Phase transition and diffusion among socially interacting self-propelled agents

TL;DR

This paper investigates a hydrodynamic model of swarming behavior derived from kinetic particle systems, revealing a phase transition from disordered to ordered motion and deriving diffusive corrections to extend the model's applicability.

Contribution

It introduces a new hydrodynamic model for swarming that captures phase transitions and derives diffusive corrections to overcome previous model restrictions.

Findings

Identifies a phase transition at a critical noise level.

Derives a hyperbolic 'Self-Organized Hydrodynamics' model.

Computes Navier-Stokes diffusive corrections to extend the model.

Abstract

We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsion force limit, we provide evidence of a phase transition from disordered to ordered motion which manifests itself as a change of type of the limit model (from hyperbolic to diffusive) at the crossing of a critical noise intensity. In the hyperbolic regime, the resulting model, referred to as the `Self-Organized Hydrodynamics (SOH)', consists of a system of compressible Euler equations with a speed constraint. We show that the range of SOH models obtained by this limit is restricted. To waive this restriction, we compute the Navier-Stokes diffusive corrections to the hydrodynamic model. Adding these diffusive corrections, the limit of a large propulsion force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints.