Phase transition and diffusion among socially interacting self-propelled agents
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.
Cite
@article{arxiv.1207.1926,
title = {Phase transition and diffusion among socially interacting self-propelled agents},
author = {Alethea B. T. Barbaro and Pierre Degond},
journal= {arXiv preprint arXiv:1207.1926},
year = {2012}
}