forked from lijiext/lammps
23 lines
886 B
TeX
23 lines
886 B
TeX
\documentclass[12pt]{article}
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\usepackage{amssymb,amsmath}
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\begin{document}
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\begin{eqnarray*}
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E & = & \sum_{j \ne i} \phi_{2}(R_{ij}, Z_{i}) + \sum_{j \ne i} \sum_{k \ne i,k > j} \phi_{3}(R_{ij}, R_{ik}, Z_{i}) \\
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\phi_{2}(r, Z) & = & A\left[\left(\frac{B}{r}\right)^{\rho} - e^{-\beta Z^2}\right]exp{\left(\frac{\sigma}{r-a}\right)} \\
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\phi_{3}(R_{ij}, R_{ik}, Z_i) & = & exp{\left(\frac{\gamma}{R_{ij}-a}\right)}exp{\left(\frac{\gamma}{R_{ik}-a}\right)}h(cos\theta_{ijk},Z_i) \\
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Z_i & = & \sum_{m \ne i} f(R_{im}) \qquad
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f(r) = \begin{cases}
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1 & \quad r<c \\
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\exp\left(\frac{\alpha}{1-x^{-3}}\right) & \quad c<r<a \\
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0 & \quad r>a
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\end{cases} \\
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h(l,Z) & = & \lambda [(1-e^{-Q(Z)(l+\tau(Z))^2}) + \eta Q(Z)(l+\tau(Z))^2 ] \\
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Q(Z) & = & Q_0 e^{-\mu Z} \qquad \tau(Z) = u_1 + u_2 (u_3 e^{-u_4 Z} - e^{-2u_4 Z})
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\end{eqnarray*}
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\end{document}
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