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 and 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 and 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.
Cite
@article{arxiv.1512.07781,
title = {Comb model with slow and ultraslow diffusion},
author = {Trifce Sandev and Alexander Iomin and Holger Kantz and Ralf Metzler and Aleksei Chechkin},
journal= {arXiv preprint arXiv:1512.07781},
year = {2016}
}