On the Bulk Velocity of Brownian Ratchets

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

Proceedings of the 10th Australasian Heat and Mass Transfer Conference (AHMT2016)

Proceedings of The 10th Australasian Heat and Mass Transfer Conference (AHMT2016). The proceedings contain the selected full-length papers from the 10th Australasian Conference of Heat and Mass Transfer held in Brisbane, Australia on 14-15 July 2016. The conference was organised by Queensland University of Technology under the auspices of the Australasian Fluid and Thermal Engineering Society (AFTES) of Engineers Australia. Scientifically, these collected articles reflect recent progress made in heat and mass transfer in the Australasian community, including both fundamental and applied topics in the broad areas of convection, conduction, radiation, turbulence, multi-phase flow, combustion, drying, heat exchangers, phase change, computational methods, experimental methods, and other significant thermal processes in environmental, industrial, and process engineering. All the papers published in this volume were reviewed under a rigorous review process, where at least two reviews were received for each paper, according to the HERDC standard. The Organizing Committee is grateful to all of the contributors who made this volume possible. We would like to express our sincere appreciation to all authors and reviewers for their excellent contributions as well as the AHMT2016 scientific committee and financial support provided by Queensland University of Technology and Engineers Australi