The narrow capture problem on general Riemannian surfaces
Probability
2022-09-27 v1 Analysis of PDEs
Differential Geometry
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.
Keywords
Cite
@article{arxiv.2209.12425,
title = {The narrow capture problem on general Riemannian surfaces},
author = {Medet Nursultanov and William Trad and Justin C. Tzou and Leo Tzou},
journal= {arXiv preprint arXiv:2209.12425},
year = {2022}
}
Comments
22 pages