Destruction of ultra-slow diffusion in a three dimensional cylindrical comb structure

2015/08/21 by Alexander Iomin, Iomin, A., Vicenç Méndez +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Fractional Differential Equations Solutions #Soft Condensed Matter (cond-mat.soft) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1508.05262

openalex publication_date 2015/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present a rigorous result on ultra-slow diffusion by solving a Fokker-Planck equation, which describes anomalous transport in a three dimensional (3D) comb. This 3D cylindrical comb consists of a cylinder of discs threaten on a backbone. It is shown that the ultra-slow contaminant spreading along the backbone is described by the mean squared displacement (MSD) of the order of ln (t). This phenomenon takes place only for normal two dimensional diffusion inside the infinite secondary branches (discs). When the secondary branches have finite boundaries, the ultra-slow motion is a transient process and the asymptotic behavior is normal diffusion. In another example, when anomalous diffusion takes place in the secondary branches, a destruction of ultra-slow (logarithmic) diffusion takes place as well. As the result, one observes "enhanced" subdiffusion with the MSD ∼ t^1-αln t, where 0

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