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

  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},
  volume={87 4},
  • A. Cheviakov, D. Zawada
  • Published 22 April 2013
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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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