remove unused equation file

doc/src/Eqs/fix_langevin_spin_sLLG.tex

@@ -1,14 +0,0 @@
-\documentclass[preview]{standalone}
-\usepackage{varwidth}
-\usepackage[utf8x]{inputenc}
-\usepackage{amsmath, amssymb, graphics, setspace}
-
-\begin{document}
-\begin{varwidth}{50in}
-  \begin{equation}
-    \frac{d \vec{s}_{i}}{dt} = \frac{1}{\left(1+\lambda^2 \right)} \left( \left(
-    \vec{\omega}_{i} +\vec{\eta} \right) \times \vec{s}_{i} + \lambda\, \vec{s}_{i}
-  \times\left( \vec{\omega}_{i} \times\vec{s}_{i} \right) \right), \nonumber
-  \end{equation}
-\end{varwidth}
-\end{document}

doc/src/Eqs/fix_ti_spring_force.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-
-\usepackage{amsmath}
-
-\begin{document}
-
-$$
-  F = \left( 1-\lambda \right) F_{\text{solid}} + \lambda F_{\text{harm}}
-$$
-
-\end{document}

doc/src/Eqs/fix_ti_spring_function_1.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  \lambda(\tau) = \tau
-$$
-
-\end{document}

doc/src/Eqs/fix_ti_spring_function_2.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  \lambda(\tau) = \tau^5 \left( 70 \tau^4 - 315 \tau^3 + 540 \tau^2 - 420 \tau + 126 \right)
-$$
-
-\end{document}

doc/src/Eqs/heat_flux_J.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-\mathbf{J} & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\
-& = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \mathbf{v}_j \right) \mathbf{x}_{ij} \right] \\
-& = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \frac{1}{2} \sum_{i<j} \left( \mathbf{f}_{ij} \cdot \left(\mathbf{v}_i + \mathbf{v}_j \right)  \right) \mathbf{x}_{ij} \right]
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/heat_flux_k.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-\kappa  = \frac{V}{k_B T^2} \int_0^\infty \langle J_x(0)  J_x(t) \rangle \, dt
-= \frac{V}{3 k_B T^2} \int_0^\infty \langle \mathbf{J}(0) \cdot  \mathbf{J}(t)  \rangle \, dt
-$$
-
-\end{document}
-

doc/src/Eqs/pair_comb1.tex

@@ -1,7 +0,0 @@
-\documentclass[12pt]{article}
-\begin{document} \large
-\begin{eqnarray*}
-E_T & = & \sum_i [ E_i^{self} (q_i) + \sum_{j>i} [E_{ij}^{short} (r_{ij}, q_i, q_j) + E_{ij}^{Coul} (r_{ij}, q_i, q_j)] + \\
-&& E^{polar} (q_i, r_{ij}) + E^{vdW} (r_{ij}) + E^{barr} (q_i) + E^{corr} (r_{ij}, \theta_{jik})] \\
-\end{eqnarray*}                           
-\end{document}

doc/src/Eqs/pair_comb2.tex

@@ -1,23 +0,0 @@
-\documentclass[10pt]{article}
-
-\begin{document}
-
-\begin{table}[h]
-\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
-\hline
-   & $O$ & $Cu$ & $N$ & $C$ & $H$ & $Ti$ & $Zn$ & $Zr$ \\ \hline
-$O$	& F & F & F & F & F & F & F & F\\ \hline
-$Cu$	& F & F & P & F & F & P & F & P \\ \hline
-$N$ 	& F & P & F & M & F & P & P & P \\ \hline
-$C$   	& F & F & M & F & F & M & M & M \\ \hline
-$H$   	& F & F & F & F & F & M & M & F \\ \hline
-$Ti$   	& F & P & P & M & M & F & P & P \\ \hline
-$Zn$  	& F & F & P & M & M & P & F & P \\ \hline
-$Zr$  	& F & P & P & M & F & P & P & F \\ \hline
-\multicolumn{9}{l}{F: Fully optimized} \\
-\multicolumn{9}{l}{M: Only optimized for dimer molecule} \\
-\multicolumn{9}{l}{P: in Progress but have it from mixing rule} \\
-\end{tabular}
-\end{table}
-
-\end{document}

