Log-periodic Oscillations for Biased Diffusion in 3D Random Lattices

TL;DR

This paper investigates how biased random walks on 3D percolation lattices exhibit log-periodic oscillations in diffusion behavior, highlighting the interplay of bias and dilution effects.

Contribution

It introduces a scaling argument explaining the emergence of log-periodic oscillations in biased diffusion on 3D lattices, emphasizing the combined role of bias and dilution.

Findings

Log-periodic oscillations observed in effective exponents over time.

Scaling argument successfully explains the numerical results.

Log-periodicity dominates over previously predicted anomalous diffusion effects.

Abstract

Random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log-periodic oscillations in the effective exponent versus time. A scaling argument accounts for the numerical results in the limit of large biases and small dilution and shows the importance of the interplay of these two ingredients in the generation of the log-periodicity. These results show that log-periodicity is the dominant effect compared to previous predictions of and reports on anomalous diffusion.