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Narrow-escape problem for the unit sphere: Homogenization limit, optimal arrangements of large numbers of traps, and theN2conjecture

2013
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Physical Review E
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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

doi:10.1103/physreve.87.042118
pmid:23679384
fatcat:var5h5yuovd2ngx4mmg7kpl6by