium_ion.U_n_ref\n", - ")\n", - "V_av_1D = solutions[\"Average DFN\"][\"Terminal voltage\"]\n", + "V_av = solutions[\"Average DFN\"][\"Terminal voltage\"]\n", "I_av = solutions[\"Average DFN\"][\"Total current density\"]\n", "\n", - "\n", - "def V_av(t):\n", - " \"Include effect of current collector resistance\"\n", - " return V_av_1D(t) - I_av(t) * R_cc\n", - "\n", - "\n", - "def V_av_dim(t):\n", - " return U_ref + V_av(t) * pot_scale\n", - "\n", - "potentials = cc_model.get_processed_potentials(\n", + "dfncc_vars = cc_model.post_process(\n", " solutions[\"Current collector\"], param, V_av, I_av\n", ")" ] @@ -169,7 +144,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -206,7 +181,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -234,7 +209,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 21, "metadata": {}, "outputs": [], "source": [ @@ -251,7 +226,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 22, "metadata": {}, "outputs": [], "source": [ @@ -261,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 23, "metadata": {}, "outputs": [], "source": [ @@ -272,8 +247,8 @@ " var_name,\n", " units,\n", " comsol_var_fun,\n", - " pybamm_var_fun,\n", - " pybamm_bar_var_fun,\n", + " dfn_var_fun,\n", + " dfncc_var_fun,\n", " param,\n", " cmap=\"viridis\",\n", "):\n", @@ -312,29 +287,29 @@ " for ind, t in enumerate(t_slices_non_dim):\n", " color = ccmap(float(ind) / len(t_slices))\n", " comsol_var_slice = comsol_var_fun(t=t, z=z_plot_non_dim)\n", - " pybamm_var_slice = pybamm_var_fun(t=t, z=z_plot_non_dim)\n", - " pybamm_bar_var_slice = pybamm_bar_var_fun(t=np.array([t]), z=z_plot_non_dim)\n", + " dfn_var_slice = dfn_var_fun(t=t, z=z_plot_non_dim)\n", + " dfncc_var_slice = dfncc_var_fun(t=np.array([t]), z=z_plot_non_dim)\n", " ax[0, 1].plot(\n", " z_plot * 1e3, comsol_var_slice, \"o\", fillstyle=\"none\", color=color\n", " )\n", " ax[0, 1].plot(\n", " z_plot * 1e3,\n", - " pybamm_var_slice,\n", + " dfn_var_slice,\n", " \"-\",\n", " color=color,\n", " label=\"{:.0f} s\".format(t_slices[ind]),\n", " )\n", - " ax[0, 1].plot(z_plot * 1e3, pybamm_bar_var_slice, \":\", color=color)\n", + " ax[0, 1].plot(z_plot * 1e3, dfncc_var_slice, \":\", color=color)\n", " # add dummy points for legend of styles\n", " comsol_p, = ax[0, 1].plot(np.nan, np.nan, \"ko\", fillstyle=\"none\")\n", " pybamm_p, = ax[0, 1].plot(np.nan, np.nan, \"k-\", fillstyle=\"none\")\n", - " pybamm_bar_p, = ax[0, 1].plot(np.nan, np.nan, \"k:\", fillstyle=\"none\")\n", + " dfncc_p, = ax[0, 1].plot(np.nan, np.nan, \"k:\", fillstyle=\"none\")\n", "\n", " # compute errors\n", - " pybamm_var = pybamm_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", - " pybamm_bar_var = pybamm_bar_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", - " error = np.abs(comsol_var - pybamm_var)\n", - " error_bar = np.abs(comsol_var - pybamm_bar_var)\n", + " dfn_var = dfn_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", + " dfncc_var = dfncc_var_fun(t=t_non_dim, z=z_plot_non_dim)\n", + " error = np.abs(comsol_var - dfn_var)\n", + " error_bar = np.abs(comsol_var - dfncc_var)\n", "\n", " # plot time averaged error\n", " ax[1, 0].plot(z_plot * 1e3, np.mean(error, axis=1), \"k-\", label=r\"$1+1$D\")\n", @@ -385,7 +360,7 @@ " )\n", "\n", " leg2 = ax[0, 1].legend(\n", - " [comsol_p, pybamm_p, pybamm_bar_p],\n", + " [comsol_p, pybamm_p, dfncc_p],\n", " [\"COMSOL\", r\"$1+1$D\", \"DFNCC\"],\n", " bbox_to_anchor=(0, 1.5, 1.0, 0.102),\n", " loc=\"lower left\",\n", @@ -411,7 +386,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 24, "metadata": {}, "outputs": [], "source": [ @@ -422,7 +397,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 25, "metadata": {}, "outputs": [ { @@ -442,9 +417,9 @@ "# plot negative current collector potential\n", "var = \"Negative current collector potential [V]\"\n", "comsol_var_fun = comsol_solution[var]\n", - "pybamm_var_fun = solutions[\"1+1D DFN\"][var]\n", + "dfn_var_fun = solutions[\"1+1D DFN\"][var]\n", "\n", - "pybamm_bar_var_fun = potentials[var]\n", + "dfncc_var_fun = dfncc_vars[var]\n", "plot(\n", " t_plot,\n", " z_plot,\n", @@ -452,8 +427,8 @@ " \"$\\phi^*_{\\mathrm{s,cn}}$\",\n", " \"[V]\",\n", " comsol_var_fun,\n", - " pybamm_var_fun,\n", - " pybamm_bar_var_fun,\n", + " dfn_var_fun,\n", + " dfncc_var_fun,\n", " param,\n", " cmap=\"cividis\",\n", ")" @@ -461,7 +436,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 26, "metadata": {}, "outputs": [ { @@ -478,7 +453,7 @@ } ], "source": [ - "# plot positive current collector potential\n", + "# plot positive current collector potential with respect to terminal voltage\n", "var = \"Positive current collector potential [V]\"\n", "comsol_var = comsol_solution[var]\n", "V_comsol = comsol_solution[\"Terminal voltage [V]\"]\n", @@ -488,19 +463,19 @@ " return comsol_var(t=t, z=z) - V_comsol(t=t)\n", "\n", "\n", - "pybamm_var = solutions[\"1+1D DFN\"][var]\n", + "dfn_var = solutions[\"1+1D DFN\"][var]\n", "V = solutions[\"1+1D DFN\"][\"Terminal voltage [V]\"]\n", "\n", "\n", - "def pybamm_var_fun(t, z):\n", - " return pybamm_var(t=t, z=z) - V(t=t)\n", - "\n", + "def dfn_var_fun(t, z):\n", + " return dfn_var(t=t, z=z) - V(t=t)\n", "\n", - "pybamm_bar_var = potentials[var]\n", "\n", + "dfncc_var = dfncc_vars[var]\n", + "V_dfncc = dfncc_vars[\"Terminal voltage [V]\"]\n", "\n", - "def pybamm_bar_var_fun(t, z):\n", - " return pybamm_bar_var(t=t, z=z) - V_av_dim(t)\n", + "def dfncc_var_fun(t, z):\n", + " return dfncc_var(t=t, z=z) - V_dfncc(t)\n", "\n", "\n", "plot(\n", @@ -510,8 +485,8 @@ " \"$\\phi^*_{\\mathrm{s,cp}} - V^*$\",\n", " \"[V]\",\n", " comsol_var_fun,\n", - " pybamm_var_fun,\n", - " pybamm_bar_var_fun,\n", + " dfn_var_fun,\n", + " dfncc_var_fun,\n", " param,\n", " cmap=\"viridis\",\n", ")" @@ -519,7 +494,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 27, "metadata": {}, "outputs": [ { @@ -539,13 +514,14 @@ "# plot through-cell current\n", "var = \"Current collector current density [A.m-2]\"\n", "comsol_var_fun = comsol_solution[var]\n", - "pybamm_var_fun = solutions[\"1+1D DFN\"][var]\n", + "dfn_var_fun = solutions[\"1+1D DFN\"][var]\n", "\n", "I_av = solutions[\"Average DFN\"][var]\n", "\n", "\n", - "def pybamm_bar_var_fun(t, z):\n", - " return np.transpose(np.repeat(I_av(t)[:, np.newaxis], len(z), axis=1))\n", + "def dfncc_var_fun(t, z):\n", + " \"In the DFNCC the current is just the average current\"\n", + " return np.transpose(np.repeat(I_av(t)[:, np.newaxis], len(z), axis=1))\n", "\n", "\n", "plot(\n", @@ -555,8 +531,8 @@ " \"$\\mathcal{I}^*$\",\n", " \"[A/m${}^2$]\",\n", " comsol_var_fun,\n", - " pybamm_var_fun,\n", - " pybamm_bar_var_fun,\n", + " dfn_var_fun,\n", + " dfncc_var_fun,\n", " param,\n", " cmap=\"plasma\",\n", ")" @@ -564,7 +540,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -581,7 +557,7 @@ } ], "source": [ - "# plot temperature\n", + "# plot temperature with respect to reference temperature\n", "T_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.T_ref)\n", "var = \"X-averaged cell temperature [K]\"\n", "comsol_var = comsol_solution[var]\n", @@ -591,18 +567,19 @@ " return comsol_var(t=t, z=z) - T_ref\n", "\n", "\n", - "pybamm_var = solutions[\"1+1D DFN\"][var]\n", + "dfn_var = solutions[\"1+1D DFN\"][var]\n", "\n", "\n", - "def pybamm_var_fun(t, z):\n", - " return pybamm_var(t=t, z=z) - T_ref\n", + "def dfn_var_fun(t, z):\n", + " return dfn_var(t=t, z=z) - T_ref\n", "\n", "\n", "T_av = solutions[\"Average DFN\"][var]\n", "\n", "\n", - "def pybamm_bar_var_fun(t, z):\n", - " return np.transpose(np.repeat(T_av(t)[:, np.newaxis], len(z), axis=1)) - T_ref\n", + "def dfncc_var_fun(t, z):\n", + " \"In the DFNCC the temperature is just the average temperature\"\n", + " return np.transpose(np.repeat(T_av(t)[:, np.newaxis], len(z), axis=1)) - T_ref\n", "\n", "\n", "plot(\n", @@ -612,12 +589,19 @@ " \"$\\\\bar{T}^* - \\\\bar{T}_0^*$\",\n", " \"[K]\",\n", " comsol_var_fun,\n", - " pybamm_var_fun,\n", - " pybamm_bar_var_fun,\n", + " dfn_var_fun,\n", + " dfncc_var_fun,\n", " param,\n", " cmap=\"inferno\",\n", ")" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md b/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md deleted file mode 100644 index 702df98440..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Chen2020/README.md +++ /dev/null @@ -1,7 +0,0 @@ -# LG M50 Graphite anode parameters - -Parameters for a LG M50 graphite anode, from the paper - -> 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." Submitted for publication (2020). - -and references therein. For more information or how to cite please contact Ferran.Brosa-Planella (at) warwick.ac.uk. diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py deleted file mode 100644 index a877cafc06..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_diffusivity_Chen2020.py +++ /dev/null @@ -1,33 +0,0 @@ -from pybamm import exp, constants - - -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]. - - 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." Submitted for - publication (2020). - - Parameters - ---------- - sto: :class:`pybamm.Symbol` - Electrode stochiometry - T: :class:`pybamm.Symbol` - Dimensional temperature - - Returns - ------- - :class:`pybamm.Symbol` - Solid diffusivity - """ - - D_ref = 3.3e-14 - E_D_s = 42770 - arrhenius = exp(E_D_s / constants.R * (1 / 298.15 - 1 / T)) - - return D_ref * arrhenius diff --git a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py b/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py deleted file mode 100644 index 51b9a3e90b..0000000000 --- a/input/parameters/lithium-ion/anodes/graphite_Chen2020/graphite_LGM50_electrolyte_exchange_current_density_Chen2020.py +++ /dev/null @@ -1,39 +0,0 @@ -from pybamm import exp, constants, standard_parameters_lithium_ion - - -def graphite_LGM50_electrolyte_exchange_current_density_Chen2020(c_e, c_s_surf, T): - """ - Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in - EC:DMC. - - 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." Submitted for - publication (2020). - - 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 = 6.48e-7 # (A/m2)(mol/m3)**1.5 - includes ref concentrations - E_r = 35000 - arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T)) - - c_n_max = standard_parameters_lithium_ion.c_n_max - - 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/models/base_model.py b/pybamm/models/base_model.py index 0776e40ba8..3f21c43e30 100644 --- a/pybamm/models/base_model.py +++ b/pybamm/models/base_model.py @@ -96,9 +96,9 @@ class BaseModel(object): """ - def __init__(self, name="Unnamed model"): + def __init__(self, options=None, name="Unnamed model"): + self.options = options or {} self.name = name - self.options = {} # Initialise empty model self.rhs = {} diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py index fe63efd631..6ecb4d883a 100644 --- a/pybamm/models/full_battery_models/base_battery_model.py +++ b/pybamm/models/full_battery_models/base_battery_model.py @@ -65,8 +65,7 @@ class BaseBatteryModel(pybamm.BaseModel): """ def __init__(self, options=None, name="Unnamed battery model"): - super().__init__(name) - self.options = options + super().__init__(options, name) self.submodels = {} self._built = False self._built_fundamental_and_external = False diff --git a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py index 01b890f4fb..c7ce9e9fd5 100644 --- a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py +++ b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py @@ -4,8 +4,8 @@ import pybamm -class EffectiveResistance1D(pybamm.BaseModel): - """A model which calculates the effective Ohmic resistance of the 1D current +class EffectiveResistance(pybamm.BaseModel): + """A model which calculates the effective Ohmic resistance of the current collectors in the limit of large electrical conductivity. For details see [1]_. References @@ -16,11 +16,18 @@ class EffectiveResistance1D(pybamm.BaseModel): **Extends:** :class:`pybamm.BaseModel` """ - def __init__(self): - super().