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\begin{eqnarray*}
 \vec{f} & = & (F^C + F^D + F^R) \hat{r_{ij}} \qquad \qquad r < r_c \\
 F^C & = & A w(r) \\
 F^D & = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v_{ij}}) \\
 F^R & = & \sigma w(r) \alpha (\Delta t)^{-1/2} \\
 w(r) & = & 1 - r/r_c
\end{eqnarray*}                           

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