First-passage time of run-and-tumble particles

TL;DR

This paper derives exact formulas for the mean first-passage time of run-and-tumble particles in one dimension, accounting for external and chemotactic fields, with validation through simulations, aiding understanding of active particle phenomena.

Contribution

It provides the first analytical solutions for first-passage times of run-and-tumble particles under complex external and chemotactic influences.

Findings

Analytical expressions match numerical simulations.

Applicable to various external force and chemotactic fields.

Insights into bacterial motion, intracellular transport, and animal foraging.

Abstract

We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force-fields and chemotactic-fields, giving rise to space dependent swim-speed and tumble rate. Agreement between theoretical formulae and numerical simulations is obtained in the analyzed case studies -- constant and sinusoidal force fields, constant gradient chemotactic field. Reported findings can be useful to get insights into very different phenomena involving active particles, such as bacterial motion in external fields, intracellular transport, cell migration, animal foraging.