__init__() - self.name = "Effective resistance in current collector model (1D)" + def __init__( + self, options=None, name="Effective resistance in current collector model" + ): + super().__init__(options, name) self.param = pybamm.standard_parameters_lithium_ion + self.variables = self.get_fundamental_variables() + self.set_algebraic(self.variables) + self.set_boundary_conditions(self.variables) + self.set_initial_conditions(self.variables) + + def get_fundamental_variables(self): # Get necessary parameters param = self.param l_cn = param.l_cn @@ -40,43 +47,17 @@ def __init__(self): R_cn = delta * R_cn_scaled / (l_cn * sigma_cn_dbl_prime) R_cp = delta * R_cp_scaled / (l_cp * sigma_cp_dbl_prime) - # Governing equations - self.algebraic = { - R_cn_scaled: pybamm.laplacian(R_cn_scaled) - 1, - R_cp_scaled: pybamm.laplacian(R_cp_scaled) - 1, - } - - # Boundary conditons - self.boundary_conditions = { - R_cn_scaled: { - "left": (0, "Neumann"), - "right": (0, "Dirichlet"), - # "negative tab": (0, "Dirichlet"), - # "positive tab": (0, "Neumann"), - # "no tab": (0, "Neumann"), - }, - R_cp_scaled: { - "negative tab": (0, "Neumann"), - "positive tab": (0, "Dirichlet"), - "no tab": (0, "Neumann"), - }, - } - - # "Initial conditions" provides initial guess for solver - self.initial_conditions = { - R_cn_scaled: pybamm.Scalar(0), - R_cp_scaled: pybamm.Scalar(0), - } - # Define effective current collector resistance - R_cc_n = -pybamm.z_average(R_cn) - R_cc_p = -pybamm.z_average(R_cp) + R_cc_n = -self.average(R_cn) + R_cc_p = -self.average(R_cp) R_cc = R_cc_n + R_cc_p R_scale = param.potential_scale / param.I_typ - self.variables = { + variables = { + "Scaled negative current collector resistance": R_cn_scaled, "Negative current collector resistance": R_cn, "Negative current collector resistance [Ohm]": R_cn * R_scale, + "Scaled positive current collector resistance": R_cp_scaled, "Positive current collector resistance": R_cp, "Positive current collector resistance [Ohm]": R_cp * R_scale, "Effective current collector resistance": R_cc, @@ -87,15 +68,32 @@ def __init__(self): "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, } - def get_processed_potentials(self, solution, param_values, V_av, I_av): + return variables + + def set_algebraic(self, variables): + R_cn_scaled = variables["Scaled negative current collector resistance"] + R_cp_scaled = variables["Scaled positive current collector resistance"] + self.algebraic = { + R_cn_scaled: pybamm.laplacian(R_cn_scaled) - pybamm.source(1, R_cn_scaled), + R_cp_scaled: pybamm.laplacian(R_cp_scaled) - pybamm.source(1, R_cp_scaled), + } + + def set_initial_conditions(self, variables): + R_cn_scaled = variables["Scaled negative current collector resistance"] + R_cp_scaled = variables["Scaled positive current collector resistance"] + self.initial_conditions = { + R_cn_scaled: pybamm.Scalar(0), + R_cp_scaled: pybamm.Scalar(0), + } + + def post_process(self, solution, param_values, V_av, I_av): """ - Calculates the potentials in the current collector given - the average voltage and current. + Calculates the potentials in the current collector and the terminal + voltage given the average voltage and current. Note: This takes in the *processed* V_av and I_av from a 1D simulation representing the average cell behaviour and returns a dictionary of processed potentials. """ - # Get required processed parameters param = self.param pot_scale = param_values.evaluate(param.potential_scale) U_ref = param_values.evaluate(param.U_p_ref - param.U_n_ref) @@ -103,35 +101,46 @@ def get_processed_potentials(self, solution, param_values, V_av, I_av): # Process resistances R_cn = solution["Negative current collector resistance"] R_cp = solution["Positive current collector resistance"] + R_cc = solution["Effective current collector resistance"] # Create callable combination of ProcessedVariable objects for potentials - def phi_s_cn(t, z): - return R_cn(z=z) * I_av(t=t) + # and terminal voltage + def V(t): + "Account for effective current collector resistance" + return V_av(t) - I_av(t) * R_cc(t) + + def phi_s_cn(t, z, y=None): + return R_cn(y=y, z=z) * I_av(t=t) + + def phi_s_cp(t, z, y=None): + return V(t) - R_cp(y=y, z=z) * I_av(t=t) - def phi_s_cp(t, z): - return V_av(t=t) - R_cp(z=z) * I_av(t=t) + def V_cc(t, z, y=None): + return phi_s_cp(t, z, y=y) - phi_s_cn(t, z, y=y) - def V_cc(t, z): - return phi_s_cp(t, z) - phi_s_cn(t, z) + def V_dim(t): + return U_ref + V(t) * pot_scale - def phi_s_cn_dim(t, z): - return phi_s_cn(t, z) * pot_scale + def phi_s_cn_dim(t, z, y=None): + return phi_s_cn(t, z, y=y) * pot_scale - def phi_s_cp_dim(t, z): - return U_ref + phi_s_cp(t, z) * pot_scale + def phi_s_cp_dim(t, z, y=None): + return U_ref + phi_s_cp(t, z, y=y) * pot_scale - def V_cc_dim(t, z): - return U_ref + V_cc(t, z) * pot_scale + def V_cc_dim(t, z, y=None): + return U_ref + V_cc(t, z, y=y) * pot_scale - potentials = { + processed_vars = { "Negative current collector potential": phi_s_cn, "Negative current collector potential [V]": phi_s_cn_dim, "Positive current collector potential": phi_s_cp, "Positive current collector potential [V]": phi_s_cp_dim, "Local current collector potential difference": V_cc, "Local current collector potential difference [V]": V_cc_dim, + "Terminal voltage": V, + "Terminal voltage [V]": V_dim, } - return potentials + return processed_vars @property def default_parameter_values(self): @@ -144,7 +153,7 @@ def default_geometry(self): @property def default_var_pts(self): var = pybamm.standard_spatial_vars - return {var.z: 32} + return {var.y: 32, var.z: 32} @property def default_submesh_types(self): @@ -159,7 +168,37 @@ def default_solver(self): return pybamm.CasadiAlgebraicSolver() -class EffectiveResistance2D(pybamm.BaseModel): +class EffectiveResistance1D(EffectiveResistance): + """A model which calculates the effective Ohmic resistance of the 1D current + collectors in the limit of large electrical conductivity. For details see [1]_. + + References + ---------- + .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic + Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + + **Extends:** :class:`pybamm.EffectiveResistance` + """ + + def __init__( + self, options=None, name="Effective resistance in current collector model (1D)" + ): + super().__init__(options, name) + + def set_boundary_conditions(self, variables): + R_cn_scaled = variables["Scaled negative current collector resistance"] + R_cp_scaled = variables["Scaled positive current collector resistance"] + self.boundary_conditions = { + R_cn_scaled: {"negative tab": (0, "Dirichlet"), "no tab": (0, "Neumann")}, + R_cp_scaled: {"positive tab": (0, "Dirichlet"), "no tab": (0, "Neumann")}, + } + + def average(self, variable): + "Compute the average over the 1D current collector" + return pybamm.z_average(variable) + + +class EffectiveResistance2D(EffectiveResistance): """A model which calculates the effective Ohmic resistance of the 2D current collectors in the limit of large electrical conductivity. For details see [1]_. Note that unlike the model in [1]_, this formulation assumes uniform potential @@ -171,133 +210,36 @@ class EffectiveResistance2D(pybamm.BaseModel): .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. - **Extends:** :class:`pybamm.BaseModel` + **Extends:** :class:`pybamm.EffectiveResistance` """ - def __init__(self): + def __init__( + self, options=None, name="Effective resistance in current collector model (2D)" + ): super().__init__() - self.name = "Effective resistance in current collector model (2D)" - self.param = pybamm.standard_parameters_lithium_ion - - # Get necessary parameters - param = self.param - l_cn = param.l_cn - l_cp = param.l_cp - sigma_cn_dbl_prime = param.sigma_cn_dbl_prime - sigma_cp_dbl_prime = param.sigma_cp_dbl_prime - delta = param.delta # aspect ratio - # Set model variables - R_cn = pybamm.Variable( - "Negative current collector resistance", domain="current collector" - ) - R_cp = pybamm.Variable( - "positive current collector resistance", domain="current collector" - ) - - # We solve using a scaled version that is better conditioned - R_cn_scaled = R_cn * l_cn * sigma_cn_dbl_prime / delta - R_cp_scaled = R_cp * l_cp * sigma_cp_dbl_prime / delta - - # Governing equations - self.algebraic = { - R_cn: pybamm.laplacian(R_cn_scaled) - pybamm.source(1, R_cn_scaled), - R_cp: pybamm.laplacian(R_cp_scaled) - pybamm.source(1, R_cp_scaled), - } - - # Boundary conditons + def set_boundary_conditions(self, variables): + R_cn_scaled = variables["Scaled negative current collector resistance"] + R_cp_scaled = variables["Scaled positive current collector resistance"] self.boundary_conditions = { R_cn_scaled: { "negative tab": (0, "Dirichlet"), "positive tab": (0, "Neumann"), }, R_cp_scaled: { - "negative tab": (0, "Neumann"), "positive tab": (0, "Dirichlet"), + "negative tab": (0, "Neumann"), }, } - # "Initial conditions" provides initial guess for solver - self.initial_conditions = {R_cn: pybamm.Scalar(0), R_cp: pybamm.Scalar(0)} - - # Define effective current collector resistance - R_cc_n = -pybamm.yz_average(R_cn) - R_cc_p = -pybamm.yz_average(R_cp) - R_cc = R_cc_n + R_cc_p - R_scale = param.potential_scale / param.I_typ - - self.variables = { - "Negative current collector resistance": R_cn, - "Negative current collector resistance [Ohm]": R_cn * R_scale, - "Positive current collector resistance": R_cp, - "Positive current collector resistance [Ohm]": R_cp * R_scale, - "Effective current collector resistance": R_cc, - "Effective current collector resistance [Ohm]": R_cc * R_scale, - "Effective negative current collector resistance": R_cc_n, - "Effective negative current collector resistance [Ohm]": R_cc_n * R_scale, - "Effective positive current collector resistance": R_cc_p, - "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, - } - - def get_processed_potentials(self, solution, param_values, V_av, I_av): - """ - Calculates the potentials in the current collector given - the average voltage and current. - Note: This takes in the *processed* V_av and I_av from a 1D simulation - representing the average cell behaviour and returns a dictionary of - processed potentials. - """ - # Get required processed parameters - param = self.param - pot_scale = param_values.evaluate(param.potential_scale) - U_ref = param_values.evaluate(param.U_p_ref - param.U_n_ref) - - # Process resistances - R_cn = solution["Negative current collector resistance"] - R_cp = solution["Positive current collector resistance"] - - # Create callable combination of ProcessedVariable objects for potentials - def phi_s_cn(t, y, z): - return R_cn(y=y, z=z) * I_av(t=t) - - def phi_s_cp(t, y, z): - return V_av(t=t) - R_cp(y=y, z=z) * I_av(t=t) - - def V_cc(t, y, z): - return phi_s_cp(t, y, z) - phi_s_cn(t, y, z) - - def phi_s_cn_dim(t, y, z): - return phi_s_cn(t, y, z) * pot_scale - - def phi_s_cp_dim(t, y, z): - return U_ref + phi_s_cp(t, y, z) * pot_scale - - def V_cc_dim(t, y, z): - return U_ref + V_cc(t, y, z) * pot_scale - - potentials = { - "Negative current collector potential": phi_s_cn, - "Negative current collector potential [V]": phi_s_cn_dim, - "Positive current collector potential": phi_s_cp, - "Positive current collector potential [V]": phi_s_cp_dim, - "Local current collector potential difference": V_cc, - "Local current