Voltage distribution in growing conducting networks
Jožef Stefan Institute, PO Box 3000, 1001 Ljubljana, Slovenia
2 Bogolubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, 141980 Dubna, Russia
Corresponding author: a Bosiljka.Tadic@ijs.si
Published online: 29 November 2002
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 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.
PACS: 89.75.Hc – Networks and genealogical trees / 05.40.Fb – Random walks and Levy flights / 89.20.-a – Interdisciplinary applications of physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002