git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@12421 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/compute_sna_atom1.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+\theta_0 = {\tt rfac0} \frac{r-r_{min0}}{R_{ii'}-r_{min0}} \pi
+\end{eqnarray*}
+
+\end{document}

doc/Eqs/compute_sna_atom2.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+u^j_{m,m'} = U^j_{m,m'}(0,0,0) + \sum_{r_{ii'} < R_{ii'}}{f_c(r_{ii'}) w_{i'} U^j_{m,m'}(\theta_0,\theta,\phi)} 
+\end{eqnarray*}
+
+\end{document}

doc/Eqs/compute_sna_atom3.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\newcommand{\hcoeff}[9]{H\!\!{\tiny\begin{array}{l}#1 #2 #3 \\ #4 #5 #6 \\ #7 #8 #9 \end{array}}}
+
+\begin{equation}
+B_{j_1,j_2,j}  = \\
+\sum_{m_1,m'_1=-j_1}^{j_1}\sum_{m_2,m'_2=-j_2}^{j_2}\sum_{m,m'=-j}^{j} (u^j_{m,m'})^*
+\hcoeff{j}{m}{m'}{j_1}{\!m_1}{\!m'_1}{j_2}{m_2}{m'_2}
+u^{j_1}_{m_1,m'_1} u^{j_2}_{m_2,m'_2}
+\end{equation}
+
+\end{document}

doc/Eqs/compute_sna_atom4.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+\label{eqn:f_c}
+f_c(r)  & = & \frac{1}{2}(\cos(\pi \frac{r-r_{min0}}{R_{ii'}-r_{min0}}) + 1), r \leq R_{ii'} \\
+& = & 0,  r > R_{ii'}
+\end{eqnarray*}
+
+
+\end{document}

doc/Eqs/compute_sna_atom5.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+
+\begin{equation}
+- \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}  }}{\partial {\bf r}_i}
+\end{equation}
+
+\end{document}

doc/Eqs/compute_sna_atom6.tex

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+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+
+\begin{eqnarray*}
+- {\bf r}_i \otimes \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}}}{\partial {\bf r}_i}
+\end{eqnarray*}
+
+\end{document}

doc/Eqs/pair_snap.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+E^i_{SNAP}(B_1^i,...,B_K^i) = \beta^{\alpha_i}_0 + \sum_{k=1}^K \beta_k^{\alpha_i} B_k^i
+$$
+
+\end{document}