On mathematical foundation of the Brownian motor theory

被引：0

作者：

Koralov, L. ^{[1
]}

Molchanov, S. ^{[2
]}

Vainberg, B. ^{[2
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ N Carolina, Dept Math Stat, Charlotte, NC 28223 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 06期

基金：

美国国家科学基金会;

关键词：

Brownian motors; Effective drift; Effective diffusivity; Bloch decomposition; HOMOGENIZATION; COEFFICIENTS; TRANSPORT; SYSTEMS; CHANNEL;

D O I：

10.1016/j.jfa.2014.06.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 as well as in terms of the harmonic coordinate and the density of the invariant measure. We apply the formulas for the effective parameters to study the motion in periodic tubes with nearly separated dead zones. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1725 / 1750

页数：26

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