From e313ec94c0cc021cb84d7f86206e9d0f46315a1a Mon Sep 17 00:00:00 2001
From: wjy <15151829012@163.com>
Date: Mon, 2 Sep 2019 22:59:13 -0400
Subject: [PATCH] Add md docs for eos fomulations

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---
 docs/src/Collections.md | 132 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 131 insertions(+), 1 deletion(-)

diff --git a/docs/src/Collections.md b/docs/src/Collections.md
index c1fca7a..e1d781a 100644
--- a/docs/src/Collections.md
+++ b/docs/src/Collections.md
@@ -145,14 +145,144 @@ The $E(V)$ relation of equations of state are listed as below:
    ```math
    E(V) = E_{0}+\frac{1}{2} B_{0} V_{0} \ln ^{2} x.
    ```
-
+   
 6. `PoirierTarantola3rd`:
 
    ```math
    E(V) = E_{0}+\frac{1}{6} B_{0} V_{0} \ln ^{2} x\left[\left(B_{0}^{\prime}+2\right) \ln x+3\right].
    ```
 
+7. `PoirierTarantola4th`:
+
+   ```math
+   E(V) = E_{0}+\frac{1}{24} B_{0} V_{0} \ln ^{2} x\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{2} x\right.
+\left.+4\left(B_{0}^{\prime}+2\right) \ln x+12\right\}.
+   ```
+   where ``H = B_0 B_0'' + (B_0')^2``.
+   
+8. `Vinet`:
+
+   ```math
+   E(V) = E_{0}+\frac{9}{16} V_{0} B_{0} \frac{\left(x^{2 / 3}-1\right)^{2}}{x^{7 / 3}}\left\{x^{1 / 3}\left(B_{0}^{\prime}-4\right)-x\left(B_{0}^{\prime}-6\right)\right\}.
+   ```
+   
+9. `AntonSchmidt`:
+
+   ```math
+   E(V)=\frac{\beta V_{0}}{n+1}\left(\frac{V}{V_{0}}\right)^{n+1}\left[\ln \left(\frac{V}{V_{0}}\right)-\frac{1}{n+1}\right]+E_{\infty}.
+   ```
+   
+### Calculate pressures on an `EquationOfState`
+
+The $P(V)$ relation of equations of state are listed as below:
+
+1. `Murnaghan`:
+
+   ```math
+   P(V) = \frac{B_{0}}{B_{0}^{\prime}}\left[\left(\frac{V_{0}}{V}\right)^{B_{0}^{\prime}}-1\right].
+   ```
+   
+2. `BirchMurnaghan2nd`:
+
+   ```math
+   P(V) = \frac{3}{2} B_{0}\left(x^{-7 / 3}-x^{-5 / 3}\right).
+   ```
+   
+3. `BirchMurnaghan3rd`:
+
+   ```math
+   P(V) = \frac{3}{8} B_{0} \frac{x^{2 / 3}-1}{x^{10 / 3}}\left\{3 B_{0}^{\prime} x-16 x-3 x^{1 / 3}\left(B_{0}^{\prime}-4\right)\right\}.
+   ```
+   
+4. `BirchMurnaghan4th`:
+
+   ```math
+   P(V) = \frac{1}{2} B_{0}(2 f+1)^{5 / 2}\left\{\left(9 H-63 B_{0}^{\prime}+143\right) f^{2}\right.\left.+9\left(B_{0}^{\prime}-4\right) f+6\right\}.
+   ```
+   
+5. `PoirierTarantola2nd`:
+
+   ```math
+   P(V) = -\frac{B_{0}}{x} \ln x.
+   ```
+   
+6. `PoirierTarantola3rd`:
+
+   ```math
+   P(V) = -\frac{B_{0} \ln x}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x+2\right].
+   ```
+   
+7. `PoirierTarantola4th`:
+
+   ```math
+   P(V) = -\frac{B_{0} \ln x}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{2} x+3\left(B_{0}^{\prime}+6\right) \ln x+6\right\}.
+   ```
+   
+8. `Vinet`:
+
+   ```math
+   P(V) = 3 B_{0} \frac{1-\eta}{\eta^{2}} \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.
+   ```
    
+9. `AntonSchmidt`:
+
+   ```math
+   P(V) = -\beta\left(\frac{V}{V_{0}}\right)^{n} \ln \left(\frac{V}{V_{0}}\right).
+   ```
+
+### Calculate bulk moduli on an `EquationOfState`
+
+The $B(V)$ relation of equations of state are listed as below:
+
+1. `BirchMurnaghan2nd`:
+
+   ```math
+   B(V) = B_{0}(7 f+1)(2 f+1)^{5 / 2}.
+   ```
+
+2. `BirchMurnaghan3rd`:
+
+   ```math
+   B(V) = \frac{B_{0}}{8 \chi^{10 / 3}}\left\{x^{5 / 3}\left(15 B_{0}^{\prime}-80\right)-x\left(42 B_{0}^{\prime}-196\right)\right.\left.+27 x^{1 / 3}\left(B_{0}^{\prime}-4\right)\right\}.
+   ```
+
+3. `BirchMurnaghan4th`:
+
+   ```math
+   B(V) = \frac{1}{6} B_{0}(2 f+1)^{5 / 2}\left\{\left(99 H-693 B_{0}^{\prime}+1573\right) f^{3}\right.\left.+\left(27 H-108 B_{0}^{\prime}+105\right) f^{2}+6\left(3 B_{0}^{\prime}-5\right) f+6\right\}.
+   ```
+   
+4. `PoirierTarantola2nd`:
+
+   ```math
+   B(V) = \frac{B_{0}}{x}(1-\ln x).
+   ```
+   
+5. `PoirierTarantola3rd`:
+
+   ```math
+   B(V) = -\frac{B_{0}}{2 x}\left[\left(B_{0}^{\prime}+2\right) \ln x(\ln x-1)-2\right].
+   ```
+
+6. `PoirierTarantola4th`:
+
+   ```math
+   B(V) = -\frac{B_{0}}{6 x}\left\{\left(H+3 B_{0}^{\prime}+3\right) \ln ^{3} x-3\left(H+2 B_{0}^{\prime}+1\right) \ln ^{2} x\right.\left.-6\left(B_{0}^{\prime}+1\right) \ln x-6\right\}.
+   ```
+   
+7. `Vinet`:
+
+   ```math
+   B(V) = -\frac{B_{0}}{2 \eta^{2}}\left[3 \eta(\eta-1)\left(B_{0}^{\prime}-1\right)+2(\eta-2)\right]\times \exp \left\{-\frac{3}{2}\left(B_{0}^{\prime}-1\right)(\eta-1)\right\}.
+   ```
+   
+8. `AntonSchmidt`:
+
+   ```math
+   B(V) = \beta\left(\frac{V}{V_{0}}\right)^{n}\left[1+n \ln \frac{V}{V_{0}}\right].
+   ```
+
+
 ## Public interfaces
 
 ```@docs