doc/src/Eqs/pair_coul_gauss.tex

@@ -1,15 +0,0 @@
-\documentclass[12pt]{article}
-
-\pagestyle{empty}
-\begin{document}
-
-$$
-  E = \frac{C_{q_i q_j}}{\epsilon r_{ij}}\,\, \textrm{erf}\left(\alpha_{ij} r_{ij}\right)\quad\quad\quad r < r_c
-$$
-
-\end{document}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End:

doc/src/Eqs/pair_coul_shield.tex

@@ -1,33 +0,0 @@
-\documentclass[aps,pr,onecolumn,superscriptaddress,noshowpacs,a4paper,15pt]{revtex4}
-\pdfoutput=1
-\bibliographystyle{apsrev4}
-\usepackage{color}
-\usepackage{dcolumn} %Align table columns on decimal point
-\usepackage{amssymb}
-\usepackage{amsmath}
-\usepackage{amsthm}
-\usepackage{graphicx}
-\usepackage[pdftex]{hyperref}
-\hypersetup{colorlinks=true,citecolor=blue,linkcolor=red,urlcolor=blue}
-\usepackage[all]{hypcap}
-\newcommand{\red}{\color{red}}
-\newcommand{\blue}{\color{blue}}
-\definecolor{green}{rgb}{0,0.5,0}
-\newcommand{\green}{\color{green}}
-\newcommand{\white}{\color{white}}
-%\newcommand{\cite}[1]{\hspace{-1 ex} % \nocite{#1}\citenum{#1}}
-\thickmuskip=0.5\thickmuskip %shorter spaces in math
-
-\begin{document}
-\begingroup
-\Large
-\begin{eqnarray*}
-  E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\[15pt]
-  V_{ij} & = & {\rm Tap}(r_{ij})\frac{\kappa q_i q_j}{\sqrt[3]{r_{ij}^3+(1/\lambda_{ij})^3}}\\[15pt]
-  {\rm Tap}(r_{ij}) & = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 -
-                          70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 +
-                          84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 -
-                          35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1
-\end{eqnarray*}
-\endgroup
-\end{document}

doc/src/Eqs/pair_coulgauss.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-  \thispagestyle{empty}
-\begin{eqnarray*}
-  E &=& \frac{q_i q_j \mathrm{erf}\left( r/\sqrt{\gamma_1^2+\gamma_2^2} \right) }{\epsilon r_{ij}}
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/pair_dipole.tex

@@ -1,38 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
-                        \left(\frac{\sigma}{r}\right)^6 \right] \\
-E_{qq} & = & \frac{q_i q_j}{r} \\
-E_{qp} & = & \frac{q}{r^3} (p \bullet \vec{r}) \\
-E_{pp} & = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) - 
-             \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r}) 
-\end{eqnarray*}                           
-
-\begin{eqnarray*}
-F_{qq} & = & \frac{q_i q_j}{r^3} \vec{r} \\
-F_{qp} & = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5} 
-             (\vec{p} \bullet \vec{r}) \vec{r} \\
-F_{pp} & = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
-             \frac{15}{r^7} (\vec{p_i} \bullet \vec{r}) 
-	     (\vec{p_j} \bullet \vec{r}) \vec{r} + 
-             \frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + 
-             (\vec{p_i} \bullet \vec{r}) \vec{p_j} \right]
-\end{eqnarray*}                           
-
-\begin{eqnarray*}
-T_{pq} = T_{ij} & = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
-T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
-T_{pp} = T_{ij} & = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) + 
-                      \frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
-		      (\vec{p_i} \times \vec{r}) \\
-T_{pp} = T_{ji} & = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) + 
-                      \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) 
-		      (\vec{p_j} \times \vec{r}) \\
-\end{eqnarray*}                           
-
-\end{document}
-
-

