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

Abstract

Abstract 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 investigate the accessibility of the target points to Brownian motion. In particular, we study the effects of confinement and target anisotropy. The limits of a segment and a disk are also discussed. 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.