Show simple item record

Crystallinity of the homogenized energy density of periodic lattice systems

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChambolle, Antonin
hal.structure.identifierFachbereich Mathematik und Informatik [Münster] = Fachbereich Mathematik und Informatik [Münster] [FB 10]
dc.contributor.authorKreutz, Leonard
dc.date.accessioned2021-11-26T15:06:55Z
dc.date.available2021-11-26T15:06:55Z
dc.date.issued2023
dc.identifier.issn1540-3459
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22271
dc.language.isoenen
dc.subjectΓ-convergence
dc.subjectIsing system
dc.subjectCrystallinity
dc.subjectWulff Shape
dc.subject.ddc515en
dc.titleCrystallinity of the homogenized energy density of periodic lattice systems
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the homogenized energy densities of periodic ferromagnetic Ising systems. We prove that, for finite range interactions, the homogenized energy density, identifying the effective limit, is crystalline, i.e. its Wulff crystal is a polytope, for which we can (exponentially) bound the number of vertices. This is achieved by deriving a dual representation of the energy density through a finite cell formula. This formula also allows easy numerical computations: we show a few experiments where we compute periodic patterns which minimize the anisotropy of the surface tension.
dc.relation.isversionofjnlnameMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
dc.relation.isversionofjnlvol21
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2023
dc.relation.isversionofdoi10.1137/21M1442073
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-04T10:12:15Z
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail
Name:
Crystallinity_final.pdf
Size:
880.8Kb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record