git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@1089 f3b2605a-c512-4ea7-a41b-209d697bcdaa

This commit is contained in:
sjplimp 2007-10-22 22:21:44 +00:00
parent e5bb1dec27
commit df57eab562
6 changed files with 6 additions and 4 deletions

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\begin{document}
\begin{eqnarray}
U_A &=& - \frac{A}{6} \left[
U_A &=& - \frac{A_{cc}}{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}
@ -12,7 +12,7 @@ U_A &=& - \frac{A}{6} \left[
\right)
\right] \nonumber \\
\nonumber \\
U_R &=& \frac{A}{37800} \frac{\sigma^6}{r}
U_R &=& \frac{A_{cc}}{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 \\

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\begin{document}
\begin{eqnarray}
U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A}{9 \left( a^2 - r^2 \right)^3}
U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{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}

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\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
U &=& \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r}
\right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], ~~
r < r_c \nonumber
\end{eqnarray}
\end{document}