Phase transition and diffusion among socially interacting self-propelled agents

2012/07/09 by Barbaro, Alethea B. T., Degond, Pierre
#35K55 #35L60 #35Q80 #82C05 #82C22 #82C70 #92D50 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1207.1926

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.

Related

• Self-Organized Hydrodynamics with nonconstant velocity
• Fluid models with phase transition for kinetic equations in swarming
• Dynamical Self-regulation in Self-propelled Particle Flows
• From Kinetic Flocking Model of Cucker-Smale Type to Self-Organized Hydrodynamic model
• Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles