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The European Physical Journal Special Topics

, Volume 223, Issue 14, pp 3027–3043 | Cite as

Effective transport equations in quasi 1D systems

Review
Part of the following topical collections:
  1. Brownian Motion in Confined Geometries. Guest Editors: S.M. Bezrukov, L. Schimansky-Geier and G. Schmid (Eds.)

Abstract

The mapping methods reducing 2D or 3D transport equations in quasi 1D structures onto the longitudinal coordinate x are revisited. The general formalism based on homogenization is explained on the simplest case, diffusion in a 2D channel of varying width A(x). Then its modifications to diffusion in an external field (Smoluchowski equation), and nonzero mass of the particles (Klein-Kramers equation) are demonstrated. A special attention is payed to the role of the “natural” curvilinear coordinates, connected with the stationary flow, in the mapping and derivation of the effective equations.

Keywords

European Physical Journal Special Topic Stochastic Resonance Mapping Procedure Boundary Condition Smoluchowski Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Institute of PhysicsSlovak Academy of SciencesBratislavaSlovakia

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