Confined run-and-tumble swimmers in one dimension

TL;DR

This paper analyzes the behavior of run-and-tumble active particles confined in a one-dimensional box, deriving probability distributions, wall pressure, and effects of boundary interactions, revealing a crossover length and escape dynamics.

Contribution

It provides analytical expressions for particle distribution and pressure in 1D confinement, including boundary effects and escape conditions, advancing understanding of active particle confinement.

Findings

Identified a crossover box length affecting pressure dynamics.

Derived probability distributions for confined run-and-tumble particles.

Analyzed escape behavior through partially permeable boundaries.

Abstract

The persistent character of the motion of active particles gives rise to accumulation at boundaries. I investigate the problem of run-and-tumble swimmers confined in a 1D box with hard walls, reporting expressions for the particles probability distribution and wall pressure. A crossover box length value is found below which the initial value of the pressure turns out to be higher than the asymptotic one, indicating a bounce effect of the active "wave" of swimmers. The case of attracting and repelling boundaries are also investigated using two different tumble rates for particles in the bulk and at walls. Escape problems are finally analyzed by considering partially permeable walls through which particles can leave the box.