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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• Mean exit time for diffusion on irregular domains
• Asymptotic analysis and simulation of mean first passage time for active Brownian particles in 1-D
• Diffusion towards a nanoforest of absorbing pillars
• Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
• 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