Active Brownian Motion with Directional Reversals

TL;DR

This paper analyzes the dynamics of active Brownian particles with directional reversals, revealing four distinct regimes, and provides analytical characterizations of their position distribution and persistence properties.

Contribution

It introduces a comprehensive analytical framework for understanding active Brownian motion with reversals, identifying four dynamical regimes and deriving exact distributions and exponents.

Findings

Identification of four dynamical regimes based on time scales

Analytical form of position distribution showing crossover behaviors

Discovery of a novel persistence exponent =1 in the reversal regime

Abstract

Active Brownian motion with intermittent direction reversals are common in a class of bacteria like {\it Myxococcus xanthus} and {\it Pseudomonas putida}. We show that, for such a motion in two dimensions, the presence of the two time scales set by the rotational diffusion constant $D_R$ and the reversal rate $\gamma$ gives rise to four distinct dynamical regimes: (I) $t\ll \min (\gamma^{-1}, D_R^{-1}),$ (II) $\gamma^{-1}\ll t\ll D_R^{-1}$, (III) $D_R^{-1} \ll t \ll \gamma^{-1}$, and (IV) $t\gg \max (\gamma^{-1}$, $D_R^{-1})$, showing distinct behaviors. We characterize these behaviors by analytically computing the position distribution and persistence exponents. The position distribution shows a crossover from a strongly non-diffusive and anisotropic behavior at short-times to a diffusive isotropic behavior via an intermediate regime (II) or (III). In regime (II), we show that, the position distribution along the direction orthogonal to the initial orientation is a function of the scaled variable $z\propto x_{\perp}/t$ with a non-trivial scaling function, $f(z)=(2\pi^3)^{-1/2}\Gamma(1/4+iz)\Gamma(1/4-iz)$. Furthermore, by computing the exact first-passage time distribution, we show that a novel persistence exponent $\alpha=1$ emerges due to the direction reversal in this regime.