collector potential difference [V]": V_cc_dim, - } - return potentials - - @property - def default_parameter_values(self): - return pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019) + def average(self, variable): + "Compute the average over the 2D current collector" + return pybamm.yz_average(variable) @property def default_geometry(self): return pybamm.Geometry("2D current collector") - @property - def default_var_pts(self): - var = pybamm.standard_spatial_vars - return {var.y: 32, var.z: 32} - @property def default_submesh_types(self): return { @@ -308,10 +250,6 @@ def default_submesh_types(self): def default_spatial_methods(self): return {"current collector": pybamm.ScikitFiniteElement()} - @property - def default_solver(self): - return pybamm.CasadiAlgebraicSolver() - class AlternativeEffectiveResistance2D(pybamm.BaseModel): """A model which calculates the effective Ohmic resistance of the 2D current @@ -405,7 +343,7 @@ def __init__(self): "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, } - def get_processed_potentials(self, solution, param_values, V_av, I_av): + def post_process(self, solution, param_values, V_av, I_av): """ Calculates the potentials in the current collector given the average voltage and current. @@ -427,18 +365,28 @@ def get_processed_potentials(self, solution, param_values, V_av, I_av): f_n = solution["Unit solution in negative current collector"] f_p = solution["Unit solution in positive current collector"] + # Get effective resistance + R_cc = solution["Effective current collector resistance"] + # Create callable combination of ProcessedVariable objects for potentials + def V(t): + "Account for effective current collector resistance" + return V_av(t) - I_av(t) * R_cc(t) + def phi_s_cn(t, y, z): return -(delta * I_av(t=t) / l_cn / sigma_cn_dbl_prime) * f_n(y=y, z=z) def phi_s_cp(t, y, z): - return V_av(t=t) + (delta * I_av(t=t) / l_cp / sigma_cp_dbl_prime) * f_p( + return V(t) + (delta * I_av(t=t) / l_cp / sigma_cp_dbl_prime) * f_p( y=y, z=z ) def V_cc(t, y, z): return phi_s_cp(t, y, z) - phi_s_cn(t, y, z) + def V_dim(t): + return U_ref + V(t) * pot_scale + def phi_s_cn_dim(t, y, z): return phi_s_cn(t, y, z) * pot_scale @@ -448,15 +396,17 @@ def phi_s_cp_dim(t, y, z): def V_cc_dim(t, y, z): return U_ref + V_cc(t, y, z) * pot_scale - potentials = { + processed_vars = { "Negative current collector potential": phi_s_cn, "Negative current collector potential [V]": phi_s_cn_dim, "Positive current collector potential": phi_s_cp, "Positive current collector potential [V]": phi_s_cp_dim, "Local current collector potential difference": V_cc, "Local current collector potential difference [V]": V_cc_dim, + "Terminal voltage": V, + "Terminal voltage [V]": V_dim, } - return potentials + return processed_vars @property def default_parameter_values(self): diff --git a/pybamm/solvers/processed_variable.py b/pybamm/solvers/processed_variable.py index c158e66d96..490fccfd5e 100644 --- a/pybamm/solvers/processed_variable.py +++ b/pybamm/solvers/processed_variable.py @@ -64,16 +64,35 @@ def __init__(self, base_variable, solution, known_evals=None): # check variable shape else: if len(solution.t) == 1: - # 1D function of space only - n = self.mesh[0].npts - base_shape = self.base_eval.shape[0] - if base_shape in [n, n + 1]: - self.initialise_1D(fixed_t=True) + if ( + isinstance(self.base_eval, numbers.Number) + or len(self.base_eval.shape) == 0 + or self.base_eval.shape[0] == 1 + ): + # Scalar value + t = self.t_sol + u = self.u_sol + inputs = {name: inp[0] for name, inp in self.inputs.items()} + + entries = self.base_variable.evaluate(t, u, inputs=inputs) + + def fun(t): + return entries + + self._interpolation_function = fun + self.entries = entries + self.dimensions = 0 else: - raise pybamm.SolverError( - "Solution time vector must have length > 1. Check whether " - "simulation terminated too early." - ) + # 1D function of space only + n = self.mesh[0].npts + base_shape = self.base_eval.shape[0] + if base_shape in [n, n + 1]: + self.initialise_1D(fixed_t=True) + else: + raise pybamm.SolverError( + "Solution time vector must have length > 1. Check whether " + "simulation terminated too early." + ) elif ( isinstance(self.base_eval, numbers.Number) or len(self.base_eval.shape) == 0 diff --git a/test.py b/test.py new file mode 100644 index 0000000000..d0caba46d6 --- /dev/null +++ b/test.py @@ -0,0 +1,13 @@ +import pybamm +import tests + +import numpy as np + +t = pybamm.t +y = pybamm.StateVector(slice(0, 3)) +var = t * y +disc = tests.get_2p1d_discretisation_for_testing() +var.mesh = disc.mesh["current collector"] +t_sol = np.array([1]) +y_sol = np.linspace(0, 5)[:, np.newaxis] +pybamm.ProcessedVariable(var, pybamm.Solution(t_sol, y_sol)) diff --git a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py index 3d6079be86..c58b92dc4d 100644 --- a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py +++ b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py @@ -54,14 +54,14 @@ def test_default_solver(self): self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) -class TestEffectiveResistancePotentials(unittest.TestCase): - def test_get_processed_potentials(self): - # solve cheap SPM to test processed potentials (think of an alternative test?) +class TestEffectiveResistancePostProcess(unittest.TestCase): + def test_get_processed_variables(self): + # solve cheap SPM to test post-processing (think of an alternative test?) models = [ pybamm.lithium_ion.SPM(), pybamm.current_collector.EffectiveResistance1D(), - # pybamm.current_collector.EffectiveResistance2D(), - # pybamm.current_collector.AlternativeEffectiveResistance2D(), + pybamm.current_collector.EffectiveResistance2D(), + pybamm.current_collector.AlternativeEffectiveResistance2D(), ] var = pybamm.standard_spatial_vars var_pts = { @@ -92,11 +92,11 @@ def test_get_processed_potentials(self): # for each current collector model for model in models[1:]: solution = model.default_solver.solve(model) - potentials = model.get_processed_potentials(solution, param, V, I) + vars = model.post_process(solution, param, V, I) pts = np.array([0.1, 0.5, 0.9]) - for var, processed_var in potentials.items(): - if isinstance(model, pybamm.current_collector.EffectiveResistance1D): - processed_var(t=solution_1D.t[5], z=pts) + for var, processed_var in vars.items(): + if "Terminal voltage" in var: + processed_var(t=solution_1D.t[5]) else: processed_var(t=solution_1D.t[5], y=pts, z=pts) diff --git a/tests/unit/test_solvers/test_processed_variable.py b/tests/unit/test_solvers/test_processed_variable.py index a2cc6a8174..d9e6a1a500 100644 --- a/tests/unit/test_solvers/test_processed_variable.py +++ b/tests/unit/test_solvers/test_processed_variable.py @@ -520,12 +520,12 @@ def test_call_failure(self): def test_solution_too_short(self): t = pybamm.t - y = pybamm.StateVector(slice(0, 1)) + y = pybamm.StateVector(slice(0, 3)) var = t * y disc = tests.get_2p1d_discretisation_for_testing() var.mesh = disc.mesh["current collector"] t_sol = np.array([1]) - y_sol = np.array([np.linspace(0, 5)]) + y_sol = np.linspace(0, 5)[:, np.newaxis] with self.assertRaisesRegex( pybamm.SolverError, "Solution time vector must have length > 1" ): From f72467223bdb66c8ccb13e57a55c7a4439884eae Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Wed, 20 May 2020 10:05:34 +0100 Subject: [PATCH 5/9] #997 fix simulation for base model --- ...effective_resistance_current_collector.rst | 6 + .../notebooks/models/pouch_cell_model.ipynb | 122 +++++++------ pouch.py | 163 ------------------ pybamm/CITATIONS.txt | 10 ++ .../effective_resistance_current_collector.py | 12 +- .../current_collector/potential_pair.py | 4 +- pybamm/simulation.py | 4 +- pybamm/solvers/processed_variable.py | 3 + test.py | 13 -- tests/unit/test_citations.py | 25 +++ 10 files changed, 130 insertions(+), 232 deletions(-) delete mode 100644 pouch.py delete mode 100644 test.py diff --git a/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst b/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst index ead0244857..c7d59c6391 100644 --- a/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst +++ b/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst @@ -1,5 +1,11 @@ Effective Current collector Resistance models ============================================= +.. autoclass:: pybamm.current_collector.EffectiveResistance1D + :members: + .. autoclass:: pybamm.current_collector.EffectiveResistance2D :members: + +.. autoclass:: pybamm.current_collector.AlternativeEffectiveResistance2D + :members: diff --git a/examples/notebooks/models/pouch_cell_model.ipynb b/examples/notebooks/models/pouch_cell_model.ipynb index d6db44bd0d..56a0fdea40 100644 --- a/examples/notebooks/models/pouch_cell_model.ipynb +++ b/examples/notebooks/models/pouch_cell_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 12, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -19,7 +19,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -31,9 +31,18 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:252: 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" + ] + } + ], "source": [ "cc_model = pybamm.current_collector.EffectiveResistance1D()\n", "dfn_av = pybamm.lithium_ion.DFN({\"thermal\": \"x-lumped\"}, name=\"Average DFN\")\n", @@ -46,7 +55,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -68,55 +77,67 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "meshes = {}\n", - "for name, model in models.items():\n", - " param.process_model(model)\n", - " geometry = model.default_geometry\n", - " param.process_geometry(geometry)\n", - "\n", - " # set mesh\n", - " var = pybamm.standard_spatial_vars\n", - " submesh_types = model.default_submesh_types\n", - " # set npts\n", - " var = pybamm.standard_spatial_vars\n", - " npts = 16\n", - " var_pts = {\n", - " var.x_n: npts,\n", - " var.x_s: npts,\n", - " var.x_p: npts,\n", - " var.r_n: npts,\n", - " var.r_p: npts,\n", - " var.z: npts,\n", - " }\n", - " meshes[name] = pybamm.Mesh(geometry, submesh_types, var_pts)\n", - " disc = pybamm.Discretisation(meshes[name], model.default_spatial_methods)\n", - " disc.process_model(model, check_model=False)" + "var = pybamm.standard_spatial_vars\n", + "npts = 16\n", + "var_pts = {\n", + " var.x_n: npts,\n", + " var.x_s: npts,\n", + " var.x_p: npts,\n", + " var.r_n: npts,\n", + " var.r_p: npts,\n", + " var.z: npts,\n", + "}" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ - "t_eval = comsol_variables[\"time\"]\n", - "solutions = {}\n", + "simulations = {}\n", + "solutions = {} # store solutions in a separate dict for easy access later\n", "for name, model in models.items():\n", + " sim = pybamm.Simulation(model, parameter_values=param, var_pts=var_pts)\n", + " simulations[name] = sim # store simulation for later\n", " if name == \"Current collector\":\n", - " solver = pybamm.CasadiAlgebraicSolver(tol=1e-6)\n", - " solutions[name] = solver.solve(model)\n", + " # model is independent of time, so just solve arbitrarily at t=0 using the default\n", + " # algebraic solver\n", + " t_eval = np.array([0])\n", + " solutions[name] = sim.solve(t_eval=t_eval) \n", " else:\n", - " solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-6, root_tol=1e-6, mode=\"fast\")\n", - " solutions[name] = solver.solve(model, t_eval)" + " # solve at COMSOL times using Casadi solver in \"fast\" mode\n", + " t_eval = comsol_variables[\"time\"] \n", + " solutions[name] = sim.solve(solver=pybamm.CasadiSolver(mode=\"fast\"), t_eval=t_eval)" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0018783599989546929\n", + "0.6773513660009485\n", + "7.014656061001006\n" + ] + } + ], + "source": [ + "for name, sol