git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@620 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/pair_colloid_cc.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray}
+U_A &=& - \frac{A}{6} \left[
+	\frac{2 a_1 a_2}{r^2-\left(a_1+a_2\right)^2}
+	+ \frac{2 a_1 a_2}{r^2 - \left(a_1 - a_2\right)^2}
+	+ \mathrm{ln}
+				\left( 
+					\frac{r^2-\left(a_1+a_2\right)^2}{r^2-\left(a_1-a_2\right)^2}
+				\right)
+\right] \nonumber \\
+\nonumber \\
+U_R &=& \frac{A}{37800}  \frac{\sigma^6}{r}
+\left[ \frac{}{} \right. \nonumber \\
+	&&\qquad		\frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
+					{\left(r-a_1-a_2\right)^7} \nonumber \\
+	&&\qquad		+\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
+					{\left(r+a_1+a_2\right)^7} \nonumber \\
+	&&\qquad		-\frac{r^2+7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
+					{\left(r+a_1-a_2\right)^7} \nonumber \\
+	&&\qquad	\left.	-\frac{r^2-7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
+					{\left(r-a_1+a_2\right)^7}
+\right] \nonumber \\
+\nonumber \\
+U &=& U_A + U_R, \qquad r < r_c \nonumber
+\end{eqnarray}
+
+\end{document}
+

doc/Eqs/pair_colloid_cs.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray}
+	U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A}{9 \left( a^2 - r^2 \right)^3} 
+ \left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6}
+ {15 \left(a-r\right)^6 \left( a+r \right)^6} \right], ~~ r < r_c \nonumber
+\end{eqnarray}
+
+\end{document}
+

doc/Eqs/pair_colloid_ss.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray}
+	U &=& \frac{A}{36}  \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], ~~ r < r_c \nonumber
+\end{eqnarray}
+
+\end{document}
+

doc/Eqs/pair_dipole.tex

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+\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}
+
+