forked from lijiext/lammps
32 lines
1017 B
TeX
32 lines
1017 B
TeX
\documentstyle[12pt]{article}
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\begin{document}
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\begin{eqnarray}
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U_A &=& - \frac{A_{cc}}{6} \left[
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\frac{2 a_1 a_2}{r^2-\left(a_1+a_2\right)^2}
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+ \frac{2 a_1 a_2}{r^2 - \left(a_1 - a_2\right)^2}
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+ \mathrm{ln}
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\left(
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\frac{r^2-\left(a_1+a_2\right)^2}{r^2-\left(a_1-a_2\right)^2}
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\right)
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\right] \nonumber \\
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\nonumber \\
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U_R &=& \frac{A_{cc}}{37800} \frac{\sigma^6}{r}
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\left[ \frac{}{} \right. \nonumber \\
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&&\qquad \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
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{\left(r-a_1-a_2\right)^7} \nonumber \\
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&&\qquad +\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
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{\left(r+a_1+a_2\right)^7} \nonumber \\
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&&\qquad -\frac{r^2+7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
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{\left(r+a_1-a_2\right)^7} \nonumber \\
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&&\qquad \left. -\frac{r^2-7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
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{\left(r-a_1+a_2\right)^7}
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\right] \nonumber \\
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\nonumber \\
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U &=& U_A + U_R, \qquad r < r_c \nonumber
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\end{eqnarray}
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\end{document}
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