Math. Model. Nat. Phenom.
Volume 11, Number 3, 2016Anomalous diffusion
|Page(s)||18 - 33|
|Published online||21 June 2016|
Comb Model with Slow and Ultraslow Diffusion
1 Max Planck Institute for the Physics
of Complex Systems Nöthnitzer Strasse 38, 01187
2 Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
3 Department of Physics, Technion, Haifa 32000, Israel
4 Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany
5 Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland
6 Akhiezer Institute for Theoretical Physics, Kharkov 61108, Ukraine
7 Department of Physics and Astronomy, University of Padova, “Galileo Galilei” - DFA 35131 Padova, Italy
⋆ Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 87.19.L- / 05.40.Fb / 82.40.-g
Key words: comb-like model / anomalous diffusion / mean squared displacement / probability density function
© EDP Sciences, 2016
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