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\begin{eqnarray*}
 E & = & LJ(r) \qquad \qquad \qquad r < r_{\rm in} \\
   & = & S(r) * LJ(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
   & = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
 E & = & C(r) \qquad \qquad \qquad r < r_{\rm in} \\
   & = & S(r) * C(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
   & = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\
 LJ(r) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
         \left(\frac{\sigma}{r}\right)^6 \right] \\
 C(r) & = & \frac{C q_i q_j}{ \epsilon r} \\
 S(r) & = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2  
   \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} 
 { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 }
\end{eqnarray*}                           

\end{document}


