Brownian Motion in Dire Straits

TL;DR

This paper investigates how the geometry and smoothness of domains affect the mean escape time of Brownian particles passing through narrow bottlenecks, revealing new behaviors in various geometries.

Contribution

It introduces novel findings on narrow escape times in different geometries, emphasizing the influence of domain shape and smoothness on Brownian motion passage.

Findings

New behavior of escape times in planar and spatial domains

Geometry significantly influences flux through bottlenecks

Applications in biological and physical systems discussed

Abstract

The passage of Brownian motion through a bottleneck in a bounded domain is a rare event and the mean time for such passage increases indefinitely as the bottleneck's radius shrinks to zero. Its calculation reveals the effect of geometry and smoothness on the flux through the bottleneck. We find new behavior of the narrow escape time through bottlenecks in planar and spatial domains and on a surface. Some applications are discussed.