Searching for a partially absorbing target by a run-and-tumble particle in a confined space

TL;DR

This paper analytically studies the search time of a run-and-tumble particle for a partially absorbing target in confined space, revealing an optimal speed and practical filtering applications.

Contribution

It provides the first analytical expression for mean search time in this setting and links high-dimensional diffusion to a 1D problem with absorption.

Findings

Mean search time exhibits non-monotonic dependence on particle speed.

Existence of an optimal particle speed for efficient search.

Proposed a filtering device based on absorption strength and particle speed.

Abstract

A random search of a partially absorbing target by a run-and-tumble particle in a confined one-dimensional space is investigated. We analytically obtain the mean searching time, which shows a non-monotonic behavior as a function of the self-propulsion speed of the active particle, indicating the existence of an optimal speed, when the absorption strength of the target is finite. In the limit of large and small absorption strengths, respectively, asymptotes of the mean searching time and the optimal speed are found. We also demonstrate that the first-passage problem of a diffusive run-and-tumble particle in high dimensions can be mapped into a one-dimensional problem with a partially absorbing target. Finally, as a practical application exploiting the existence of the optimal speed, we propose a filtering device to extract active particles with a desired speed and evaluate how the resolution of the filtering device depends on the absorption strength.