The flashing ratchet and unidirectional transport of matter

Dmitry Vorotnikov

doi:10.3934/dcdsb.2011.16.963

Article Contents

2011, Volume 16, Issue 3: 963-971. Doi: 10.3934/dcdsb.2011.16.963

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The flashing ratchet and unidirectional transport of matter

Dmitry Vorotnikov^1,

1.
CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra

Received: June 30, 2010

Revised: February 28, 2011

Published: September 2011

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Abstract

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor indeed performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.

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Mathematics Subject Classification: 35B10, 35Q84, 60J10, 60J70, 82C70.

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