Coarsening Dynamics in the Vicsek Model of Active Matter

TL;DR

This paper investigates the coarsening dynamics in the Vicsek model of active matter, revealing distinct growth laws for density and velocity fields and deviations from Porod's law due to irregular morphologies.

Contribution

It provides the first detailed analysis of coarsening laws and structure factors in the Vicsek model, highlighting different growth exponents and morphological deviations.

Findings

Density domain size grows as t^{0.25}

Velocity field size grows as t^{0.83}

Structure factors deviate from Porod's law with specific power-law decays

Abstract

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_{\rho}(t) \sim t^{\theta_\rho}$ (with $\theta_\rho \simeq 0.25$), while the velocity length scale grows much faster, $viz.$, $L_{v}(t) \sim t^{\theta_v}$ (with $\theta_v \simeq 0.83$). The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave-vector, the scaled structure factors for the density and velocity fields decay with powers $-2.6$ and $-1.52$, respectively.