Kinetic theory of pattern formation in a generalized multi-species Vicsek model

TL;DR

This paper develops a kinetic theory to understand pattern formation in multi-species active matter, accurately predicting emergent behaviors and lengthscales, and extending to cyclic interactions, validated by simulations.

Contribution

It introduces a comprehensive kinetic framework for multi-species active systems, capturing complex pattern formation and collective order beyond single-species models.

Findings

Good agreement between theory and particle simulations.

Kinetic theory captures correct lengthscale in coexistence phases.

Framework extends to cyclic alignment interactions.

Abstract

The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained from single-species models. In this paper, we derive a kinetic theory for multi-species systems of self-propelled particles with (anti-)alignment interactions. We summarize the numerical results for the binary system before employing linear stability analysis on the coarse-grained system. We find good agreement between theoretical predictions and particle simulations, and our kinetic theory is able to capture the correct lengthscale in the emergent coexistence phases through a Turing-Hopf instability. Extending the kinetic framework to multi-species systems with cyclic alignment interactions, we recover precisely the same emergent ordering as corresponding simulations of the microscopic model. More generally, our kinetic theory provides an extensible framework for analyzing pattern formation and collective order in multi-species active matter systems.