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arXiv · 1610.06686

Current Redistribution in Resistor Networks: Fat-Tail Statistics in Regular and Small-World Networks

Jörg Lehmann·Jakob Bernasconi
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Abstract

The redistribution of electrical currents in resistor networks after single-bond failures is analyzed in terms of current-redistribution factors that are shown to depend only on the topology of the network and on the values of the bond resistances. We investigate the properties of these current-redistribution factors for regular network topologies (e.g. $d$-dimensional hypercubic lattices) as well as for small-world networks. In particular, we find that the statistics of the current redistribution factors exhibits a fat-tail behavior, which reflects the long-range nature of the current redistribution as determined by Kirchhoff's circuit laws.

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Jörg Lehmann, Jakob Bernasconi. 2017-02-10. Current Redistribution in Resistor Networks: Fat-Tail Statistics in Regular and Small-World Networks. https://doi.org/10.1103/physreve.95.032310

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