Mean first-passage time to a small absorbing target in an elongated planar domain
Statistical Mechanics
2021-10-14 v1 Chemical Physics
Abstract
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary homogenisation, and Fick-Jacobs equation to express the MFPT in terms of diffusivity and geometric parameters. A systematic comparison with a numerical solution of the original problem validates its accuracy when the starting point is not too close to the target. This is a practical tool for a rapid estimation of the MFPT for various applications in chemical physics and biology.
Keywords
Cite
@article{arxiv.2010.03406,
title = {Mean first-passage time to a small absorbing target in an elongated planar domain},
author = {Denis S. Grebenkov and Alexei T. Skvortsov},
journal= {arXiv preprint arXiv:2010.03406},
year = {2021}
}