TUTCRIS - Tampereen teknillinen yliopisto

TUTCRIS

Comb Model with Slow and Ultraslow Diffusion

Tutkimustuotosvertaisarvioitu

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut18-33
Sivumäärä16
JulkaisuMathematical Modelling of Natural Phenomena
Vuosikerta11
Numero3
DOI - pysyväislinkit
TilaJulkaistu - 2016
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

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.

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