Open AccessINVESTIGATION OF THE LARGEST CURRENT IN A RANDOM RESISTOR NETWORK
Author(s) -
Bad Ke-Da,
Jun Xiong
Publication year - 1990
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.39.121
Subject(s) - resistor , exponent , current (fluid) , funnel , dimension (graph theory) , statistical physics , vertex (graph theory) , physics , channel (broadcasting) , topology (electrical circuits) , mathematics , computer science , combinatorics , telecommunications , quantum mechanics , thermodynamics , voltage , graph , philosophy , linguistics , chemistry , organic chemistry
In this paper it is shown that the expected largest current in a random resistor network can be scaled as (InL)α , where L is the size of the network and the exponent a not only depends on dimension and the ratio of two conductances in the network, but also depends on the value of vertex angle β of the defects remarkably. This result follows from an analysis of the funnel configuration with a channel in it. Here we have also suggested a qualitative explanation concerning the difference in the values of exponent α when σ2→0 of Machta et al. and DEL theory.