On the effect of boundaries on noninteracting weakly active particles in different geometries

TL;DR

This paper develops a perturbative analytical framework to study how weakly active particles distribute and behave near boundaries across various geometries, revealing how activity influences density, pressure, and flow.

Contribution

It introduces a simple expansion method for active Ornstein-Uhlenbeck particles to analyze boundary effects in different geometries, enhancing understanding of weak activity impacts.

Findings

Density and pressure profiles are affected by activity levels.

Boundary conditions can be formulated explicitly for weakly active particles.

Behavior near boundaries varies with geometry and activity strength.

Abstract

We study analytically how noninteracting weakly active particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, distribute and behave near boundaries in various geometries. In particular, we develop a perturbative approach for the model of active particles driven by an exponentially correlated random force (active Ornstein-Uhlenbeck particles). This approach involves a relatively simple expansion of the distribution in powers of the P\'{e}clet number and in terms of Hermite polynomials. We use this approach to cleanly formulate boundary conditions, which allows us to study weakly active particles in several geometries: confinement by a single wall or between two walls in 1D, confinement in a circular or wedge-shaped region in 2D, motion near a corrugated boundary, and finally absorption onto a sphere. We consider how quantities such as the density, pressure, and flow of the active particles change as we gradually increase the activity away from a purely passive system. These results for the limit of weak activity help us gain insight into how active particles behave in the presence of various types of boundaries.