forked from lijiext/lammps
25 lines
940 B
TeX
25 lines
940 B
TeX
\documentclass[12pt]{article}
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\begin{document}
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\begin{eqnarray*}
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E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\
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V_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\
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f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l}
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1 & r < R - D \\
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\frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) &
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R-D < r < R + D \\
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0 & r > R + D
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\end{array} \right. \\
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f_R(r) & = & A \exp (-\lambda_1 r) \\
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f_A(r) & = & -B \exp (-\lambda_2 r) \\
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b_{ij} & = & \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\
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\zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk})
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\exp \left[ {\lambda_3}^3 (r_{ij} - r_{ik})^m \right] \\
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g(\theta) & = & \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} -
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\frac{c^2}{\left[ d^2 +
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(\cos \theta - \cos \theta_0)^2\right]} \right)
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\end{eqnarray*}
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\end{document}
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