Effects of target anisotropy on harmonic measure and mean first-passage time

TL;DR

This paper explores how the shape anisotropy of targets affects diffusion-related properties like harmonic measure density and mean first-passage time, providing explicit formulas and analysis for prolate and oblate spheroids.

Contribution

It offers new analytical expressions for harmonic measure and mean first-passage time considering target anisotropy in three-dimensional diffusion.

Findings

Harmonic measure density varies with target shape anisotropy.

Capacitance approximation accurately predicts mean first-passage time for small targets.

Explicit formulas derived for prolate and oblate spheroidal targets.

Abstract

In this paper, we investigate the influence of target anisotropy on two characteristics of diffusion-controlled reactions: harmonic measure density and mean first-passage time. First, we compute the volume-averaged harmonic measure density on prolate and oblate spheroidal targets inside a confining domain in three dimensions. This allows us to quantify the uniformity of this density in the small target limit. Second, we derive an explicit expression of the mean first-passage time to such targets and analyze the effect of anisotropy. In particular, we illustrate the accuracy of the capacitance approximation for small targets.