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June 2007 Self-induced stochastic resonance for Brownian ratchets under load
R. E. Lee DeVille, Eric Vanden-Eijnden
Commun. Math. Sci. 5(2): 431-466 (June 2007).


We consider a Brownian ratchet model where the particle on the ratchet is coupled to a cargo. We show that in a distinguished limit where the diffusion coefficient of the cargo is small, and the amplitude of thermal fluctuations is small, the system becomes completely coherent: the times at which the particle jumps across the teeth of the ratchet become deterministic. We also show that the dynamics of the ratchet-cargo system do not depend on the fine structure of the Brownian ratchet. These results are relevant in the context of molecular motors transporting a load, which are often modeled as a ratchet-cargo compound. They explain the regularity of the motor gait that has been observed in numerical experiments, as well as justify the coarsening into Markov jump processes which is commonly done in the literature.


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R. E. Lee DeVille. Eric Vanden-Eijnden. "Self-induced stochastic resonance for Brownian ratchets under load." Commun. Math. Sci. 5 (2) 431 - 466, June 2007.


Published: June 2007
First available in Project Euclid: 9 July 2007

zbMATH: 1134.60350
MathSciNet: MR2334850

Primary: 34E13 , 60F10 , 60G35 , 60H10 , 92C10

Keywords: Brownian ratchets , molecular motors , self-induced stochastic resonance , Stochastic resonance

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 2 • June 2007
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