Geodesic
Comb Model with Slow and Ultraslow Diffusion
T. Sandev 1 ,  2   ; A. Iomin 3   ; H. Kantz 1   ; R. Metzler 4 ,  5   ; A. Chechkin 1 ,  6 ,  7
1 Max Planck Institute for the Physics of Complex Systems Nöthnitzer Strasse 38, 01187 Dresden, Germany
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
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 18-33 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/mmnp/201611302

T. Sandev  1 , 2   ; A. Iomin  3   ; H. Kantz  1   ; R. Metzler  4 , 5   ; A. Chechkin  1 , 6 , 7

1 Max Planck Institute for the Physics of Complex Systems Nöthnitzer Strasse 38, 01187 Dresden, Germany
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 
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T. Sandev; A. Iomin; H. Kantz; R. Metzler; A. Chechkin. Comb Model with Slow and Ultraslow Diffusion. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 18-33. doi: 10.1051/mmnp/201611302

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