Splitting probabilities of confined chiral active Brownian particles

TL;DR

This paper analyzes how the geometry and activity of chiral active Brownian particles influence their escape probabilities in confined environments, providing analytical and numerical insights into their transport behavior.

Contribution

It introduces a combined analytical and numerical approach to study splitting probabilities of chiral active particles in confined geometries, including a Fick--Jacobs reduction for complex channels.

Findings

Analytical solutions for 1D escape probabilities in various regimes.

Fick--Jacobs reduction effectively models transport in small aspect ratio channels.

Channel geometry and particle chirality significantly affect escape likelihoods.

Abstract

Active particles exhibit self-propulsion, leading to transport behavior that differs fundamentally from passive Brownian motion. In confined or structured domains, activity strongly influence escape probabilities and first-passage behavior. Understanding these effects is essential for describing transport in biological microenvironments, microfluidic devices, and heterogeneous media. In this work, leveraging the backward Fokker--Planck equation, we investigate the splitting probability of chiral active Brownian particles in confined domains, focusing on both a one-dimensional interval and a two-dimensional corrugated channel. Analytical solutions are derived for the one-dimensional case in various asymptotic regimes. In corrugated channels with small aspect ratios, we develop a Fick--Jacobs reduction that yields effective transport equations along the axial direction, whereas for finite aspect ratios, the splitting dynamics are characterized numerically. We demonstrate how channel geometry, particle activity, and chirality modulate the likelihood of escape through different boundaries. Our results provide quantitative predictions for the transport of active matter in complex environments and highlight the interplay between confinement and activity.