Macroscopic limits and phase transition in a system of self-propelled particles

Degond, Pierre and Frouvelle, Amic and Liu, Jian-Guo (2012) Macroscopic limits and phase transition in a system of self-propelled particles. (Submitted)

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Abstract

We investigate systems of self-propelled particles with alignment interaction. Compared to previous work [13, 19], the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at low density to aligned states at high densities. This model is the space inhomogeneous extension of [20] in which the existence and stability of the equilibrium states were investigated. When the density is lower than a threshold value, the dynamics is described by a non-linear diffusion equation. By contrast, when the density is larger than this threshold value, the dynamics is described by a similar hydrodynamic model for self-alignment interactions as derived in [13, 19]. However, the modified normalization of the force gives rise to different convection speeds and the resulting model may lose its hyperbolicity in some regions of the state space.

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: Amic Frouvelle
Date Deposited: 06 Oct 2012 09:14
Last Modified: 06 May 2017 05:44
URI: http://preprints.acmac.uoc.gr/id/eprint/148

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