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Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics

dc.contributor.authorDegond, Pierre
HAL ID: 748885
dc.contributor.authorFrouvelle, Amic
HAL ID: 874
ORCID: 0000-0001-6828-8176
dc.contributor.authorLiu, Jian-Guo
dc.date.accessioned2013-04-11T08:05:09Z
dc.date.available2013-04-11T08:05:09Z
dc.date.issued2015
dc.identifier.issn0003-9527
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11210
dc.language.isoenen
dc.subjectvon Mises-Fisher distribution
dc.subject.ddc520en
dc.titlePhase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Physics and Department of Mathematics Duke University;États-Unis
dc.contributor.editoruniversityotherUniversité Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219;France
dc.description.abstractenWe 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.
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol216
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages63-115
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00205-014-0800-7
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-09-21T10:23:18Z


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