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Effective transport equations in quasi 1D systems

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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.

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Authors and Affiliations

  1. Institute of Physics, Slovak Academy of Sciences, Dúbravská c. 9, 84511, Bratislava, Slovakia

    P. Kalinay

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  1. P. Kalinay
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Kalinay, P. Effective transport equations in quasi 1D systems. Eur. Phys. J. Spec. Top. 223, 3027–3043 (2014). https://doi.org/10.1140/epjst/e2014-02317-5

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  • DOI: https://doi.org/10.1140/epjst/e2014-02317-5

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