منابع مشابه
Fracturing the optimal paths.
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 appli...
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Let G be a connected graph of chromatic number k. For a k-coloring f of G, a full f -rainbow path is a path of order k in G whose vertices are all colored differently by f . We show that G has a k-coloring f such that every vertex of G lies on a full f -rainbow path, which provides a positive answer to a question posed by Lin (Simple proofs of results on paths representing all colors in proper ...
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We study the statistical properties of optimal paths in weighted complex networks with general distribution of weights. We find a general criterion for the strength of disorder and show the relation of optimal paths properties to percolation, in both strong and weak disorder limits. Transport in weighted networks is dominated by the minimum spanning tree (MST), the tree connecting all nodes wit...
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A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transfo...
متن کاملar X iv : 0 90 9 . 02 53 v 1 [ co nd - m at . d is - n n ] 1 S ep 2 00 9 Fracturing the optimal paths
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 a...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2009
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.103.225503