Numerical Investigation of Superslow Diffusion Laws for a Certain Class of Continuous-time Random Walks

Authors Yu.S. Bystrik

Sumy State University, 2, Rimsky Korsakov St., 40007 Sumy, Ukraine

Issue Volume 8, Year 2016, Number 1
Dates Received 15 January 2016; published online 20 March 2016
Citation Yu.S. Bystrik, J. Nano- Electron. Phys. 8 No 1, 01044 (2016)
DOI 10.21272/jnep.8(1).01044
PACS Number(s) 05.40.Fb, 02.50.Ey
Keywords Anomalous diffusion, Continuous-time random walks, Superheavy-tailed probability densities.
Annotation Using the continuous-time random walk theory we investigate the phenomenon of anomalous superslow diffusion for which the variance of the particle position increases slowly than any positive power of time. This type of diffusion emerges in the case when the probability densities of the waiting times between the successive jumps characterized by the superheavy tails with infinite moments of any fractional order. We propose a numerical method to study the behavior of the diffusion laws and show that our numerical results are in very good agreement with the theoretical predictions.

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