Continuous theory of active matter systems with metric-free interactions

TL;DR

This paper develops a hydrodynamic theory for active matter systems with topological interactions, revealing how such metric-free rules stabilize homogeneous phases and suppress density segregation, aligning with simulations.

Contribution

It introduces a kinetic derivation of nonlinear field equations for topological active matter, highlighting differences from metric-based models.

Findings

Topological interactions suppress linear instabilities.

Homogeneous ordered phases are stabilized.

Density segregation is reduced near the transition.

Abstract

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones, -a situation advocated recently to be relevant for bird flocks, fish schools, and crowds- we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.