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Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Anomalous Transport II (talks contributed by DY)

DY 17.1: Talk

Wednesday, March 24, 2010, 11:15–11:30, H38

Anomalous lateral diffusion in a layered medium — •Eugene B. Postnikov1 and Igor M. Sokolov21Staatliche Universität Kursk, Russland — 2Institut für Physik Humboldt - Universität zu Berlin, Deutschland

We consider the marker’s diffusion in a layered medium, with the lateral diffusion coefficient being the function y-coordinate, i.e. the problem described by the diffusion equation for the marker density u(x,y,t)

t u=Dx(y)∂xxu+Dyyyu

with anisotropic diffusion coefficient D. We show that the mean density averaged over the height, U(x,t), follows the Bachelor’s one-dimensional diffusion equation with time-dependent diffusion coefficient

t U=Dx(t)∂xxU

and obtain the expression of Dx(t). As an example, we discuss the exact analytical solution in the case of a parabolic distribution Dyy2, leading to the anomalous (superdiffusive) behavior of a mean-square displacement <x2>∝ t3/2. This result is confirmed by the numerical solution.

The approach is applied for the continual description of experimental results on inhomogeneous molecular diffusion in layered structures of thin liquid films deposited on solid surfaces [J. Schuster, F. Cichos, C. von Borzcyskowski. Eur. Polym. J. 40 (2004) 993].

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