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Comb Model with Slow and Ultraslow Diffusion
- 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.
| Author details: | T. Sandev, Alexander IominORCiD, Holger KantzORCiD, Ralf MetzlerORCiDGND, Aleksei V. ChechkinORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1051/mmnp/201611302 |
| ISSN: | 0973-5348 |
| ISSN: | 1760-6101 |
| Title of parent work (English): | Mathematical modelling of natural phenomena |
| Publisher: | EDP Sciences |
| Place of publishing: | Les Ulis |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2016 |
| Publication year: | 2016 |
| Release date: | 2020/03/22 |
| Tag: | anomalous diffusion; comb-like model; mean squared displacement; probability density function |
| Volume: | 11 |
| Number of pages: | 16 |
| First page: | 18 |
| Last Page: | 33 |
| Funding institution: | Israel Science Foundation [ISF-1028]; Academy of Finland within the Finland Distinguished Professor programme |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
