Brownian motion of a self-propelled particle

TL;DR

This paper analytically investigates the overdamped Brownian motion of self-propelled particles, revealing non-Gaussian behavior, super-diffusive regimes, and characteristic displacement dynamics, aiding the understanding of microswimmer motion.

Contribution

It provides an analytical solution to the Langevin equation for self-propelled particles, including moments of displacement and non-Gaussian behavior analysis, extending understanding of active particle dynamics.

Findings

Identification of non-Gaussian behavior at finite times

Characterization of super-diffusive regimes with specific time scales

Observation of t^3 behavior in mean square displacement for certain conditions

Abstract

Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along its internal orientation axis. We calculate the first four moments of the probability distribution function for displacements as a function of time for a spherical particle with isotropic translational diffusion as well as for an anisotropic ellipsoidal particle. In both cases the translational and rotational motion is either unconfined or confined to one or two dimensions. A significant non-Gaussian behavior at finite times t is signalled by a non-vanishing kurtosis. To delimit the super-diffusive regime, which occurs at intermediate times, two time scales are identified. For certain model situations a characteristic t^3 behavior of the mean square displacement is observed. Comparing the dynamics of real and artificial microswimmers like bacteria or catalytically driven Janus particles to our analytical expressions reveals whether their motion is Brownian or not.