Ordering dynamics of self-propelled particles in an inhomogeneous medium

TL;DR

This study investigates how self-propelled particles in two dimensions organize over time within an inhomogeneous medium, revealing disorder-dependent growth laws and scaling behaviors in their density and velocity fields.

Contribution

The paper develops hydrodynamic equations for self-propelled particles in disordered media and analyzes how disorder affects their ordering dynamics and scaling properties.

Findings

Velocity growth slows with increasing disorder.

Velocity exhibits disorder-dependent power-law growth and logarithmic late-time growth.

Density growth is approximately t^{0.8} in clean systems and does not show simple scaling.

Abstract

Ordering dynamics of self-propelled particles in an inhomogeneous medium in two-dimensions is studied. We write coarse-grained hydrodynamic equations of motion for coarse-grained density and velocity fields in the presence of an external random disorder field, which is quenched in time. The strength of inhomogeneity is tuned from zero disorder (clean system) to large disorder. In the clean system, the velocity field grows algebraically as $L_{\rm V} \sim t^{0.5}$. The density field does not show clean power-law growth; however, it follows $L_{\rm \rho} \sim t^{0.8}$ approximately. In the inhomogeneous system, we find a disorder dependent growth. For both the density and the velocity, growth slow down with increasing strength of disorder. The velocity shows a disorder dependent power-law growth $L_{\rm V}(t,\Delta) \sim t^{1/\bar z_{\rm V}(\Delta)}$ for intermediate times. At late times, there is a crossover to logarithmic growth $L_{\rm V}(t,\Delta) \sim (\ln t)^{1/\varphi}$, where $\varphi$ is a disorder independent exponent. Two-point correlation functions for the velocity shows dynamical scaling, but the density does not.