Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions

Details Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions

2010-01-17

arxiv.org/abs/1001.2880v1

J. Stat. Mech. (2010) L05001

Physics

Condensed Matter

Statistical Mechanics

15pages, 5figures

Scientific paper

10.1088/1742-5468/2010/05/L05001

We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square displacement versus time generated here show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. In addition, it is found that the distribution of displacement agrees to a reliable precision with the q-Gaussian type distribution in some cases and bimodal distribution in some other cases. The results obtained show that the self-similar motion may be used to describe the anomalous diffusion and nonextensive statistical distributions.

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