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A note on phase transitions for the Smoluchowski equation with dipolar potential

dc.contributor.authorLiu, Jian-Guo
dc.contributor.authorFrouvelle, Amic
HAL ID: 874
ORCID: 0000-0001-6828-8176
dc.contributor.authorDegond, Pierre
HAL ID: 748885
dc.date.accessioned2012-12-19T15:32:42Z
dc.date.available2012-12-19T15:32:42Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10750
dc.language.isoenen
dc.subjectSmoluchowski equation
dc.subjectequilibrium states
dc.subject.ddc520en
dc.titleA note on phase transitions for the Smoluchowski equation with dipolar potential
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherDepartment of Physics and Department of Mathematics Duke University;États-Unis
dc.contributor.editoruniversityotherInstitut de Mathématiques de Toulouse (IMT) Université Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées de Toulouse – CNRS : UMR5219;France
dc.description.abstractenIn this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the strength of alignment and the intensity of the diffusion as functions of the order parameter. We characterize the stable and unstable equilibrium states. For stable equilibria, we provide the exponential rate of convergence. We detail special cases, giving rise to second order and first order phase transitions, respectively. We study the hysteresis diagram, and provide numerical illustrations of this phenomena.
dc.identifier.urlsitehttps://www.aimsciences.org/book/AM/volume/Volume%208
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.conftitleHyperbolic Problems: Theory, Numerics, Applications
dc.relation.confdate2012-06
dc.relation.confcityPadova
dc.relation.confcountryITALY
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
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dc.description.audienceInternational
dc.date.updated2020-11-27T21:00:54Z


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