Comb model with slow and ultraslow diffusion

Abstract

We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both $x$ and $y$ directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.

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Cited by in corpus (13)

• Universal spectral features of different classes of random diffusivity processes
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Lévy processes on a generalized fractal comb
• Quenched and Annealed Disorder Mechanisms in Comb-Models with Fractional Operators
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