The narrow capture problem on general Riemannian surfaces

2022/09/26 by Medet Nursultanov, William Trad, Nursultanov, Medet +5 · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Diffusion and Search Dynamics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2209.12425

Abstract

In this article, we study the narrow capture problem on a Riemannian 2-manifold. This involves the derivation of the mean first passage (sojourn) time of a surface-bound ion modelled as a Brownian particle. We use a layer potential argument in conjunction with microlocal analysis in order to derive the leading order singularity as well as the O(1) term of the mean first passage time and the associated spatial average.

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