in solutions.items():\n", + " print(sol.solve_time)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -144,15 +165,18 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ + "# set up times\n", "tau = param.evaluate(pybamm.standard_parameters_lithium_ion.tau_discharge)\n", "comsol_t = comsol_variables[\"time\"]\n", "pybamm_t = comsol_t / tau\n", + "# set up space\n", + "mesh = simulations[\"1+1D DFN\"].mesh\n", "L_z = param.evaluate(pybamm.standard_parameters_lithium_ion.L_z)\n", - "pybamm_z = meshes[\"1+1D DFN\"][\"current collector\"][0].nodes\n", + "pybamm_z = mesh[\"current collector\"][0].nodes\n", "z_interp = pybamm_z * L_z\n", "\n", " \n", @@ -173,7 +197,7 @@ " # Make sure to use dimensional time\n", " fun = pybamm.Function(myinterp, pybamm.t * tau, name=variable_name + \"_comsol\")\n", " fun.domain = \"current collector\"\n", - " fun.mesh = meshes[\"1+1D DFN\"].combine_submeshes(\"current collector\")\n", + " fun.mesh = mesh.combine_submeshes(\"current collector\")\n", " fun.secondary_mesh = None\n", " \n", " return fun" @@ -181,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -209,7 +233,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -226,7 +250,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -236,7 +260,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -386,7 +410,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -397,7 +421,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -436,7 +460,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -494,7 +518,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -540,7 +564,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 18, "metadata": {}, "outputs": [ { diff --git a/pouch.py b/pouch.py deleted file mode 100644 index e2ca2b49f1..0000000000 --- a/pouch.py +++ /dev/null @@ -1,163 +0,0 @@ -import pybamm -import numpy as np -import matplotlib.pyplot as plt - -pybamm.set_logging_level("DEBUG") - -# load model -options = { - "current collector": "potential pair", - "dimensionality": 2, - "thermal": "x-lumped", - # The below option replaces the PDEs in the particles with ODEs under the - # assumption of fast diffusion (so that the concentration is uniform within - # each particle). This will speed up the simulation and is an OK assumption - # for a lot of cases. Uncomment it to switch it on/off. - # "particle": "fast diffusion", -} -model = pybamm.lithium_ion.SPM(options) - -# parameters can be updated here -param = model.default_parameter_values - -# set mesh points -var = pybamm.standard_spatial_vars -var_pts = { - var.x_n: 10, - var.x_s: 10, - var.x_p: 10, - var.r_n: 10, - var.r_p: 10, - var.y: 10, - var.z: 10, -} - -# solver -# casadi fast mode is pretty quick, but doesn't support events out of the box -# solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-3, root_tol=1e-3, mode="fast") -# KLU is sometimes better for bigger problems and supports events -solver = pybamm.IDAKLUSolver(atol=1e-6, rtol=1e-3, root_tol=1e-6, root_method="hybr") -# KLU performs better if you convert the final model to a python function -if isinstance(solver, pybamm.IDAKLUSolver): - model.convert_to_format = "python" - -# simulation object -simulation = pybamm.Simulation( - model, parameter_values=param, var_pts=var_pts, solver=solver -) - -# build simulation -# by default pybamm performs some checks on the discretised model. this can -# be a little slow for bigger problems, so you can turn if off. if you start to -# get obscure errors when you change things, set this to True and the error should -# get caught sooner and give a more informative message -simulation.build(check_model=False) - -# solve simulation -t_eval = np.linspace(0, 3600, 100) # time in seconds -simulation.solve(t_eval=t_eval) -solution = simulation.solution - -# plotting -# TO DO: 2+1D automated plotting - -# post-process variables -phi_s_cn = solution["Negative current collector potential [V]"] -phi_s_cp = solution["Positive current collector potential [V]"] -I = solution["Current collector current density [A.m-2]"] -T = solution["X-averaged cell temperature [K]"] - -# get y and z points for plotting (these are non-dimensional) -l_y = phi_s_cp.y_sol[-1] -l_z = phi_s_cp.z_sol[-1] -y_plot = np.linspace(0, l_y, 21) -z_plot = np.linspace(0, l_z, 21) - -# Can multiply by L_z to get dimensional y and z. Note that both y and z are -# scaled with L_z -L_z = param.evaluate(pybamm.standard_parameters_lithium_ion.L_z) -y_plot_dim = np.linspace(0, l_y, 21) * L_z -z_plot_dim = np.linspace(0, l_z, 21) * L_z - - -# define plotting function -def plot(time_in_seconds): - fig, ax = plt.subplots(figsize=(15, 8)) - plt.tight_layout() - plt.subplots_adjust(left=-0.1) - - # get non-dim time - tau = param.evaluate(pybamm.standard_parameters_lithium_ion.tau_discharge) - t_non_dim = time_in_seconds / tau - - # negative current collector potential - plt.subplot(221) - phi_s_cn_plot = plt.pcolormesh( - y_plot_dim, - z_plot_dim, - np.transpose( - phi_s_cn(y=y_plot, z=z_plot, t=t_non_dim) - ), # accepts non-dim values - shading="gouraud", - ) - plt.axis([0, l_y * L_z, 0, l_z * L_z]) - plt.xlabel(r"$y$ [m]") - plt.ylabel(r"$z$ [m]") - plt.title(r"$\phi_{s,cn}$ [V]") - plt.set_cmap("cividis") - plt.colorbar(phi_s_cn_plot) - - # positive current collector potential - plt.subplot(222) - phi_s_cp_plot = plt.pcolormesh( - y_plot_dim, - z_plot_dim, - np.transpose( - phi_s_cp(y=y_plot, z=z_plot, t=t_non_dim) - ), # accepts non-dim values - shading="gouraud", - ) - plt.axis([0, l_y * L_z, 0, l_z * L_z]) - plt.xlabel(r"$y$ [m]") - plt.ylabel(r"$z$ [m]") - plt.title(r"$\phi_{s,cp}$ [V]") - plt.set_cmap("viridis") - plt.colorbar(phi_s_cp_plot) - - # through-cell current - plt.subplot(223) - I_plot = plt.pcolormesh( - y_plot_dim, - z_plot_dim, - np.transpose(I(y=y_plot, z=z_plot, t=t_non_dim)), # accepts non-dim values - shading="gouraud", - ) - plt.axis([0, l_y * L_z, 0, l_z * L_z]) - plt.xlabel(r"$y$ [m]") - plt.ylabel(r"$z$ [m]") - plt.title(r"$I$ [A.m-2]") - plt.set_cmap("plasma") - plt.colorbar(I_plot) - # temperature - plt.subplot(224) - T_plot = plt.pcolormesh( - y_plot_dim, - z_plot_dim, - np.transpose(T(y=y_plot, z=z_plot, t=t_non_dim)), # accepts non-dim values - shading="gouraud", - ) - plt.axis([0, l_y * L_z, 0, l_z * L_z]) - plt.xlabel(r"$y$ [m]") - plt.ylabel(r"$z$ [m]") - plt.title(r"$T$ [K]") - plt.set_cmap("inferno") - plt.colorbar(T_plot) - - plt.subplots_adjust( - top=0.92, bottom=0.15, left=0.10, right=0.9, hspace=0.5, wspace=0.5 - ) - plt.show() - - -# call plot -plot(1000) diff --git a/pybamm/CITATIONS.txt b/pybamm/CITATIONS.txt index a3ff7baa30..4fc4d5f1a6 100644 --- a/pybamm/CITATIONS.txt +++ b/pybamm/CITATIONS.txt @@ -177,3 +177,13 @@ doi = "https://doi.org/10.1016/j.electacta.2020.135862", url = "http://www.sciencedirect.com/science/article/pii/S0013468620302541", author = "G. Richardson and I. Korotkin and R. Ranom and M. Castle and J.M. Foster", } + +@article{timms2020, +title={Asymptotic Reduction of a Lithium-ion Pouch Cell Model} +journal={Submitted for publication}, +author={R Timms and SG Marquis and V Sulzer and CP Please and SJ Chapman}, +year={2020}, +eprint={2005.05127}, +archivePrefix={arXiv}, +primaryClass={physics.app-ph}, +} diff --git a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py index c7ce9e9fd5..459f490a18 100644 --- a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py +++ b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py @@ -11,7 +11,7 @@ class EffectiveResistance(pybamm.BaseModel): References ---------- .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. **Extends:** :class:`pybamm.BaseModel` """ @@ -27,6 +27,8 @@ def __init__( self.set_boundary_conditions(self.variables) self.set_initial_conditions(self.variables) + pybamm.citations.register("timms2020") + def get_fundamental_variables(self): # Get necessary parameters param = self.param @@ -175,7 +177,7 @@ class EffectiveResistance1D(EffectiveResistance): References ---------- .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. **Extends:** :class:`pybamm.EffectiveResistance` """ @@ -208,7 +210,7 @@ class EffectiveResistance2D(EffectiveResistance): References ---------- .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. **Extends:** :class:`pybamm.EffectiveResistance` """ @@ -260,7 +262,7 @@ class AlternativeEffectiveResistance2D(pybamm.BaseModel): References ---------- .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. **Extends:** :class:`pybamm.BaseModel` """ @@ -343,6 +345,8 @@ def __init__(self): "Effective positive current collector resistance [Ohm]": R_cc_p * R_scale, } + pybamm.citations.register("timms2020") + def post_process(self, solution, param_values, V_av, I_av): """ Calculates the potentials in the current collector given diff --git a/pybamm/models/submodels/current_collector/potential_pair.py b/pybamm/models/submodels/current_collector/potential_pair.py index f7addb7086..1eecdb80d6 100644 --- a/pybamm/models/submodels/current_collector/potential_pair.py +++ b/pybamm/models/submodels/current_collector/potential_pair.py @@ -17,7 +17,7 @@ class BasePotentialPair(BaseModel): References ---------- .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. In preparation, 2020. + Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. .. [2] SG Marquis, R Timms, V Sulzer, CP Please and SJ Chapman. “A Suite of Reduced-Order Models of a Single-Layer Lithium-ion Pouch Cell”. In preparation, 2020. @@ -28,6 +28,8 @@ class BasePotentialPair(BaseModel): def __init__(self, param): super().__init__(param) + pybamm.citations.register("timms2020") + def get_fundamental_variables(self): phi_s_cn = pybamm.standard_variables.phi_s_cn diff --git a/pybamm/simulation.py b/pybamm/simulation.py index 9b9f58a086..b1ceb7bdeb 100644 --- a/pybamm/simulation.py +++ b/pybamm/simulation.py @@ -447,10 +447,10 @@ def solve( ): pybamm.logger.warning( "\n\n\tExperiment is infeasible: '{}' ".format( - self._solution.termination, + self._solution.termination ) + "was triggered during '{}'. ".format( - self.experiment.operating_conditions_strings[idx], + self.experiment.operating_conditions_strings[idx] ) + "Try reducing current, shortening the time interval, " "or reducing the period.