Anisotropic anomalous diffusion modulated by log-periodic oscillations

Abstract

We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites, where the diffusion of a single random walk presents an anomalous {\it anisotropic} behavior modulated by log-periodic oscillations. The anisotropy is revealed by two different random walk exponents, ${\nu }_x$ and ${\nu }_y$, in the {\it x} and {\it y} direction, respectively. The values of these exponents, as well as the period of the oscillation, are analytically obtained and confirmed by Monte Carlo simulations.

7 pages, 7 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

Cited by in corpus (2)

• Local Einstein relation for fractals
• Universal behavior for single-file diffusion on a disordered fractal