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

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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Submitted on : Wednesday, December 9, 2020 - 9:36:27 AM
Last modification on : Thursday, December 10, 2020 - 3:35:22 AM
Long-term archiving on: : Wednesday, March 10, 2021 - 6:33:22 PM

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Denis Grebenkov, Alexei Skvortsov. Mean first-passage time to a small absorbing target in an elongated planar domain. New Journal of Physics, Institute of Physics: Open Access Journals, 2020, 22 (11), pp.113024. ⟨10.1088/1367-2630/abc91f⟩. ⟨hal-03047939⟩

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