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arXiv · 2010.03406

Mean first-passage time to a small absorbing target in an elongated planar domain

Denis S. Grebenkov·Alexei T. Skvortsov
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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.

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BibTeXRIS

Denis S. Grebenkov, Alexei T. Skvortsov. 2020-10-07. Mean first-passage time to a small absorbing target in an elongated planar domain. https://doi.org/10.1088/1367-2630/abc91f

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