# Narrow-escape problem for the unit sphere: homogenization limit, optimal arrangements of large numbers of traps, and the N(2) conjecture.

@article{Cheviakov2013NarrowescapePF, title={Narrow-escape problem for the unit sphere: homogenization limit, optimal arrangements of large numbers of traps, and the N(2) conjecture.}, author={Alexei F. Cheviakov and Daniel Zawada}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={87 4}, pages={ 042118 } }

A narrow-escape problem is considered to calculate the mean first passage time (MFPT) needed for a Brownian particle to leave a unit sphere through one of its N small boundary windows (traps). A procedure is established to calculate optimal arrangements of N>>1 equal small boundary traps that minimize the asymptotic MFPT. Based on observed characteristics of such arrangements, a remarkable property is discovered, that is, the sum of squared pairwise distances between optimally arranged N traps… Expand

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