delete no longer used equations

doc/src/Eqs/cnp_cutoff.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt,article]{article}
-
-\usepackage{indentfirst}
-\usepackage{amsmath}
-
-\begin{document}
-
-\begin{eqnarray*}
-  r_{c}^{fcc} & = & \frac{1}{2} \left(\frac{\sqrt{2}}{2} + 1\right) \mathrm{a} \simeq 0.8536 \:\mathrm{a} \\
-  r_{c}^{bcc} & = & \frac{1}{2}(\sqrt{2} + 1) \mathrm{a} \simeq 1.207 \:\mathrm{a} \\
-  r_{c}^{hcp} & = & \frac{1}{2}\left(1+\sqrt{\frac{4+2x^{2}}{3}}\right) \mathrm{a}
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/compute_dpd.tex

@@ -1,13 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-   U^{cond} = \displaystyle\sum_{i=1}^{N} u_{i}^{cond} \\ 
-   U^{mech} = \displaystyle\sum_{i=1}^{N} u_{i}^{mech} \\
-   U^{chem} = \displaystyle\sum_{i=1}^{N} u_{i}^{chem} \\
-   U = \displaystyle\sum_{i=1}^{N} (u_{i}^{cond} + u_{i}^{mech} + u_{i}^{chem}) \\
-   \theta_{avg} = (\frac{1}{N}\displaystyle\sum_{i=1}^{N} \frac{1}{\theta_{i}})^{-1} \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/compute_fep_bar.tex

@@ -1,7 +0,0 @@
-\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/src/Eqs/compute_fep_fdti.tex

@@ -1,10 +0,0 @@
-\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/src/Eqs/compute_fep_fep.tex

@@ -1,9 +0,0 @@
-\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/src/Eqs/compute_fep_lambda.tex

@@ -1,10 +0,0 @@
-\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/src/Eqs/compute_fep_ti.tex

@@ -1,10 +0,0 @@
-\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/src/Eqs/compute_fep_u.tex

@@ -1,7 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-\[  U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \]
-
-\end{document}

doc/src/Eqs/compute_fep_vol.tex

@@ -1,9 +0,0 @@
-\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}