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dc.contributor.authorDolbeault, Jean
dc.contributor.authorKinderlehrer, David
dc.contributor.authorKowalczyk, Michal
dc.date.accessioned2011-08-30T14:06:10Z
dc.date.available2011-08-30T14:06:10Z
dc.date.issued2002
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6893
dc.language.isoenen
dc.subjectdiffusion-transport cooperationen
dc.subjectphase diagramen
dc.subjectGalerkin schemeen
dc.subjectnumerical methods for diff usionsen
dc.subjectPoincaré inequalityen
dc.subjectlogarithmic Sobolev inequalityen
dc.subjectuniquenessen
dc.subjectlong time behaviouren
dc.subjectattractoren
dc.subjectentropyen
dc.subjectSchauder Theoremen
dc.subjectfixed-point methodsen
dc.subjecttime-periodic solutionsen
dc.subjectmass-spring-dashpot systemen
dc.subjectminimum energy dissipation principleen
dc.subjectsteepest descenten
dc.subjectgradient flowen
dc.subjectMonge-Ampère equationen
dc.subjecttransfer functionen
dc.subjectWasserstein distanceen
dc.subjectmass transfer problemen
dc.subjectmolecular ratchetsen
dc.subjectBrownian motorsen
dc.subjectflashing ratcheten
dc.subjectLinear parabolic equationsen
dc.subject.ddc515en
dc.titleThe flashing ratchet: long time behavior and dynamical systems interpretationen
dc.typeDocument de travail / Working paper
dc.description.abstractenThe flashing ratchet is a model for certain types of molecular motors as well as a convenient model problem in the more general context of diffusion mediated transport. In this paper we show that it can be derived using a minimum energy dissipation principle for transport in a viscous environment. We then study the long time behavior of the flashing ratchet model. By entropy methods, we prove the existence of periodic solutions which are global attractors for the dynamics, with an exponential rate. Large time qualitative behaviour and especially mass accumulation are then investigated from a numerical point of view. For that purpose, we introduce a numerical method based on the minimum energy dissipation principle, which allows us to reduce the problem to a simple dynamical system.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages19en
dc.relation.ispartofseriestitleCahiers du Ceremadeen
dc.relation.ispartofseriesnumber44en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen


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