\n\n" diff --git a/pybamm/solvers/processed_variable.py b/pybamm/solvers/processed_variable.py index 490fccfd5e..901d26b559 100644 --- a/pybamm/solvers/processed_variable.py +++ b/pybamm/solvers/processed_variable.py @@ -64,6 +64,9 @@ def __init__(self, base_variable, solution, known_evals=None): # check variable shape else: if len(solution.t) == 1: + # Implementing a workaround for 0D and 1D variables. Processing + # variables that are functions of space only needs to be implemented + # properly, see #1006 if ( isinstance(self.base_eval, numbers.Number) or len(self.base_eval.shape) == 0 diff --git a/test.py b/test.py deleted file mode 100644 index d0caba46d6..0000000000 --- a/test.py +++ /dev/null @@ -1,13 +0,0 @@ -import pybamm -import tests - -import numpy as np - -t = pybamm.t -y = pybamm.StateVector(slice(0, 3)) -var = t * y -disc = tests.get_2p1d_discretisation_for_testing() -var.mesh = disc.mesh["current collector"] -t_sol = np.array([1]) -y_sol = np.linspace(0, 5)[:, np.newaxis] -pybamm.ProcessedVariable(var, pybamm.Solution(t_sol, y_sol)) diff --git a/tests/unit/test_citations.py b/tests/unit/test_citations.py index 39ed2da20c..b6e2407452 100644 --- a/tests/unit/test_citations.py +++ b/tests/unit/test_citations.py @@ -74,6 +74,31 @@ def test_sulzer_2019(self): pybamm.lead_acid.Full(build=False) self.assertIn("sulzer2019physical", citations._papers_to_cite) + def test_timms_2020(self): + # Test that calling relevant bits of code adds the right paper to citations + citations = pybamm.citations + + citations._reset() + self.assertNotIn("timms2020", citations._papers_to_cite) + options = {"dimensionality": 2} + pybamm.lithium_ion.DFN(options, build=False) + self.assertIn("timms", citations._papers_to_cite) + + citations._reset() + self.assertNotIn("timms2020", citations._papers_to_cite) + pybamm.current_collector.EffectiveResistance1D() + self.assertIn("timms", citations._papers_to_cite) + + citations._reset() + self.assertNotIn("timms2020", citations._papers_to_cite) + pybamm.current_collector.EffectiveResistance2D() + self.assertIn("timms", citations._papers_to_cite) + + citations._reset() + self.assertNotIn("timms2020", citations._papers_to_cite) + pybamm.current_collector.AlternativeEffectiveResistance2D() + self.assertIn("timms", citations._papers_to_cite) + def test_scikit_fem(self): citations = pybamm.citations From c3f9b0ef055a7257041a2e18de24399ffe75ab01 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Wed, 20 May 2020 14:17:03 +0100 Subject: [PATCH 6/9] #997 update pouch cell notebook --- .flake8 | 2 +- .../5-a-simple-SEI-model.ipynb | 2 +- examples/notebooks/models/SPM.ipynb | 2 +- examples/notebooks/models/SPMe.ipynb | 2 +- ...ell_model.ipynb => pouch-cell-model.ipynb} | 301 ++++++++++++++---- .../comsol_results/comsol_1plus1D_3C.pickle | Bin 0 -> 2967396 bytes tests/unit/test_citations.py | 11 +- 7 files changed, 241 insertions(+), 79 deletions(-) rename examples/notebooks/models/{pouch_cell_model.ipynb => pouch-cell-model.ipynb} (97%) create mode 100644 pybamm/input/comsol_results/comsol_1plus1D_3C.pickle diff --git a/.flake8 b/.flake8 index bad0d2ef96..a69ea9bf0e 100644 --- a/.flake8 +++ b/.flake8 @@ -12,7 +12,7 @@ exclude= share, pyvenv.cfg, third-party, - sundials-5.0.0, + KLU_module_deps, ignore= # False positive for white space before ':' on list slice # black should format these correctly diff --git a/examples/notebooks/Creating Models/5-a-simple-SEI-model.ipynb b/examples/notebooks/Creating Models/5-a-simple-SEI-model.ipynb index d9ae44aa71..4e74a1c3cd 100644 --- a/examples/notebooks/Creating Models/5-a-simple-SEI-model.ipynb +++ b/examples/notebooks/Creating Models/5-a-simple-SEI-model.ipynb @@ -653,7 +653,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.5" + "version": "3.6.9" } }, "nbformat": 4, diff --git a/examples/notebooks/models/SPM.ipynb b/examples/notebooks/models/SPM.ipynb index dbb53e4ec1..53d70da811 100644 --- a/examples/notebooks/models/SPM.ipynb +++ b/examples/notebooks/models/SPM.ipynb @@ -894,7 +894,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.9" } }, "nbformat": 4, diff --git a/examples/notebooks/models/SPMe.ipynb b/examples/notebooks/models/SPMe.ipynb index e20dbb19cf..8a46bd1f53 100644 --- a/examples/notebooks/models/SPMe.ipynb +++ b/examples/notebooks/models/SPMe.ipynb @@ -262,7 +262,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.3" + "version": "3.6.9" } }, "nbformat": 4, diff --git a/examples/notebooks/models/pouch_cell_model.ipynb b/examples/notebooks/models/pouch-cell-model.ipynb similarity index 97% rename from examples/notebooks/models/pouch_cell_model.ipynb rename to examples/notebooks/models/pouch-cell-model.ipynb index 56a0fdea40..27c5dc90bb 100644 --- a/examples/notebooks/models/pouch_cell_model.ipynb +++ b/examples/notebooks/models/pouch-cell-model.ipynb @@ -1,5 +1,41 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Pouch cell model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this notebook we compare the solutions of two reduced-order models of a lithium-ion pouch cell with the full solution obtained using COMSOL. This example is based on the results in [[1]](#ref). The code used to produce the results in [[1]](#ref) can be found [here](https://github.com/rtimms/asymptotic-pouch-cell).\n", + "\n", + "The full model is based on the Doyle-Fuller-Newman model [[2]](#ref2) and, in the interest of simplicity, considers a one-dimensional current collector (i.e. variation in one of the current collector dimensions is ignored), resulting in a 2D macroscopic model.\n", + "\n", + "The first of the reduced order models, which is applicable in the limit of large conductivity in the current collectors, solves a one-dimensional problem in the current collectors coupled to a one-dimensional DFN model describing the through-cell electrochemistry at each point. We refer to this as a 1+1D model, though since the DFN is already a pseudo-two-dimensional model, perhaps it is more properly a 1+1+1D model.\n", + "\n", + "The second reduced order model, which is applicable in the limit of very large conductivity in the current collectors, solves a single (averaged) one-dimensional DFN model for the through-cell behaviour and an uncoupled problem for the distribution of potential in the current collectors (from which the resistance and heat source can be calculated). We refer to this model as the DFNCC, where the \"CC\" indicates the additional (uncoupled) current collector problem.\n", + "\n", + "All of the model equations, and derivations of the reduced-order models, can be found in [[1]](#ref)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solving the reduced-order pouch cell models in PyBaMM" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by importing PyBaMM along with the other packages required in this notebook" + ] + }, { "cell_type": "code", "execution_count": 1, @@ -18,20 +54,17 @@ ] }, { - "cell_type": "code", - "execution_count": 2, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "comsol_results_path = pybamm.get_parameters_filepath(\n", - " \"input/comsol_results/comsol_1plus1D_3C.pickle\"\n", - ")\n", - "comsol_variables = pickle.load(open(comsol_results_path, \"rb\"))" + "We then need to load up the appropriate models. For the DFNCC we require a 1D model of the current collectors and an average 1D DFN model for the through-cell electrochemistry. The 1+1D pouch cell model is built directly into PyBaMM and are accessed by passing the model option \"dimensionality\" which can be 1 or 2, corresponding to 1D or 2D current collectors. This option can be passed to any existing electrochemical model (e.g. [SPM](./SPM.ipynb), [SPMe](./SPMe.ipynb), [DFN](./DFN.ipynb)). Here we choose the DFN model. \n", + "\n", + "For both electrochemical models we choose an \"x-lumped\" thermal model, meaning we assume that the temperature is uniform in the through-cell direction $x$, but account for the variation in temperature in the transverse direction $z$." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -49,10 +82,32 @@ "dfn = pybamm.lithium_ion.DFN(\n", " {\"current collector\": \"potential pair\", \"dimensionality\": 1, \"thermal\": \"x-lumped\"},\n", " name=\"1+1D DFN\",\n", - ")\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then add the models to a dictionary for easy access later" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ "models = {\"Current collector\": cc_model, \"Average DFN\": dfn_av, \"1+1D DFN\": dfn}" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we update the parameters to match those used in the COMSOL simulation. In particular, we set the current to correspond to a 3C discharge and assume uniform Newton cooling on all boundaries." + ] + }, { "cell_type": "code", "execution_count": 4, @@ -75,6 +130,13 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example we choose to discretise in space using 16 nodes per domain." + ] + }, { "cell_type": "code", "execution_count": 5, @@ -93,11 +155,37 @@ "}" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before solving the models we load the COMSOL data so that we can request the output at the times in the COMSOL solution" + ] + }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], + "source": [ + "comsol_results_path = pybamm.get_parameters_filepath(\n", + " \"input/comsol_results/comsol_1plus1D_3C.pickle\"\n", + ")\n", + "comsol_variables = pickle.load(open(comsol_results_path, \"rb\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we loop over the models, creating and solving a simulation for each." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], "source": [ "simulations = {}\n", "solutions = {} # store solutions in a separate dict for easy access later\n", @@ -105,8 +193,8 @@ " sim = pybamm.Simulation(model, parameter_values=param, var_pts=var_pts)\n", " simulations[name] = sim # store simulation for later\n", " if name == \"Current collector\":\n", - " # model is independent of time, so just solve arbitrarily at t=0 using the default\n", - " # algebraic solver\n", + " # model is independent of time, so just solve arbitrarily at t=0 using \n", + " # the default algebraic solver\n", " t_eval = np.array([0])\n", " solutions[name] = sim.solve(t_eval=t_eval) \n", " else:\n", @@ -116,56 +204,29 @@ ] }, { - "cell_type": "code", - "execution_count": 7, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0018783599989546929\n", - "0.6773513660009485\n", - "7.014656061001006\n" - ] - } - ], "source": [ - "for name, sol in solutions.items():\n", - " print(sol.solve_time)" + "## Creating the COMSOL model" ] }, { - "cell_type": "code", - "execution_count": 8, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "V_av = solutions[\"Average DFN\"][\"Terminal voltage\"]\n", - "I_av = solutions[\"Average DFN\"][\"Total current density\"]\n", - "\n", - "dfncc_vars = cc_model.post_process(\n", - " solutions[\"Current collector\"], param, V_av, I_av\n", - ")" + "In this section we show how to create a PyBaMM \"model\" from the COMSOL solution. If you are just interested in seeing the comparison the skip ahead to the section \" Comparing the full and reduced-order models\".\n" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "To create a PyBaMM model from the COMSOL data we must create a `pybamm.Function` object for each variable. We do this by interpolating in space to match the PyBaMM mesh and then creating a function to interpolate in time. The following cell defines the function that handles the creation of the `pybamm.Function` object." + ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -182,9 +243,8 @@ " \n", "def get_interp_fun_curr_coll(variable_name):\n", " \"\"\"\n", - " Create a :class:`pybamm.Function` object using the variable, to allow plotting with\n", - " :class:`pybamm.QuickPlot` (interpolate in space to match edges, and then create\n", - " function to interpolate in time)\n", + " Create a :class:`pybamm.Function` object using the variable (interpolate in space \n", + " to match nodes, and then create function to interpolate in time)\n", " \"\"\"\n", "\n", " comsol_z = comsol_variables[variable_name + \"_z\"]\n", @@ -203,9 +263,16 @@ " return fun" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then pass the variables of interest to the interpolating function" + ] + }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -216,31 +283,28 @@ ")\n", "comsol_voltage.mesh = None\n", "comsol_voltage.secondary_mesh = None\n", - "comsol_vol_av_temperature = pybamm.Function(\n", - " interp.interp1d(\n", - " comsol_t, comsol_variables[\"volume-averaged temperature\"], kind=\"linear\"\n", - " ),\n", - " pybamm.t * tau,\n", - " name=\"av_temperature_comsol\",\n", - ")\n", - "comsol_vol_av_temperature.mesh = None\n", - "comsol_vol_av_temperature.secondary_mesh = None\n", "comsol_phi_s_cn = get_interp_fun_curr_coll(\"phi_s_cn\")\n", "comsol_phi_s_cp = get_interp_fun_curr_coll(\"phi_s_cp\")\n", "comsol_current = get_interp_fun_curr_coll(\"current\")\n", "comsol_temperature = get_interp_fun_curr_coll(\"temperature\")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and add them to a `pybamm.BaseModel` object" + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "comsol_model = pybamm.BaseModel()\n", "comsol_model.variables = {\n", " \"Terminal voltage [V]\": comsol_voltage,\n", - " \"Volume-averaged cell temperature [K]\": comsol_vol_av_temperature,\n", " \"Negative current collector potential [V]\": comsol_phi_s_cn,\n", " \"Positive current collector potential [V]\": comsol_phi_s_cp,\n", " \"Current collector current density [A.m-2]\": comsol_current,\n", @@ -248,9 +312,16 @@ "}" ] }, + { + "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." + ] + }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -258,6 +329,43 @@ "comsol_solution.model = comsol_model" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparing the full and reduced-order models" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The DFNCC requires some post-processing to extract the solution variables. In particular, we need to pass the current and voltage from the average DFN model to the current collector model in order to compute the distribution of the potential in the current collectors and to account for the effect of the current collector resistance in the terminal voltage. \n", + "\n", + "This process is automated by the method `post_process` which accepts the current collector solution object, the parameters and the voltage and current from the average DFN model. The results are stored in the dictionary `dfncc_vars`" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "V_av = solutions[\"Average DFN\"][\"Terminal voltage\"]\n", + "I_av = solutions[\"Average DFN\"][\"Total current density\"]\n", + "\n", + "dfncc_vars = cc_model.post_process(\n", + " solutions[\"Current collector\"], param, V_av, I_av\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we create a function to create some custom plots. For a given variable the plots will show: (a) the COMSOL results as a function of position in the current collector $z$ and time $t$; (b) a comparison of the full and reduced-order models and a sequence of times; (c) the time-averaged error between the full and reduced-order models as a function of space; and (d) the space-averaged error between the full and reduced-order models as a function of time." + ] + }, { "cell_type": "code", "execution_count": 13, @@ -408,6 +516,13 @@ " )" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then set up the times a points in space to use in the plots " + ] + }, { "cell_type": "code", "execution_count": 14, @@ -419,6 +534,13 @@ "t_slices = np.array([600, 1200, 1800, 2400, 3000]) / 3" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and plot the negative current collector potential" + ] + }, { "cell_type": "code", "execution_count": 15, @@ -438,7 +560,6 @@ } ], "source": [ - "# plot negative current collector potential\n", "var = \"Negative current collector potential [V]\"\n", "comsol_var_fun = comsol_solution[var]\n", "dfn_var_fun = solutions[\"1+1D DFN\"][var]\n", @@ -458,6 +579,13 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the positive current collector potential with respect to terminal voltage" + ] + }, { "cell_type": "code", "execution_count": 16, @@ -477,7 +605,6 @@ } ], "source": [ - "# plot positive current collector potential with respect to terminal voltage\n", "var = \"Positive current collector potential [V]\"\n", "comsol_var = comsol_solution[var]\n", "V_comsol = comsol_solution[\"Terminal voltage [V]\"]\n", @@ -516,9 +643,16 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "the through-cell current " + ] + }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -535,7 +669,6 @@ } ], "source": [ - "# plot through-cell current\n", "var = \"Current collector current density [A.m-2]\"\n", "comsol_var_fun = comsol_solution[var]\n", "dfn_var_fun = solutions[\"1+1D DFN\"][var]\n", @@ -562,9 +695,16 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "and the temperature with respect to reference temperature" + ] + }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -581,7 +721,6 @@ } ], "source": [ - "# plot temperature with respect to reference temperature\n", "T_ref = param.evaluate(pybamm.standard_parameters_lithium_ion.T_ref)\n", "var = \"X-averaged cell temperature [K]\"\n", "comsol_var = comsol_solution[var]\n", @@ -620,6 +759,30 @@ ")" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the electrical conductivity of the current collectors is sufficiently\n", + "high that the potentials remain fairly uniform in space, and both the 1+1D DFN and DFNCC models are able to accurately capture the potential distribution in the current collectors.\n", + "\n", + "\n", + "In the plot of the current we see that positioning both tabs at the top of the cell means that for most of the simulation the current preferentially travels through the upper part of the cell. Eventually, as the cell continues to discharge, this part becomes more (de)lithiated until the resultant local increase in through-cell resistance is sufficient for it to become preferential for the current to travel further along the current collectors and through the lower part of the cell. This behaviour is well captured by the 1+1D model. In the DFNCC formulation the through-cell current density is assumed uniform,\n", + "so the greatest error is found at the ends of the current collectors where the current density deviates most from its average.\n", + "\n", + "For the parameters used in this example we find that the temperature exhibits a relatively weak variation along the length of the current collectors. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. Asymptotic\n", + " Reduction of a Lithium-ion Pouch Cell Model. Submitted, 2020\n", + " \n", + "[2] M Doyle, TF Fuller, and J Newman. Modeling of galvanostatic charge and discharge of thelithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6):1526–1533, 1993" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/pybamm/input/comsol_results/comsol_1plus1D_3C.pickle b/pybamm/input/comsol_results/comsol_1plus1D_3C.pickle new file mode 100644 index 0000000000000000000000000000000000000000..85af9b637e8b2046e7da76e32ece90dcde45bf02 GIT binary patch literal 2967396 zcmagFX*gAH8@OF4!(K=!LL-?n&(m(-k%VT1Oc5bt#?13PPsyx)WtO3Yq9sZy(PRu2 zkp?P-4Dnvev)&Ky@&1qF|NGGS*tWIq`?}9-So_#dFhfT2%!YNue*x*j@eCgJPB!WB zTb(_fTzw?YySUj%IC(mH*ju`}S^A{MV-{{U=UtrLJ={Fcd!(nO$8T7BV|qNJv-SVp zl9sN!E+SoHy;XWt`ss9G-Sx+e=pxeXHpFkR_V97FA^wK$f)cz*cm4m~Kp($eE&cfM z<2tMG-`YRA>paq}V$@qUudQnBpVl*aalISYq5p9c;-~xf@*oR0`SWgcNlaKGo=Jdw zT^RNBy>g$Yh>^dSLfH?SO=}os$oI)1-OSY03(N}S`<2kLqwRG*iVFF6YN$e8P4hK& zfc$%e;NpKY7!Q)yQAZo+-5&2`(m-x&_dSH(TMl1YVA3S7dl=PsYT3PI)*`Qe1SKif zDp#>+llRd<#NA>ky6ElNI*%g68Z~5%9V7319C2U%RY_w#LEir)TKh5TB)N`L=#$|2 z65ps(wm?I2{YGdo*D&I8tP!~nV+6sO9*;F9_j4B2G7=|qmfV*K+ClZk zTjET}{h6Y;wLqDY`!qxI#UGP%;?2nYnxk_>_!7*?eOsXJ%}1@g5-iC5pF=xu1dsnZ ze2$F6IrQehyDZ@+=g4?iqL=~s;}%+$WLzu}%_Eua$`ea6K2~U!?c3c>Eh{okR;avG z(}BLjij3EJbnZ~$E|nwa$+(?IT<;g(xOSW;<7bV!AezNTtjRc9qj1h@wUG{MGM+X_ zwTk5zr?w3lR~z(G+vcY3QyVhA7f{hB+&EPG0$RTo=L_g;5D#19(+gz0ZP6AU&( zwq)FGQOBKbFTrQFWc=-r{|V9kW;%A{IoKh&ui@|0p4pM-VUN~+)UhYe#U2s6S^wOg zJfDl`%)N9t@r&d+T|}$~KdPOdUnI}V0m02-!4BlPIiSn2H?|KwcOdh@5lQY_eX;qd zBZ^%+M@KYHY^T$aJWnT-bM}rx@KGo7T%FLVwSYUJ%C$UlMoh`}1ye_z(fPG=c190G zAL$9aa3;^&1-U~unH+N=&)o%yp7Q~PT~OOv-n$~#fA&hB1YJoFT+wqKB7t2=A6(JC ztB=0(6uXjMxS|lSMd7n6>Bl8BB(v+_&R!hK$z|(v9@X9YJzI zy(xBvc!Y*(gR7~Z~yXb(u4HV6Rnjm5l_-nPxRSfPySwePtsRUr2gOWztmDs z(pyiI_tWpR@fT0hUoQl|tnd)=B0cs(r=c1r+k269!wXgS(_5C8dLh#_ue}hnAh7~3 z(r<5M?QXtxRKy!?Uh~`=L2+>TXYWn=?v03S;4bqfz4t~QCKLQ}U%g5HFQeBbTLMpr zUPeJ{d2ku+pF{l@FJ30|;WCQUaF&TIyG-WAWi$rW<=WTFWPbP{NY;raQ6Dl-d{E}v z1$@YS@j-ts^XL37^C9!b2c2j?2?qNhkOV5VFDfH$zu%Y4BVWV-yVZ2?CG*J_S==H5 z;7jI}FS@t1!QB6wFPUF{XsfntL*{-z)V7vqe#qs@xy`p7{Ls#|I_Za=jU_mCmHUx- z=ZDt9_sx&YKYs)=?A{>ePv)UN8hXAJ6!0hW(H|*n*XU8L@F(-qAEjP!l{EbBPv&O; 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zX)}4dW23cw8#>;x}gGDLI_otbH81cl>E2S6+0ma)asrn1{$KC%$-{ zpqXtcqdTl*a*QE+y#9!Iz)+w102dqFD!!^J1zC!=kNq}hb& zc5fK?DfvAaJG$2G6x3>JX7Pa{Mo-eoeXKRwr=eQ*;$c$hjr#>($lA{&;|B};OB={m zhLn^3P~~F=e*nzY`S_C5ND_4kgbgdMaGilAr2;QV`B&x6XJM&eI8P9~{mQO_)VXfz z6%1<*?Oz)L=f52LK#nzB4G)Et>8};f!6iQ!$H+QXozyUBr+n2S93H>fz2ZD Date: Wed, 20 May 2020 14:51:13 +0100 Subject: [PATCH 7/9] #997 fix docstring --- CHANGELOG.md | 2 + .../effective_resistance_current_collector.py | 49 +++++++------------ 2 files changed, 19 insertions(+), 32 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index c3d3e72b7a..c4fe81daa3 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,6 +2,8 @@ ## Features +- Updated effectiv current collector models and added example notebook ([#1007](https://github.com/pybamm-team/PyBaMM/pull/1007)) +- Added `parameters` attribute to `pybamm.BaseModel` and `pybamm.Geometry` that lists all of the required parameters ([#993](https://github.com/pybamm-team/PyBaMM/pull/993)) - Added tab, edge, and surface cooling ([#965](https://github.com/pybamm-team/PyBaMM/pull/965)) - Added functionality to solver to automatically discretise a 0D model ([#947](https://github.com/pybamm-team/PyBaMM/pull/947)) - Added sensitivity to `CasadiAlgebraicSolver` ([#940](https://github.com/pybamm-team/PyBaMM/pull/940)) diff --git a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py index 459f490a18..2356391b72 100644 --- a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py +++ b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py @@ -5,7 +5,8 @@ class EffectiveResistance(pybamm.BaseModel): - """A model which calculates the effective Ohmic resistance of the current + """ + A model which calculates the effective Ohmic resistance of the current collectors in the limit of large electrical conductivity. For details see [1]_. References @@ -171,13 +172,9 @@ def default_solver(self): class EffectiveResistance1D(EffectiveResistance): - """A model which calculates the effective Ohmic resistance of the 1D current - collectors in the limit of large electrical conductivity. For details see [1]_. - - References - ---------- - .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. + """ + A model which calculates the effective Ohmic resistance of the 1D current + collectors in the limit of large electrical conductivity. **Extends:** :class:`pybamm.EffectiveResistance` """ @@ -201,16 +198,12 @@ def average(self, variable): class EffectiveResistance2D(EffectiveResistance): - """A model which calculates the effective Ohmic resistance of the 2D current - collectors in the limit of large electrical conductivity. For details see [1]_. - Note that unlike the model in [1]_, this formulation assumes uniform potential - across the tabs. See :class:`pybamm.AlternativeEffectiveResistance2D` for the - exact formulation in [1]_ that assumes a uniform current density at the tabs. - - References - ---------- - .