Phase transition and diffusion among socially interacting self-propelled agents

Alethea B.T. Barbaro, Pierre Degond

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)


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-propulsive 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 propulsive force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints.

Original languageEnglish
Pages (from-to)1249-1278
Number of pages30
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number5
Publication statusPublished - Jul 2014
Externally publishedYes


  • Chapman-Enskog expansion
  • Cucker-Smale model
  • Diffusion
  • Hydrodynamic model
  • Self-propulsion
  • Swarm
  • Vicsek model

Fingerprint Dive into the research topics of 'Phase transition and diffusion among socially interacting self-propelled agents'. Together they form a unique fingerprint.

Cite this