Mean first-passage time to a small absorbing target in an elongated planar domain
arXiv:2010.03406 · doi:10.1088/1367-2630/abc91f
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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- Diffusion in a fluid flow generated by a source at the apex of a wedge
- Mean exit time in irregularly-shaped annular and composite disc domains
- Mean first-passage time to a small absorbing target in three-dimensional elongated domains
- Survival probability of random walks leaping over traps