Anomalous diffusion with log-periodic modulation in a selected time interval
arXiv:1012.4112 · doi:10.1103/PhysRevE.83.020105
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.
4 pages, 5 figures
References in corpus (4)
- Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
- On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals
- Log-periodic modulation in one-dimensional random walks
- Log-periodic oscillations for diffusion on self-similar finitely ramified structures