Abstract
We consider correlated Lévy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter , playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a single-long-jump approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution as a function of and of the dynamic exponent associated with the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated Lévy-walk models.
4 More- Received 4 May 2011
DOI:https://doi.org/10.1103/PhysRevE.84.021105
©2011 American Physical Society