Asymptotic analysis for the mean first passage time in finite or spatially periodic 2D domains with a cluster of small traps

Authors

DOI:

https://doi.org/10.21914/anziamj.v63.15976

Keywords:

trap clusters, logarithmic capacitance, mean first passage time, splitting probability, Green’s function

Abstract

A hybrid asymptotic-numerical method is developed to approximate the mean first passage time (MFPT) and the splitting probability for a Brownian particle in a bounded two-dimensional (2D) domain that contains absorbing disks, referred to as "traps”, of asymptotically small radii. In contrast to previous studies that required traps to be spatially well separated, we show how to readily incorporate the effect of a cluster of closely spaced traps by adapting a recently formulated least-squares approach in order to numerically solve certain local problems for the Laplacian near the cluster. We also provide new asymptotic formulae for the MFPT in 2D spatially periodic domains where a trap cluster is centred at the lattice points of an oblique Bravais lattice. Over all such lattices with fixed area for the primitive cell, and for each specific trap set, the average MFPT is smallest for a hexagonal lattice of traps.

doi:10.1017/S1446181121000018

Author Biographies

Sarafa Iyaniwura, University of British Columbia

Department of Mathematics, University of British Columbia,

Vancouver, British Columbia, Canada.

Michael Ward, University of British Columbia

Department of Mathematics, University of British Columbia,

Vancouver, British Columbia, Canada.

Published

2021-07-30

Issue

Section

Articles for Printed Issues