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

Pierre Degond Institut de Mathématiques de Toulouse, Université de Toulouse Amic Frouvelle Institut de Mathématiques de Toulouse Jian-Guo Liu Duke University

Mathematical Physics mathscidoc:1702.22005

Best Paper Award in 2018

Journal of Nonlinear Science, 23, (3), 427–456, 2013.6
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work (Degond and Motsch, Math. Models Methods Appl. Sci. 18:1193–1215, 2008a; Frouvelle, Math. Models Methods Appl. Sci., 2012), 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 (Frouvelle and Liu, Dynamics in a kinetic model of oriented particles with phase transition, 2012), 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 nonlinear 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 (Degond and Motsch, Math. Models Methods Appl. Sci. 18:1193–1215, 2008a; Frouvelle, Math. Models Methods Appl. Sci., 2012). 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.
Self-propelled particlesAlignment interactionVicsek modelPhase transitionHydrodynamic limitNonhyperbolicityDiffusion limitChapman–Enskog expansion
[ Download ] [ 2017-02-08 22:20:09 uploaded by jianguo ] [ 690 downloads ] [ 0 comments ]
@inproceedings{pierre2013macroscopic,
  title={Macroscopic limits and phase transition in a system of self-propelled particles},
  author={Pierre Degond, Amic Frouvelle, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222009908710321},
  booktitle={Journal of Nonlinear Science},
  volume={23},
  number={3},
  pages={427–456},
  year={2013},
}
Pierre Degond, Amic Frouvelle, and Jian-Guo Liu. Macroscopic limits and phase transition in a system of self-propelled particles. 2013. Vol. 23. In Journal of Nonlinear Science. pp.427–456. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222009908710321.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved