S. Molchanov, B. Vainberg
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drift. The study is based on an application of the Bloch decomposition. The effective drift and effective diffusivity are expressed in terms of the principal eigenvalue of the Bloch spectral problem on the cell of periodicity. We apply the formulas for the effective parameters to study the motion in periodic tubes with nearly separated dead zones.
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http://arxiv.org/abs/1304.6790
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