How local cracks can contribute to the global cracks landscape is a goal of several scientific topics, for example, how bottlenecks can impact the robustness of traffic into a city? In one direction, cracks from cascading failures into networks were generated using a modified Optimal Path-Cracking (OPC) model proposed by Andrade et al \cite{Andrade2009}. In this model, we broke links of maximum energies from optimal paths between two sites with internal (euclidean) distances l in networks with linear size L. Each link of this network has an energy value that scales with a power-law that can be controlled using a parameter of the disorder β. Using finite-size scaling and the exponents from percolation theory we found that the mass of the cracked links on local optimal paths scales with a power-law l0.4 as a separable equation from L and that can be independent of the disorder parameter.
@article{arxiv.2203.08623,
title = {Scaling in Local Optimal Paths Cracks},
author = {Aurelio W. T. de Noronha and Levi R. Leite},
journal= {arXiv preprint arXiv:2203.08623},
year = {2022}
}