On the bulk velocity of brownian ratchets

Stanislav Kondratyev, José Miguel Urbano, Dmitry Vorotnikov

Research output: Contribution to journalArticlepeer-review


In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker-Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential.
Original languageEnglish (US)
Pages (from-to)950-980
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Issue number2
StatePublished - Jan 1 2016
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • General Computer Science


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