Paper Info
Title
Macroscopic Limits and Phase Transition in a System of Self-propelled Particles.
Abstract
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, ; Frouvelle, Math. Models Methods Appl. Sci., ), 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, ), 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, ; Frouvelle, Math. Models Methods Appl. Sci., ). 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.
Year
DOI
Venue
2013
10.1007/s00332-012-9157-y
J. Nonlinear Science
Keywords
Field
DocType
Self-propelled particles,Alignment interaction,Vicsek model,Phase transition,Hydrodynamic limit,Nonhyperbolicity,Diffusion limit,Chapman–Enskog expansion,35L60,35K55,35Q80,82C05,82C22,82C70,92D50
Statistical physics,Convection,Normalization (statistics),Phase transition,Self-propelled particles,Kinetic model,Nonlinear diffusion equation,Classical mechanics,State space,Mathematics,Low density
Journal
Volume
Issue
ISSN
23
3
Journal of Nonlinear Science 23, 3 (2013) 427-456
Citations 
PageRank 
References 
3
1.34
4
Authors
3
Name
Order
Citations
PageRank
Pierre Degond125143.75
Amic Frouvelle2113.80
Jian-Guo Liu319363.14