Title :

Travelling fronts in stochastic Stokes' drifts

Author(s) :

Blanchet, Adrien [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Dolbeault, Jean [Auteur]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kowalczyk, Michal [Auteur]

Journal title :

Physica A: Statistical Mechanics and its Applications

Pages :

5741-5751

Publisher :

Elsevier

Publication date :

2008-10

ISSN :

0378-4371

English keyword(s) :

Stochastic Stokes' drift
drift velocity
effective diffusion
ratchet
Brownian motion
molecular motors
transport coherence

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

By analytical methods we study the large time properties of the solution of a simple one-dimensional model of stochastic Stokes' drift. Semi-explicit formulae allow us to characterize the behaviour of the solutions and ...
Show more >By analytical methods we study the large time properties of the solution of a simple one-dimensional model of stochastic Stokes' drift. Semi-explicit formulae allow us to characterize the behaviour of the solutions and compute global quantities such as the asymptotic speed of the center of mass or the effective diffusion coefficient. Using an equivalent tilted ratchet model, we observe that the speed of the center of mass converges exponentially to its limiting value. A diffuse, oscillating front attached to the center of mass appears. The description of the front is given using an asymptotic expansion. The asymptotic solution attracts all solutions at an algebraic rate which is determined by the effective diffusion coefficient. The proof relies on an entropy estimate based on homogenized logarithmic Sobolev inequalities. In the traveling frame, the macroscopic profile obeys to an isotropic diffusion. Compared with the original diffusion, diffusion is enhanced or reduced, depending on the regime. At least in the limit cases, the rate of convergence to the effective profile is always decreased. All these considerations allow us to define a notion of efficiency for coherent transport, characterized by a dimensionless number, which is illustrated on two simple examples of traveling potentials with a sinusoidal shape in the first case, and a sawtooth shape in the second case.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL