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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• Finite-velocity diffusion on a comb
• Ergodic property of random diffusivity system with trapping events
• Interplay between particle trapping and heterogeneity in anomalous diffusion
• Exact first-passage time distributions for three random diffusivity models
• Probability distribution functions of sub- and super-diffusive systems
• Anomalous diffusion and FRAP dynamics in the random comb model
• Generalised Diffusion and Wave Equations: Recent Advances
• Local equilibrium properties of ultraslow diffusion in the Sinai model
• Relations between anomalous diffusion and fluctuation scaling: The case of ultraslow diffusion and time-scale-independent fluctuation scaling in language