Show simple item record

dc.contributor.authorBlanchet, Adrien
dc.contributor.authorDolbeault, Jean
dc.contributor.authorKowalczyk, MichaŁ
dc.date.accessioned2016-02-28T06:08:41Z
dc.date.available2016-02-28T06:08:41Z
dc.date.issued2009-01
dc.identifier.citationBlanchet A, Dolbeault J, Kowalczyk M (2009) Stochastic Stokes’ Drift, Homogenized Functional Inequalities, and Large Time Behavior of Brownian Ratchets. SIAM J Math Anal 41: 46–76. Available: http://dx.doi.org/10.1137/080720322.
dc.identifier.issn0036-1410
dc.identifier.issn1095-7154
dc.identifier.doi10.1137/080720322
dc.identifier.urihttp://hdl.handle.net/10754/599738
dc.description.abstractA periodic perturbation of a Gaussian measure modifies the sharp constants in Poincarae and logarithmic Sobolev inequalities in the homogeniz ation limit, that is, when the period of a periodic perturbation converges to zero. We use variational techniques to determine the homogenized constants and get optimal convergence rates toward s equilibrium of the solutions of the perturbed diffusion equations. The study of these sharp constants is motivated by the study of the stochastic Stokes' drift. It also applies to Brownian ratchets and molecular motors in biology. We first establish a transport phenomenon. Asymptotically, the center of mass of the solution moves with a constant velocity, which is determined by a doubly periodic problem. In the reference frame attached to the center of mass, the behavior of the solution is governed at large scale by a diffusion with a modified diffusion coefficient. Using the homogenized logarithmic Sobolev inequality, we prove that the solution converges in self-similar variables attached to t he center of mass to a stationary solution of a Fokker-Planck equation modulated by a periodic perturbation with fast oscillations, with an explicit rate. We also give an asymptotic expansion of the traveling diffusion front corresponding to the stochastic Stokes' drift with given potential flow. © 2009 Society for Industrial and Applied Mathematics.
dc.description.sponsorshipThis author’s research was partially supported by the KAUST investigator award.This author’s research was partially supported by FONDECYT 1050311, Nucleo Milenio P04-069-F, FONDAP, and ECOSCONYCIT# C05E05.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectAsymptotic expansion
dc.subjectBrownian ratchets
dc.subjectContraction
dc.subjectDoubly periodic equation
dc.subjectEffective diffusion
dc.subjectFokker-planck equation
dc.subjectIntermediate asymptotics
dc.subjectMolecular motors
dc.subjectMoment estimates
dc.subjectStochastic stokes' drift
dc.subjectTransport
dc.subjectTraveling front
dc.subjectTraveling potential
dc.titleStochastic Stokes' Drift, Homogenized Functional Inequalities, and Large Time Behavior of Brownian Ratchets
dc.typeArticle
dc.identifier.journalSIAM Journal on Mathematical Analysis
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
dc.contributor.institutionCentre de Recherche en Mathematiques de la Decision, Paris, France
dc.contributor.institutionUniversidad de Chile, Santiago, Chile


This item appears in the following Collection(s)

Show simple item record