Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo (2015), Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, Archive for Rational Mechanics and Analysis, 216, 1, p. 63-115. http://dx.doi.org/10.1007/s00205-014-0800-7
Type
Article accepté pour publication ou publiéDate
2015Nom de la revue
Archive for Rational Mechanics and AnalysisVolume
216Numéro
1Éditeur
Springer
Pages
63-115
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function.Mots-clés
von Mises-Fisher distributionPublications associées
Affichage des éléments liés par titre et auteur.
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Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre (2012) Communication / Conférence
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Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo; Motsch, Sébastien; Navoret, Laurent (2013) Article accepté pour publication ou publié
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Navoret, Laurent; Motsch, Sébastien; Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre (2013) Rapport
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Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo (2021) Document de travail / Working paper
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Frouvelle, Amic; Liu, Jian-Guo (2019) Chapitre d'ouvrage