Brownian dynamics of a self-propelled particle in shear flow

TL;DR

This paper analytically and via simulation investigates the motion of a self-propelled particle in shear flow, revealing complex trajectories and MSD scaling behaviors influenced by temperature and propulsion.

Contribution

It provides an analytical solution for the Langevin dynamics of a self-propelled particle in shear flow, including mean trajectories and MSD regimes, with new insights into accelerated motion.

Findings

Mean trajectories are cycloids modified by temperature.

MSD exhibits multiple scaling regimes, including t^4 for accelerated motion.

Analytical and simulation results are consistent across regimes.

Abstract

Brownian dynamics of a self-propelled particle in linear shear flow is studied analytically by solving the Langevin equation and in simulation. The particle has a constant propagation speed along a fluctuating orientation and is additionally subjected to a constant torque. In two spatial dimensions, the mean trajectory and the mean square displacement (MSD) are calculated as functions of time t analytically. In general, the mean trajectories are cycloids that are modified by finite temperature effects. With regard to the MSD different regimes are identified where the MSD scales with t^a with a = 0,1,2,3,4. In particular, an accelerated (a = 4) motion emerges if the particle is self-propelled along the gradient direction of the shear flow.