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. + """ + A model which calculates the effective Ohmic resistance of the 2D current + collectors in the limit of large electrical conductivity. Note that this + formulation assumes uniform potential across the tabs. + See :class:`pybamm.AlternativeEffectiveResistance2D` for the formulation that + assumes a uniform current density at the tabs. **Extends:** :class:`pybamm.EffectiveResistance` """ @@ -254,15 +247,11 @@ def default_spatial_methods(self): class AlternativeEffectiveResistance2D(pybamm.BaseModel): - """A model which calculates the effective Ohmic resistance of the 2D current + """ + A model which calculates the effective Ohmic resistance of the 2D current collectors in the limit of large electrical conductivity. This model assumes a uniform current density at the tabs and the solution is computed by first - solving and auxilliary problem which is the related to the resistances, see [1]_. - - References - ---------- - .. [1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. “Asymptotic - Reduction of a Lithium-ion Pouch Cell Model”. Submitted, 2020. + solving and auxilliary problem which is the related to the resistances. **Extends:** :class:`pybamm.BaseModel` """ @@ -274,8 +263,6 @@ def __init__(self): # Get necessary parameters param = self.param - l_y = param.l_y - l_z = param.l_z l_cn = param.l_cn l_cp = param.l_cp l_tab_p = param.l_tab_p @@ -306,7 +293,7 @@ def __init__(self): } # Boundary conditons - pos_tab_bc = l_y * l_z * l_cp / A_tab_p + pos_tab_bc = l_cp / A_tab_p self.boundary_conditions = { f_n: {"negative tab": (0, "Dirichlet"), "positive tab": (0, "Neumann")}, f_p: { @@ -323,13 +310,11 @@ def __init__(self): } # Define effective current collector resistance - R_cc_n = ( - delta * pybamm.yz_average(f_n) / (l_y * l_z * l_cn * sigma_cn_dbl_prime) - ) + R_cc_n = delta * pybamm.yz_average(f_n) / (l_cn * sigma_cn_dbl_prime) R_cc_p = ( delta * pybamm.BoundaryIntegral(f_p, "positive tab") - / (l_y * l_z * l_cp * sigma_cp_dbl_prime) + / (l_cp * sigma_cp_dbl_prime) ) R_cc = R_cc_n + R_cc_p R_scale = param.potential_scale / param.I_typ From 4b616ad6b9f96359afe0fe6bcd020a274fb27f96 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Wed, 20 May 2020 14:55:08 +0100 Subject: [PATCH 8/9] #997 changelog --- CHANGELOG.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index 00e30b1171..99d9ba9334 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,7 +2,7 @@ ## Features -- Updated effectiv current collector models and added example notebook ([#1007](https://github.com/pybamm-team/PyBaMM/pull/1007)) +- Updated effective current collector models and added example notebook ([#1007](https://github.com/pybamm-team/PyBaMM/pull/1007)) - Added SEI film resistance as an option ([#994](https://github.com/pybamm-team/PyBaMM/pull/994)) - Added `parameters` attribute to `pybamm.BaseModel` and `pybamm.Geometry` that lists all of the required parameters ([#993](https://github.com/pybamm-team/PyBaMM/pull/993)) - Added tab, edge, and surface cooling ([#965](https://github.com/pybamm-team/PyBaMM/pull/965)) @@ -11,7 +11,7 @@ - Added `ProcessedSymbolicVariable` class, which can handle symbolic variables (i.e. variables for which the inputs are symbolic) ([#940](https://github.com/pybamm-team/PyBaMM/pull/940)) - Made `QuickPlot` compatible with Google Colab ([#935](https://github.com/pybamm-team/PyBaMM/pull/935)) - Added `BasicFull` model for lead-acid ([#932](https://github.com/pybamm-team/PyBaMM/pull/932)) -- Added 'arctan' function ([#973]https://github.com/pybamm-team/PyBaMM/pull/973) +- Added 'arctan' function ([#973](https://github.com/pybamm-team/PyBaMM/pull/973)) ## Optimizations From 92666ff6c7b5ec81cf919a7874c939a8614c10c7 Mon Sep 17 00:00:00 2001 From: Robert Timms Date: Fri, 22 May 2020 13:57:12 +0100 Subject: [PATCH 9/9] #997 tino comments --- ...effective_resistance_current_collector.rst | 5 +- .../Tutorial 4 - Model Options.ipynb | 19 +- .../notebooks/models/pouch-cell-model.ipynb | 63 +++---- pybamm/models/base_model.py | 4 +- .../full_battery_models/base_battery_model.py | 9 +- .../submodels/current_collector/__init__.py | 3 +- .../effective_resistance_current_collector.py | 169 +++++++++--------- pybamm/solvers/processed_variable.py | 8 +- tests/unit/test_citations.py | 7 +- .../test_effective_current_collector.py | 47 ++--- 10 files changed, 163 insertions(+), 171 deletions(-) diff --git a/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst b/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst index c7d59c6391..7210f2c510 100644 --- a/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst +++ b/docs/source/models/submodels/current_collector/effective_resistance_current_collector.rst @@ -1,10 +1,7 @@ Effective Current collector Resistance models ============================================= -.. autoclass:: pybamm.current_collector.EffectiveResistance1D - :members: - -.. autoclass:: pybamm.current_collector.EffectiveResistance2D +.. autoclass:: pybamm.current_collector.EffectiveResistance :members: .. autoclass:: pybamm.current_collector.AlternativeEffectiveResistance2D diff --git a/examples/notebooks/Getting Started/Tutorial 4 - Model Options.ipynb b/examples/notebooks/Getting Started/Tutorial 4 - Model Options.ipynb index 3b21989fcd..3cbcea305a 100644 --- a/examples/notebooks/Getting Started/Tutorial 4 - Model Options.ipynb +++ b/examples/notebooks/Getting Started/Tutorial 4 - Model Options.ipynb @@ -50,7 +50,18 @@ "cell_type": "code", "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "model = pybamm.lithium_ion.SPMe(options=options) # loading in options\n", "sim = pybamm.Simulation(model)\n", @@ -78,12 +89,12 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "17368df63d2b44d3982c151286110d41", + "model_id": "6424823b40b548c8ad170e2e6797b5cb", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "interactive(children=(FloatSlider(value=0.0, description='t', max=0.2014814814814815, step=0.05), Output()), _…" + "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…" ] }, "metadata": {}, @@ -125,7 +136,7 @@ "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 27c5dc90bb..2beba71799 100644 --- a/examples/notebooks/models/pouch-cell-model.ipynb +++ b/examples/notebooks/models/pouch-cell-model.ipynb @@ -22,6 +22,17 @@ "All of the model equations, and derivations of the reduced-order models, can be found in [[1]](#ref)." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "[1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. Asymptotic\n", + " Reduction of a Lithium-ion Pouch Cell Model. Submitted, 2020\n", + " \n", + "[2] M Doyle, TF Fuller, and J Newman. Modeling of galvanostatic charge and discharge of thelithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6):1526–1533, 1993" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -64,20 +75,20 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:252: 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:308: 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" ] } ], "source": [ - "cc_model = pybamm.current_collector.EffectiveResistance1D()\n", + "cc_model = pybamm.current_collector.EffectiveResistance({\"dimensionality\": 1})\n", "dfn_av = pybamm.lithium_ion.DFN({\"thermal\": \"x-lumped\"}, name=\"Average DFN\")\n", "dfn = pybamm.lithium_ion.DFN(\n", " {\"current collector\": \"potential pair\", \"dimensionality\": 1, \"thermal\": \"x-lumped\"},\n", @@ -94,7 +105,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -110,7 +121,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -139,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -164,7 +175,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -183,7 +194,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -214,7 +225,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this section we show how to create a PyBaMM \"model\" from the COMSOL solution. If you are just interested in seeing the comparison the skip ahead to the section \" Comparing the full and reduced-order models\".\n" + "In this section we show how to create a PyBaMM \"model\" from the COMSOL solution. If you are just interested in seeing the comparison the skip ahead to the section \"Comparing the full and reduced-order models\".\n" ] }, { @@ -226,7 +237,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -272,7 +283,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -298,7 +309,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -321,7 +332,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -347,7 +358,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -368,7 +379,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -520,12 +531,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We then set up the times a points in space to use in the plots " + "We then set up the times and points in space to use in the plots " ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -543,7 +554,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -588,7 +599,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -652,7 +663,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -704,7 +715,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -773,16 +784,6 @@ "For the parameters used in this example we find that the temperature exhibits a relatively weak variation along the length of the current collectors. " ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "[1] R Timms, SG Marquis, V Sulzer, CP Please and SJ Chapman. Asymptotic\n", - " Reduction of a Lithium-ion Pouch Cell Model. Submitted, 2020\n", - " \n", - "[2] M Doyle, TF Fuller, and J Newman. Modeling of galvanostatic charge and discharge of thelithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6):1526–1533, 1993" - ] - }, { "cell_type": "code", "execution_count": null, diff --git a/pybamm/models/base_model.py b/pybamm/models/base_model.py index 3f21c43e30..0776e40ba8 100644 --- a/pybamm/models/base_model.py +++ b/pybamm/models/base_model.py @@ -96,9 +96,9 @@ class BaseModel(object): """ - def __init__(self, options=None, name="Unnamed model"): - self.options = options or {} + def __init__(self, name="Unnamed model"): self.name = name + self.options = {} # Initialise empty model self.rhs = {} diff --git a/pybamm/models/full_battery_models/base_battery_model.py b/pybamm/models/full_battery_models/base_battery_model.py index 82565bb6cf..a39e5f6c5c 100644 --- a/pybamm/models/full_battery_models/base_battery_model.py +++ b/pybamm/models/full_battery_models/base_battery_model.py @@ -92,7 +92,8 @@ class BaseBatteryModel(pybamm.BaseModel): """ def __init__(self, options=None, name="Unnamed battery model"): - super().__init__(options, name) + super().__init__(name) + self.options = options self.submodels = {} self._built = False self._built_fundamental_and_external = False @@ -281,11 +282,7 @@ def options(self, extra_options): "interstitial-diffusion limited", ]: raise pybamm.OptionError("Unknown sei model '{}'".format(options["sei"])) - if options["sei film resistance"] not in [ - None, - "distributed", - "average", - ]: + if options["sei film resistance"] not in [None, "distributed", "average"]: raise pybamm.OptionError( "Unknown sei film resistance model '{}'".format( options["sei film resistance"] diff --git a/pybamm/models/submodels/current_collector/__init__.py b/pybamm/models/submodels/current_collector/__init__.py index daea5b0b24..40be04244d 100644 --- a/pybamm/models/submodels/current_collector/__init__.py +++ b/pybamm/models/submodels/current_collector/__init__.py @@ -2,8 +2,7 @@ from .homogeneous_current_collector import Uniform from .effective_resistance_current_collector import ( - EffectiveResistance1D, - EffectiveResistance2D, + EffectiveResistance, AlternativeEffectiveResistance2D, ) from .potential_pair import ( diff --git a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py index 2356391b72..34e0845bc2 100644 --- a/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py +++ b/pybamm/models/submodels/current_collector/effective_resistance_current_collector.py @@ -8,6 +8,18 @@ class EffectiveResistance(pybamm.BaseModel): """ A model which calculates the effective Ohmic resistance of the current collectors in the limit of large electrical conductivity. For details see [1]_. + Note that this formulation assumes uniform *potential* across the tabs. See + :class:`pybamm.AlternativeEffectiveResistance2D` for the formulation that + assumes a uniform *current density* at the tabs (in 1D the two formulations + are equivalent). + + options: dict + A dictionary of options to be passed to the model. The options that can + be set are listed below. + + * "dimensionality" : int, optional + Sets the dimension of the current collector problem. Can be 1 + (default) or 2. References ---------- @@ -20,7 +32,8 @@ class EffectiveResistance(pybamm.BaseModel): def __init__( self, options=None, name="Effective resistance in current collector model" ): - super().