Splitting probabilities for dynamics in corrugated channels: passive VS active Brownian motion

TL;DR

This paper analyzes splitting probabilities in corrugated channels for both passive and active Brownian particles, revealing how activity influences transport behavior through analytical methods within the Fick-Jacobs framework.

Contribution

It provides an analytical comparison of splitting probabilities for passive and active Brownian motion in 3D corrugated channels, highlighting activity-related differences.

Findings

Active particles show distinct splitting probability patterns compared to passive particles.

Analytical expressions for splitting probabilities depend on system parameters.

Differences in behavior serve as fingerprints of particle activity.

Abstract

In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or connected to a broader channel), is reached before the other one. In mathematical literature, the latter are called the "splitting" probabilities (SPs). Here, within the Fick-Jacobs approach, we study analytically the SPs as functions of system's parameters for dynamics in three-dimensional corrugated channels, confronting standard diffusion and active Brownian motion. Our analysis reveals some similarities in the behavior and also some markedly different features, which can be seen as fingerprints of the activity of particles.