doc/src/Eqs/pair_dipole_sf.tex

@@ -1,51 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-E_{LJ} & = &  4\epsilon \left\{ \left[ \left( \frac{\sigma}{r} \right)^{\!12} -
-  \left( \frac{\sigma}{r} \right)^{\!6}  \right] +
-  \left[ 6\left( \frac{\sigma}{r_c} \right)^{\!12} - 
-  3\left(\frac{\sigma}{r_c}\right)^{\!6}\right]\left(\frac{r}{r_c}\right)^{\!2}
-  - 7\left( \frac{\sigma}{r_c} \right)^{\!12} +
-  4\left( \frac{\sigma}{r_c} \right)^{\!6}\right\} \\
-E_{qq} & = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^{\!2} \\
-E_{pq} & = & E_{ji} = -\frac{q}{r^3} \left[ 1 -
-  3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
-E_{qp} & = & E_{ij} = \frac{q}{r^3} \left[ 1 -
-  3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
-E_{pp} & = & \left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
-  3\left(\frac{r}{r_c}\right)^{\!4}\right]\left[\frac{1}{r^3} 
-  (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5} 
-  (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right] \\
-\end{eqnarray*}                           
-
-\begin{eqnarray*}
-F_{LJ} & = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{\!12} - 
-  24\epsilon \left(\frac{\sigma}{r}\right)^{\!6} \right]\frac{1}{r^2} - 
-  \left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{\!12} - 24\epsilon 
-  \left(\frac{\sigma}{r_c}\right)^{\!6} \right]\frac{1}{r_c^2}\right\}\vec{r}\\
-F_{qq} & = & \frac{q_i q_j}{r}\left(\frac{1}{r^2} -
-  \frac{1}{r_c^2}\right)\vec{r} \\
-F_{pq} &=& F_{ij } =  -\frac{3q}{r^5} \left[ 1 -
-  \left(\frac{r}{r_c}\right)^{\!2}\right](\vec{p}\bullet\vec{r})\vec{r} +
-  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
-F_{qp} &=& F_{ij}  = \frac{3q}{r^5} \left[ 1 - 
-  \left(\frac{r}{r_c}\right)^{\!2}\right] (\vec{p}\bullet\vec{r})\vec{r} -
-  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
-F_{pp} & = &\frac{3}{r^5}\Bigg\{\left[1-\left(\frac{r}{r_c}\right)^{\!4}\right]
-  \left[(\vec{p_i}\bullet\vec{p_j}) - \frac{3}{r^2} (\vec{p_i}\bullet\vec{r}) 
-  (\vec{p_j} \bullet \vec{r})\right] \vec{r} + \\
-  & & \left[1 -
-  4\left(\frac{r}{r_c}\right)^{\!3}+3\left(\frac{r}{r_c}\right)^{\!4}\right]
-  \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + (\vec{p_i} \bullet \vec{r}) 
-  \vec{p_j} -\frac{2}{r^2} (\vec{p_i} \bullet \vec{r})
-  (\vec{p_j} \bullet \vec{r})\vec{r}\right] \Bigg\} \\
-\end{eqnarray*}                           
-
-\end{document}
-

doc/src/Eqs/pair_dipole_sf2.tex

@@ -1,24 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-T_{pq} = T_{ij} & = & \frac{q_j}{r^3} \left[ 1 - 
-  3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
-T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} \left[ 1 -
-  3\left(\frac{r}{r_c}\right)^{\!2} +
-  2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
-T_{pp} = T_{ij} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
-  e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
-  & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
-  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
-  (\vec{p_i} \times \vec{r}) \\
-T_{pp} = T_{ji} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
-  3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
-  & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
-  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r}) 
-  (\vec{p_j} \times \vec{r}) \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/pair_entropy.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-\thispagestyle{empty}
-
-$$
-   s_S^i=-2\pi\rho k_B \int\limits_0^{r_m} \left [ g(r) \ln g(r) - g(r) + 1 \right ] r^2 dr ,
-$$
-
-\end{document}

