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arXiv · 1012.4112

Anomalous diffusion with log-periodic modulation in a selected time interval

L. Padilla·H. O. Mártin·J. L. Iguain
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Abstract

On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the modulating oscillations are washed out but subdiffusion remains as in the perfect self-similar case. Also, if disorder distribution is appropriately chosen the oscillations are localized in a selected time interval. Both the overall random walk exponent and the period of the oscillations are analytically obtained and confirmed by Monte Carlo simulations.

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L. Padilla, H. O. Mártin, J. L. Iguain. 2010-12-18. Anomalous diffusion with log-periodic modulation in a selected time interval. https://doi.org/10.1103/physreve.83.020105

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