# Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view (ABPDE III)

28-31 August 2018
Europe/Paris timezone

## Swarming models with local alignment effects: phase transitions & hydrodynamics

29 Aug 2018, 14:30
45m

Cité Scientifique, Villeneuve d'Ascq

### Speaker

Prof. Jose Antonio Carrillo de la Plata (Imperial College London)

### Description

We will discuss a collective behavior model in which individuals try to imitate each other’s velocity and have a preferred asymptotic speed. It is a variant of the well-known Cucker-Smale model in which the alignment term is localized. We showed that a phase change phenomenon takes place as diffusion decreases, bringing the system from a disordered'' to anordered'' state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We analysed the expansion of the large friction limit around the limiting Vicsek model on the sphere leading to the so-called Self-Organized Hydrodynamics (SOH). This talk is based on papers in collaboration with Bostan, and with Barbaro, Cañizo and Degond.

### Presentation Materials

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