Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines

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, $d_f=1.2168\pm 0.0005$ in 2D and $d_f=2.487\pm 0.003$ in 3D, and the same exponent of the leading correction, $\Omega =0.9\pm 0.1$ and $\Omega =1.0\pm 0.1$, 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.

References in corpus (12)

• Explosive percolation via control of the largest cluster
• Correction-to-scaling exponents for two-dimensional self-avoiding walks
• Fracturing the optimal paths
• Fracturing ranked surfaces
• Gaussian model of explosive percolation in three and higher dimensions
• Correction-to-scaling exponent for two-dimensional percolation
• Optimal path cracks in correlated and uncorrelated lattices
• Abelian Manna model on various lattices in one and two dimensions
• New efficient methods to calculate watersheds
• Impact of Perturbations on Watersheds
• Scaling Relations for Watersheds
• Multiple Invaded Consolidating Materials

Cited by in corpus (11)

• Recent advances in percolation theory and its applications
• Recent advances and open challenges in percolation
• Percolation with long-range correlated disorder
• Watersheds are Schramm-Loewner Evolution curves
• Stacked triangular lattice: Percolation properties
• How to share underground reservoirs
• Exact evaluation of the cutting path length in a percolation model on a hierarchical network
• Retention capacity of correlated surfaces
• Loop erased random walk on percolation cluster: Crossover from Euclidean to fractal geometry
• Dynamical Crossover in Invasion Percolation
• Vulnerability of Transport through Evolving Spatial Networks