Date
2002
Publisher city
Paris
Publisher
Université Paris-Dauphine
Collection title
Cahiers du Ceremade
Collection Id
44
Dewey
Analyse
Sujet
diffusion-transport cooperation; phase diagram; Galerkin scheme; numerical methods for diff usions; Poincaré inequality; logarithmic Sobolev inequality; uniqueness; long time behaviour; attractor; entropy; Schauder Theorem; fixed-point methods; time-periodic solutions; mass-spring-dashpot system; minimum energy dissipation principle; steepest descent; gradient flow; Monge-Ampère equation; transfer function; Wasserstein distance; mass transfer problem; molecular ratchets; Brownian motors; flashing ratchet; Linear parabolic equations
Author
Dolbeault, Jean
Kinderlehrer, David
Kowalczyk, Michal
Type
Document de travail / Working paper
Item number of pages
19
Abstract (EN)
The 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.
