Abstract
We study the superlinear diffusion 〈x 2(t) 〉 ∼t α,α > 1, in layered media containing random velocity fields. The superlinear behavior holds in the case of random velocities along thex direction accompanied by diffusional motion in the space transverse to it. The transverse space can be either Euclidean, fractal, or ultrametric. For a one-dimensional transverse space we derive exact expressions for the higher moments of the displacement. Furthermore, we investigate the propagatorP(x, t) along thex direction and establish its scaling behavior. Our analysis highlights the resemblance between the stretched-Gaussian behavior of the propagator and the stretched-exponential form of the survivial probability in the trapping problem; both show late crossover behavior.
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This work is dedicated to Prof. George H. Weiss.
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Zumofen, G., Klafter, J. & Blumen, A. Trapping aspects in enhanced diffusion. J Stat Phys 65, 991–1013 (1991). https://doi.org/10.1007/BF01049594
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DOI: https://doi.org/10.1007/BF01049594