Fracturing the Optimal Paths

J. S. Andrade, E. A. Oliveira, A. A. Moreira, H. J. Herrmann
2009 Physical Review Letters  
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
more » ... sorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension D_b≈ 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.
doi:10.1103/physrevlett.103.225503 pmid:20366106 fatcat:rlkracgqsjdt3nqdqoh7lzqvga