Comb Model with Slow and Ultraslow Diffusion
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Details
| Original language | English |
|---|---|
| Pages (from-to) | 18-33 |
| Number of pages | 16 |
| Journal | Mathematical Modelling of Natural Phenomena |
| Volume | 11 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2016 |
| Publication type | A1 Journal article-refereed |
Abstract
We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze 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.
ASJC Scopus subject areas
Keywords
- Anomalous diffusion, Comb-like model, Mean squared displacement, Probability density function