Regensburg 2010 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Anomalous Transport II (talks contributed by DY)
DY 17.1: Vortrag
Mittwoch, 24. März 2010, 11:15–11:30, H38
Anomalous lateral diffusion in a layered medium — •Eugene B. Postnikov1 and Igor M. Sokolov2 — 1Staatliche 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+Dy∂yyu |
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 Dy ∼ y2, 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].