git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@11959 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/compute_fep_bar.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /kT \right]} \right>_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + \Delta_0^1A \right) /kT \right]} \right>_1 \]
+
+\end{document}

doc/Eqs/compute_fep_fdti.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left( \frac{\partial
+    A(\lambda)}{\partial\lambda} \right)_\lambda \mathrm{d}\lambda
+\approx \sum_{i=0}^{n-1} w_i \frac{A(\lambda_{i} + \delta) -
+  A(\lambda_i)}{\delta} \]
+
+\end{document}

doc/Eqs/compute_fep_fep.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A =
+- kT \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) -
+      U(\lambda_i)}{kT} \right) \right>_{\lambda_i} \]
+
+\end{document}

doc/Eqs/compute_fep_lambda.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray*}
+  \lambda = 0 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_0 \\
+  \lambda = 1 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_1 
+\end{eqnarray*}
+
+\end{document}

doc/Eqs/compute_fep_ti.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left< \frac{\partial
+    U(\lambda)}{\partial\lambda} \right>_\lambda \mathrm{d}\lambda
+\approx \sum_{i=0}^{n-1} w_i \left< \frac{U(\lambda_{i} + \delta) -
+    U(\lambda_i)}{\delta} \right>_{\lambda_i} \]
+
+\end{document}

doc/Eqs/compute_fep_u.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[  U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \]
+
+\end{document}

doc/Eqs/compute_fep_vol.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( -
+    \frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right)
+\right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} \]
+
+\end{document}

doc/Eqs/pair_coul_soft.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[
+E = \lambda^n \frac{ C q_i q_j}{\epsilon
+\left[ \alpha_{\mathrm{C}} (1-\lambda)^2 + r^2 \right]^{1/2}} \qquad r < r_c
+\]
+
+\end{document}

doc/Eqs/pair_lj_soft.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[
+E = \lambda^n 4 \epsilon
+\left\{
+  \frac{1}{ \left[ \alpha_{\mathrm{LJ}} (1-\lambda)^2 +
+    \left( \displaystyle\frac{r}{\sigma} \right)^6 \right]^2 } -
+  \frac{1}{ \alpha_{\mathrm{LJ}} (1-\lambda)^2 +
+    \left( \displaystyle\frac{r}{\sigma} \right)^6 }
+\right\} \qquad r < r_c
+ \]
+
+\end{document}