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dc.contributor.authorDegond, Pierre*
dc.contributor.authorDiez, Antoine*
dc.contributor.authorFrouvelle, Amic*
dc.contributor.authorMerino-Aceituno, Sara*
dc.date.accessioned2019-07-24T11:11:29Z
dc.date.available2019-07-24T11:11:29Z
dc.date.issued2019-05
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19398
dc.language.isoenen
dc.subjectrotation groupen
dc.subjectgeneralized collision invarianten
dc.subjectVicsek modelen
dc.subjectCollective motionen
dc.subject.ddc515en
dc.titlePhase transitions and macroscopic limits in a BGK model of body-attitude coordinationen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn 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 rotation matrix in \R3 as in \cite{degondfrouvellemerino17}. 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 macroscopic models associated to the stable equilibria in the spirit of \cite{degondfrouvellemerino17} and \cite{degondfrouvelleliu15}.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages52en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02126060en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-05
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-07-24T11:08:05Z
hal.person.labIds4553*
hal.person.labIds4553*
hal.person.labIds60*
hal.person.labIds454362$$$7255*


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