Self-Affinity in the Gradient Percolation Problem
Disordered Systems and Neural Networks
2013-05-29 v2 Statistical Mechanics
Abstract
We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self affine with a Hurst exponent equal to 2/3 up to a cutoff-length proportional to the gradient to the power (-4/7). Beyond this length scale, the front position has the character of uncorrelated noise. Importantly, the self-affine behavior is robust even after removing local jumps of the front. The previously observed multi affinity, is due to the dominance of overhangs at small distances in the structure function. This is a crossover effect.
Keywords
Cite
@article{arxiv.cond-mat/0511545,
title = {Self-Affinity in the Gradient Percolation Problem},
author = {Alex Hansen and G. George Batrouni and Thomas Ramstad and Jean Schmittbuhl},
journal= {arXiv preprint arXiv:cond-mat/0511545},
year = {2013}
}
Comments
4 pages, 4 figures