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\begin{eqnarray*}
\label{eqn:f_c}
f_c(r)  & = & \frac{1}{2}(\cos(\pi \frac{r-r_{min0}}{R_{ii'}-r_{min0}}) + 1), r \leq R_{ii'} \\
& = & 0,  r > R_{ii'}
\end{eqnarray*}


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