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

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...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-02, Vol.83 (2 Pt 1), p.020105-020105, Article 020105
Hauptverfasser: Padilla, L, Mártin, H O, Iguain, J L
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.83.020105