Name
Title | ||
|---|---|---|
Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination |
Abstract | ||
|---|---|---|
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotationmatrix inR3 as in Degond et al. (Math ModelsMethods Appl Sci 27(6):1005-1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribution function of the system at a kinetic level. The main novelty of this work is to show that in the spatially homogeneous case, self-organisation may appear or not depending on the local density of agents involved. We first exhibit a connection between body-orientation models and models of nematic alignment of polymers in higher-dimensional space from which we deduce the complete description of the possible equilibria. Then, thanks to a gradient-flow structure specific to this BGK model, we are able to prove the stability and the convergence towards the equilibria in the different regimes. We then derive the macroscopicmodels associated with the stable equilibria in the spirit of Degond et al. (Arch Ration Mech Anal 216(1):63-115, 2015, Math ModelsMethods Appl Sci 27(6):1005-1049, 2017). |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s00332-020-09632-x | JOURNAL OF NONLINEAR SCIENCE |
Keywords | DocType | Volume |
Collective motion,Vicsek model,Generalised collision invariant,Rotation group | Journal | 30 |
Issue | ISSN | Citations |
6 | 0938-8974 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pierre Degond | 1 | 251 | 43.75 |
| A. Diez | 2 | 0 | 0.34 |
| A. Frouvelle | 3 | 0 | 0.34 |
| S. Merino-Aceituno | 4 | 0 | 0.34 |