__init__(options, name) + super().__init__(name) + self.options = options self.param = pybamm.standard_parameters_lithium_ion self.variables = self.get_fundamental_variables() @@ -51,8 +64,12 @@ def get_fundamental_variables(self): R_cp = delta * R_cp_scaled / (l_cp * sigma_cp_dbl_prime) # Define effective current collector resistance - R_cc_n = -self.average(R_cn) - R_cc_p = -self.average(R_cp) + if self.options["dimensionality"] == 1: + R_cc_n = -pybamm.z_average(R_cn) + R_cc_p = -pybamm.z_average(R_cp) + elif self.options["dimensionality"] == 2: + R_cc_n = -pybamm.yz_average(R_cn) + R_cc_p = -pybamm.yz_average(R_cp) R_cc = R_cc_n + R_cc_p R_scale = param.potential_scale / param.I_typ @@ -81,6 +98,33 @@ def set_algebraic(self, variables): R_cp_scaled: pybamm.laplacian(R_cp_scaled) - pybamm.source(1, R_cp_scaled), } + def set_boundary_conditions(self, variables): + R_cn_scaled = variables["Scaled negative current collector resistance"] + R_cp_scaled = variables["Scaled positive current collector resistance"] + + if self.options["dimensionality"] == 1: + self.boundary_conditions = { + R_cn_scaled: { + "negative tab": (0, "Dirichlet"), + "no tab": (0, "Neumann"), + }, + R_cp_scaled: { + "positive tab": (0, "Dirichlet"), + "no tab": (0, "Neumann"), + }, + } + elif self.options["dimensionality"] == 2: + self.boundary_conditions = { + R_cn_scaled: { + "negative tab": (0, "Dirichlet"), + "positive tab": (0, "Neumann"), + }, + R_cp_scaled: { + "positive tab": (0, "Dirichlet"), + "negative tab": (0, "Neumann"), + }, + } + def set_initial_conditions(self, variables): R_cn_scaled = variables["Scaled negative current collector resistance"] R_cp_scaled = variables["Scaled positive current collector resistance"] @@ -151,7 +195,10 @@ def default_parameter_values(self): @property def default_geometry(self): - return pybamm.Geometry("1D current collector") + if self.options["dimensionality"] == 1: + return pybamm.Geometry("1D current collector") + elif self.options["dimensionality"] == 2: + return pybamm.Geometry("2D current collector") @property def default_var_pts(self): @@ -160,97 +207,59 @@ def default_var_pts(self): @property def default_submesh_types(self): - return {"current collector": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)} + if self.options["dimensionality"] == 1: + return {"current collector": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)} + elif self.options["dimensionality"] == 2: + return { + "current collector": pybamm.MeshGenerator(pybamm.ScikitUniform2DSubMesh) + } @property def default_spatial_methods(self): - return {"current collector": pybamm.FiniteVolume()} + if self.options["dimensionality"] == 1: + return {"current collector": pybamm.FiniteVolume()} + elif self.options["dimensionality"] == 2: + return {"current collector": pybamm.ScikitFiniteElement()} @property def default_solver(self): return pybamm.CasadiAlgebraicSolver() - -class EffectiveResistance1D(EffectiveResistance): - """ - A model which calculates the effective Ohmic resistance of the 1D current - collectors in the limit of large electrical conductivity. - - **Extends:** :class:`pybamm.EffectiveResistance` - """ - - def __init__( - self, options=None, name="Effective resistance in current collector model (1D)" - ): - super().__init__(options, name) - - def set_boundary_conditions(self, variables): - R_cn_scaled = variables["Scaled negative current collector resistance"] - R_cp_scaled = variables["Scaled positive current collector resistance"] - self.boundary_conditions = { - R_cn_scaled: {"negative tab": (0, "Dirichlet"), "no tab": (0, "Neumann")}, - R_cp_scaled: {"positive tab": (0, "Dirichlet"), "no tab": (0, "Neumann")}, - } - - def average(self, variable): - "Compute the average over the 1D current collector" - return pybamm.z_average(variable) - - -class EffectiveResistance2D(EffectiveResistance): - """ - A model which calculates the effective Ohmic resistance of the 2D current - collectors in the limit of large electrical conductivity. Note that this - formulation assumes uniform potential across the tabs. - See :class:`pybamm.AlternativeEffectiveResistance2D` for the formulation that - assumes a uniform current density at the tabs. - - **Extends:** :class:`pybamm.EffectiveResistance` - """ - - def __init__( - self, options=None, name="Effective resistance in current collector model (2D)" - ): - super().__init__() - - def set_boundary_conditions(self, variables): - R_cn_scaled = variables["Scaled negative current collector resistance"] - R_cp_scaled = variables["Scaled positive current collector resistance"] - self.boundary_conditions = { - R_cn_scaled: { - "negative tab": (0, "Dirichlet"), - "positive tab": (0, "Neumann"), - }, - R_cp_scaled: { - "positive tab": (0, "Dirichlet"), - "negative tab": (0, "Neumann"), - }, - } - - def average(self, variable): - "Compute the average over the 2D current collector" - return pybamm.yz_average(variable) - @property - def default_geometry(self): - return pybamm.Geometry("2D current collector") - - @property - def default_submesh_types(self): - return { - "current collector": pybamm.MeshGenerator(pybamm.ScikitUniform2DSubMesh) - } - - @property - def default_spatial_methods(self): - return {"current collector": pybamm.ScikitFiniteElement()} + def options(self): + return self._options + + @options.setter + def options(self, extra_options): + default_options = {"dimensionality": 1} + extra_options = extra_options or {} + + options = pybamm.FuzzyDict(default_options) + # any extra options overwrite the default options + for name, opt in extra_options.items(): + if name in default_options: + options[name] = opt + else: + raise pybamm.OptionError( + "Option '{}' not recognised. Best matches are {}".format( + name, options.get_best_matches(name) + ) + ) + + if options["dimensionality"] not in [1, 2]: + raise pybamm.OptionError( + "Dimension of current collectors must be 1 or 2, not {}".format( + options["dimensionality"] + ) + ) + self._options = options class AlternativeEffectiveResistance2D(pybamm.BaseModel): """ A model which calculates the effective Ohmic resistance of the 2D current collectors in the limit of large electrical conductivity. This model assumes - a uniform current density at the tabs and the solution is computed by first + a uniform *current density* at the tabs and the solution is computed by first solving and auxilliary problem which is the related to the resistances. **Extends:** :class:`pybamm.BaseModel` diff --git a/pybamm/solvers/processed_variable.py b/pybamm/solvers/processed_variable.py index 901d26b559..9133a6e3dd 100644 --- a/pybamm/solvers/processed_variable.py +++ b/pybamm/solvers/processed_variable.py @@ -212,12 +212,12 @@ def initialise_1D(self, fixed_t=False): # TODO: fix processing when variable is a function of space only if fixed_t: # Hack for 1D space only + interpolant = interp.interp1d( + space, entries_for_interp[:, 0], kind="linear", fill_value=np.nan + ) def interp_fun(t, z): - out = interp.interp1d( - space, entries_for_interp[:, 0], kind="linear", fill_value=np.nan - )(z) - return out[:, np.newaxis] + return interpolant(z)[:, np.newaxis] self._interpolation_function = interp_fun else: diff --git a/tests/unit/test_citations.py b/tests/unit/test_citations.py index 6e36e2a74c..e7774c34b5 100644 --- a/tests/unit/test_citations.py +++ b/tests/unit/test_citations.py @@ -85,12 +85,7 @@ def test_timms_2020(self): citations._reset() self.assertNotIn("timms2020", citations._papers_to_cite) - pybamm.current_collector.EffectiveResistance1D() - self.assertIn("timms2020", citations._papers_to_cite) - - citations._reset() - self.assertNotIn("timms2020", citations._papers_to_cite) - pybamm.current_collector.EffectiveResistance2D() + pybamm.current_collector.EffectiveResistance() self.assertIn("timms2020", citations._papers_to_cite) citations._reset() diff --git a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py index c58b92dc4d..9169fa7008 100644 --- a/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py +++ b/tests/unit/test_models/test_submodels/test_current_collector/test_effective_current_collector.py @@ -6,61 +6,44 @@ import numpy as np -class TestEffectiveResistance1D(unittest.TestCase): +class TestEffectiveResistance(unittest.TestCase): def test_well_posed(self): - model = pybamm.current_collector.EffectiveResistance1D() + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 1}) model.check_well_posedness() - def test_default_geometry(self): - model = pybamm.current_collector.EffectiveResistance1D() - self.assertIsInstance(model.default_geometry, pybamm.Geometry) - self.assertTrue("current collector" in model.default_geometry) - self.assertNotIn("negative electrode", model.default_geometry) - - def test_default_solver(self): - model = pybamm.current_collector.EffectiveResistance1D() - self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) - - -class TestEffectiveResistance2D(unittest.TestCase): - def test_well_posed(self): - model = pybamm.current_collector.EffectiveResistance2D() + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 2}) model.check_well_posedness() def test_default_geometry(self): - model = pybamm.current_collector.EffectiveResistance2D() + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 1}) self.assertIsInstance(model.default_geometry, pybamm.Geometry) self.assertTrue("current collector" in model.default_geometry) self.assertNotIn("negative electrode", model.default_geometry) - def test_default_solver(self): - model = pybamm.current_collector.EffectiveResistance2D() - self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) - - -class TestAlternativeEffectiveResistance2D(unittest.TestCase): - def test_well_posed(self): - model = pybamm.current_collector.AlternativeEffectiveResistance2D() - model.check_well_posedness() - - def test_default_geometry(self): - model = pybamm.current_collector.AlternativeEffectiveResistance2D() + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 2}) self.assertIsInstance(model.default_geometry, pybamm.Geometry) self.assertTrue("current collector" in model.default_geometry) self.assertNotIn("negative electrode", model.default_geometry) def test_default_solver(self): - model = pybamm.current_collector.AlternativeEffectiveResistance2D() + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 1}) self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) + model = pybamm.current_collector.EffectiveResistance({"dimensionality": 2}) + self.assertIsInstance(model.default_solver, pybamm.CasadiAlgebraicSolver) + + def test_bad_option(self): + with self.assertRaisesRegex(pybamm.OptionError, "Dimension of"): + pybamm.current_collector.EffectiveResistance({"dimensionality": 10}) + class TestEffectiveResistancePostProcess(unittest.TestCase): def test_get_processed_variables(self): # solve cheap SPM to test post-processing (think of an alternative test?) models = [ pybamm.lithium_ion.SPM(), - pybamm.current_collector.EffectiveResistance1D(), - pybamm.current_collector.EffectiveResistance2D(), + pybamm.current_collector.EffectiveResistance({"dimensionality": 1}), + pybamm.current_collector.EffectiveResistance({"dimensionality": 2}), pybamm.current_collector.AlternativeEffectiveResistance2D(), ] var = pybamm.standard_spatial_vars

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