Fracturing the optimal paths

Abstract

Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is activated once this optimal path fails and what happens when this new path also fails and so on, until the system is completely disconnected. In fact numerous applications can be found for this novel fracture problem. In the limit of strong disorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension $D_b\approx 1.22$. For weak disorder, the number of cracks spreads all over the entire network before global connectivity is lost. Strikingly, the disconnecting path (backbone) is, however, completely independent on the disorder.

4 pages,4 figures

Cited by in corpus (23)

• Recent advances in percolation theory and its applications
• Fracturing highly disordered materials
• Watersheds are Schramm-Loewner Evolution curves
• Fracturing ranked surfaces
• Gaussian model of explosive percolation in three and higher dimensions
• Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
• Optimal path cracks in correlated and uncorrelated lattices
• Current challenges for preseismic electromagnetic emissions: shedding light from micro-scale plastic flow, granular packings, phase transitions and self-affinity notion of fracture process
• Impact of Perturbations on Watersheds
• Scaling Relations for Watersheds
• A universal approach for drainage basins
• Multi-scale approach to invasion percolation of rock fracture networks
• Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
• Stacked triangular lattice: Percolation properties
• A percolation model with continuously varying exponents
• Watersheds and Explosive percolation
• Exact evaluation of the cutting path length in a percolation model on a hierarchical network
• Cracking urban mobility
• Loop erased random walk on percolation cluster: Crossover from Euclidean to fractal geometry
• Invasion Percolation with a Hardening Interface under Gravity
• Loop erased random walk on a percolation cluster is compatible with Schramm-Loewner evolution
• Cost of material or information flow in complex transportation networks
• Vulnerability of Transport through Evolving Spatial Networks