Remarks about the flashing rachet. (English) Zbl 1064.35065

Dolbeault, Jean; Kinderlehrer, David; Kowalczyk, Michał

Conca, Carlos (ed.) et al., Partial differential equations and inverse problems. Proceedings of the Pan-American Advanced Studies Institute on partial differential equations, nonlinear analysis and inverse problems, Santiago, Chile, January 6–18, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3448-7/pbk). Contemporary Mathematics 362, 167-175 (2004).

Summary: The flashing rachet is the simplest example of diffusion mediated transport as well as the suggested mechanism for a class of protein motors. Here the authors briefly explain these concepts and give an entropy based argument for existence and uniqueness of a model problem. They also examine the features of the system that lead to transport.
For the entire collection see [Zbl 1052.35004].

MSC:

35K05	Heat equation
35B10	Periodic solutions to PDEs
35R05	PDEs with low regular coefficients and/or low regular data
35K15	Initial value problems for second-order parabolic equations
35K20	Initial-boundary value problems for second-order parabolic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
94A17	Measures of information, entropy
28D20	Entropy and other invariants
65Z05	Applications to the sciences

Keywords:

Brownian motors; molecular ratchets; mass transfer problem; Wasserstein distance; diffusion-transport cooperation; Schauder theorem; entropy; logarithmic Sobolev inequality

Software:

RACHET