pair_edip.tex
bfb019efa901lammps-icms

pair_edip.tex
View Options

			\documentclass[12pt]{article}

			\usepackage{amssymb,amsmath}

			\begin{document}

			\begin{eqnarray*}
			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}) \\
			\phi_{2}(r, Z) & = & A\left[\left(\frac{B}{r}\right)^{\rho} - e^{-\beta Z^2}\right]exp{\left(\frac{\sigma}{r-a}\right)} \\
			\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) \\
			Z_i & = & \sum_{m \ne i} f(R_{im}) \qquad
			f(r) = \begin{cases}
			1 & \quad r<c \\
			\exp\left(\frac{\alpha}{1-x^{-3}}\right) & \quad c<r<a \\
			0 & \quad r>a
			\end{cases} \\
			h(l,Z) & = & \lambda [(1-e^{-Q(Z)(l+\tau(Z))^2}) + \eta Q(Z)(l+\tau(Z))^2 ] \\
			Q(Z) & = & Q_0 e^{-\mu Z} \qquad \tau(Z) = u_1 + u_2 (u_3 e^{-u_4 Z} - e^{-2u_4 Z})
			\end{eqnarray*}

			\end{document}