Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
Statistical Mechanics
2012-07-31 v2 Computational Physics
Abstract
We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, in 2D and in 3D, and the same exponent of the leading correction, and , respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and bridge lines are further supported by either heuristic or exact arguments.
Keywords
Cite
@article{arxiv.1203.3038,
title = {Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines},
author = {E. Fehr and K. J. Schrenk and N. A. M. Araújo and D. Kadau and P. Grassberger and J. S. Andrade and H. J. Herrmann},
journal= {arXiv preprint arXiv:1203.3038},
year = {2012}
}