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Ballistic and superdiffusive scales in the macroscopic evolution of a chain of oscillators

hal.structure.identifierInstitut of Mathematics - Polish Academy of Sciences [PAN]
dc.contributor.authorKomorowski, Tomasz
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861
dc.date.accessioned2018-01-12T12:21:06Z
dc.date.available2018-01-12T12:21:06Z
dc.date.issued2016
dc.identifier.issn0951-7715
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17289
dc.language.isoenen
dc.subjectchain of oscillatorsen
dc.subjectdiffusive scaling limit of the Riemann invariantsen
dc.subject.ddc520en
dc.titleBallistic and superdiffusive scales in the macroscopic evolution of a chain of oscillatorsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the system has only three conserved quantities: volume, momentum and energy. We show the existence of two space–time scales on which the en- ergy of the system evolves. On the hyperbolic scale (tε−1,xε−1) the limits of the conserved quantities satisfy a Euler system of equa- tions, while the thermal part of the energy macroscopic profile re- mains stationary. Thermal energy starts evolving at a longer time scale, corresponding to the superdiffusive scaling (tε−3/2, xε−1) and follows a fractional heat equation. We also prove the diffusive scal- ing limit of the Riemann invariants - the so called normal modes, corresponding to the linear hyperbolic propagation.en
dc.relation.isversionofjnlnameNonlinearity
dc.relation.isversionofjnlvol29en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2016-02
dc.relation.isversionofdoi10.1088/0951-7715/29/3/962en
dc.relation.isversionofjnlpublisherIOP Publishingen
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-12T12:18:14Z
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