First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results

TL;DR

This paper investigates the mean first-passage time of particles crossing conical channels under a transverse gravitational force, comparing analytical predictions with simulations to understand the influence of external potential and geometry.

Contribution

It derives an analytical expression for the mean first-passage time in varying-width channels under external force and validates it with extensive Brownian dynamics simulations.

Findings

Effective diffusivity decreases with increasing external potential amplitude.

Mean first-passage time exhibits a minimum at finite potential amplitudes.

The one-dimensional approximation is valid within a certain parameter range.

Abstract

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.