latex pair_lj_smooth.tex

latex pair_morse.tex

latex pair_soft.tex

latex pair_sw.tex

latex pair_tersoff.tex

latex pair_yukawa.tex

latex stress_tensor.tex

\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}

  E & = & \sum_i \sum_{j > i} \phi_2 (r_{ij}) + 

          \sum_i \sum_{j \neq i} \sum_{k > j} 

          \phi_3 (r_{ij}, r_{ik}, \theta_{ijk}) \\

  \phi_2(r) & = & A \epsilon \left[ B (\frac{\sigma}{r})^p - 

                    (\frac{\sigma}{r})^q \right] 

                    \exp \left( \frac{\sigma}{r - a \sigma} \right) \\

  \phi_3(r,s,\theta) & = & \lambda \epsilon \left[ \cos \theta - 

                    \cos \theta_0 \right]^2

                    \exp \left( \frac{\gamma \sigma}{r - a \sigma} \right)

                    \exp \left( \frac{\gamma \sigma}{s - a \sigma} \right)

\end{eqnarray*}                           

\end{document}

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\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}

  E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\

  V_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\

  f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l}

    1 & r < R - D \\

    \frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) &

      R-D < r < R + D \\

    0 & r > R + D

    \end{array} \right. \\

  f_R(r) & = & A \exp (-\lambda_1 r) \\

  f_A(r) & = & -B \exp (-\lambda_2 r) \\

  b_{ij} & = & \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\

  \zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk})

                   \exp \left[ {\lambda_3}^3 (r_{ij} - r_{ik})^3 \right] \\

  g(\theta) & = & 1 + \frac{c^2}{d^2} - 

                  \frac{c^2}{\left[ d^2 + 

		  (\cos \theta - \cos \theta_0)^2\right]}

\end{eqnarray*}                           

\end{document}

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