Active particles driven by competing spatially dependent self-propulsion and external force

TL;DR

This paper analyzes how spatially varying self-propulsion and external forces influence active particles, deriving analytical models and revealing transitions in spatial density and velocity distributions, with potential experimental validation.

Contribution

It introduces a theoretical framework for active particles with nonuniform motility and external confinement, including analytical approximations and predictions of density and velocity behaviors.

Findings

Transition from unimodal to bimodal spatial density with decreasing self-propulsion period

Pronounced deviations from Gaussian velocity distributions, including bimodality

Theoretical predictions can be validated by experiments with active colloids

Abstract

We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. Our results can be confirmed by real-space experiments on active colloidal Janus particles in external fields.