Voltage distribution in growing conducting networks |
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Authors: | B Tadić V Priezzhev |
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Institution: | (1) Jožef Stefan Institute, PO Box 3000, 1001 Ljubljana, Slovenia, SI;(2) Bogolubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, 141980 Dubna, Russia, RU |
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Abstract: | We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the
current through the emergent conducting graph, representing a digital circuit. In the interior of a large network the voltage
varies with the addition time s < t of the node as V(s) ∼ ln(s)/s
θ when constant current enters the network at last added node t and leaves at the root of the graph which is grounded. The topological closeness of the conduction path and shortest path
through a node suggests that the charged random walk determines these global graph properties by using only local search algorithms. The results agree with mean-field theory on tree structures, while the numerical method is applicable
to graphs of any complexity.
Received 26 August 2002 Published online 29 November 2002 |
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Keywords: | PACS 89 75 Hc Networks and genealogical trees – 05 40 Fb Random walks and Levy flights – 89 20 -a Interdisciplinary applications of physics |
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