doc/src/Eqs/pair_entropy2.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-\thispagestyle{empty}
-
-$$
-   g_m^i(r) = \frac{1}{4 \pi \rho r^2} \sum\limits_{j} \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(r-r_{ij})^2/(2\sigma^2)} ,
-$$
-
-\end{document}

doc/src/Eqs/pair_entropy3.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-\thispagestyle{empty}
-
-$$
-  \bar{s}_S^i  = \frac{\sum_j s_S^j + s_S^i}{N + 1} ,
-$$
-
-\end{document}

doc/src/Eqs/pair_smtbq1.tex

@@ -1,13 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-E_{tot} & = & E_{ES} + E_{OO} + E_{MO} \\
-E_{ES} & = & \sum_i{\Big[ \chi_{i}^{0}Q_i + \frac{1}{2}J_{i}^{0}Q_{i}^{2} +
- \frac{1}{2} \sum_{j\neq i}{ J_{ij}(r_{ij})f_{cut}^{R_{coul}}(r_{ij})Q_i Q_j } \Big] } \\
-E_{OO} & = & \sum_{i,j}^{i,j = O}{\Bigg[Cexp( -\frac{r_{ij}}{\rho} ) - Df_{cut}^{r_1^{OO}r_2^{OO}}(r_{ij}) exp(Br_{ij})\Bigg]}  \\
-E_{MO} & = & \sum_i{E_{cov}^{i} + \sum_{j\neq i}{ Af_{cut}^{r_{c1}r_{c2}}(r_{ij})exp\Big[-p(\frac{r_{ij}}{r_0} -1) \Big] } }  \\
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/pair_smtbq2.tex

@@ -1,12 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-E_{cov}^{i(i=M,O)} & = & - \Bigg\{\eta_i(\mu \xi^{0})^2 f_{cut}^{r_{c1}r_{c2}}(r_{ij})
-\Bigg( \sum_{j(j=O,M)}{ exp[ -2q(\frac{r_{ij}}{r_0} - 1)] } \Bigg) 
-\delta Q_i \Big( 2\frac{n_0}{\eta_i} - \delta Q_i \Big) \Bigg\}^{1/2} \\
-\delta Q_i & = & | Q_i^{F} | - | Q_i |
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/pair_smtbq3.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-\xi^0 & = & \frac{\xi_O}{m} = \frac{\xi_C}{n} \\
-\frac{\beta_O}{\sqrt{m}} & = & \frac{\beta_C}{\sqrt{n}} = \xi^0 \frac{\sqrt{m}+\sqrt{n}}{2}\\
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/stress_tensor.tex

@@ -1,20 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-S_{ab} & = & - \left[ m v_a v_b + 
-   \frac{1}{2} \sum_{n = 1}^{N_p} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) +
-   \frac{1}{2} \sum_{n = 1}^{N_b} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) + \right. \\
-&& \left. \frac{1}{3} \sum_{n = 1}^{N_a} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + 
-                                           r_{3_a} F_{3_b}) + 
-   \frac{1}{4} \sum_{n = 1}^{N_d} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + 
-				   r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) + \right. \\
-&& \left. \frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} + 
-                                          r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) +
-   {\rm Kspace}(r_{i_a},F_{i_b}) + 
-   \sum_{n = 1}^{N_f} r_{i_a} F_{i_b} \right]
-\end{eqnarray*}
-
-\end{document}
-

doc/src/pair_bop.rst

@@ -71,7 +71,7 @@ The detailed formulas for this potential are given in Ward
 The repulsive energy :math:`\phi_{ij}(r_{ij})` and the bond integrals
 :math:`\beta_{\sigma,ij}(r_{ij})` and :math:`\beta_{\phi,ij}(r_{ij})` are functions of the
 interatomic distance :math:`r_{ij}` between atom *i* and *j*\ .  Each of these
-potentials has a smooth cutoff at a radius of :math:`r_{cut,ij}.  These
+potentials has a smooth cutoff at a radius of :math:`r_{cut,ij}`.  These
 smooth cutoffs ensure stable behavior at situations with high sampling
 near the cutoff such as melts and surfaces.