Effective transport equations in quasi 1D systems
Institute of Physics, Slovak Academy of Sciences, Dúbravská c. 9, 84511 Bratislava, Slovakia
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Received: 17 October 2014
Revised: 5 November 2014
Published online: 15 December 2014
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.
© EDP Sciences, Springer-Verlag, 2014