Global Optimization of the Mean First Passage Time for Narrow Capture Problems in Elliptic Domains

Jason Gilbert, Alexei Cheviakov

Published 2021-01-20Version 1

Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known how the escape time decreases with the increase of the trap sizes, for some specific 2D and 3D domains, higher-order asymptotic formulas have been established, providing the dependence of the escape time on the sizes and locations of the traps. Such results allow the use of global optimization to seek trap arrangements that minimize average escape times. In a recent paper, the escape time expansion for a 2D elliptic domain was derived, providing the dependence of the average MFPT on sizes and locations of small internal traps. The goal of this work is to systematically seek global minima of MFPT for $1\leq N\leq 50$ traps, and compare the corresponding putative optimal trap arrangements for different values of the domain eccentricity.