Run-and-tumble particles, telegrapher's equation and absorption problems with partially reflecting boundaries

TL;DR

This paper analyzes absorption problems of run-and-tumble particles modeled by the telegrapher's equation in one dimension, providing exact solutions for probability distributions and mean absorption times under various boundary conditions.

Contribution

It offers the first exact expressions for the probability distribution and mean absorption time for run-and-tumble particles with partially reflecting boundaries.

Findings

Exact Laplace domain probability distribution functions obtained.

Mean absorption times derived for different boundary conditions.

Analysis of limits including Brownian and wave regimes.

Abstract

Absorption problems of run-and-tumble particles, described by the telegrapher's equation, are analyzed in one space dimension considering partially reflecting boundaries. Exact expressions for the probability distribution function in the Laplace domain and for the mean time to absorption are given, discussing some interesting limits (Brownian and wave limit, large volume limit) and different case studies (semi-infinite segment, equal and symmetric boundaries, totally/partially reflecting boundaries).