Mapping of forced diffusion in quasi-one-dimensional systems

Pavol Kalinay
Phys. Rev. E 80, 031106 – Published 4 September 2009

Abstract

Diffusion in an external potential in a two-dimensional channel of varying cross section is considered. We show that a rigorous mapping procedure applied on the corresponding Smoluchowski equation yields a one-dimensional evolution equation of the Fick-Jacobs type corrected by an effective coefficient D(x). The procedure enables us to derive this function within a recurrence scheme. We test this result on a model of stationary diffusion in a linear cone in a homogeneous potential, which is exactly solvable. Extension of the approximate formulas for D(x) derived for the diffusion alone is discussed.

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  • Received 16 June 2009

DOI:https://doi.org/10.1103/PhysRevE.80.031106

©2009 American Physical Society

Authors & Affiliations

Pavol Kalinay

  • Institute of Physics, Slovak Academy of Sciences, Dúbravska Cesta 9, 84511 Bratislava, Slovakia

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Vol. 80, Iss. 3 — September 2009

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