Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
Phys Rev Lett. 2009 Nov 27;103(22):225503. doi: 10.1103/PhysRevLett.103.225503. Epub 2009 Nov 25.
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 many applications can also 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) approximately = 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.
最优路径在从无规聚合物到脆性断裂、从多孔介质中的流动到信息传播等众多物理应用中起着至关重要的作用。在这里，我们首次探索了当最优路径失效后被激活的路径，以及当这条新路径也失效时会发生什么，以此类推，直到系统完全断开。事实上，这种新的断裂问题也可以在许多应用中找到。在强无序的极限下，我们的结果表明，所有的裂缝都位于一个单一的自相似连通线上，分形维数 D(b)约等于 1.22。对于弱无序，在全局连通性丧失之前，裂缝的数量会扩散到整个网络。引人注目的是，断开路径（骨干）完全独立于无序。
