TY - JOUR
T1 - Mean-field conductivity in a certain class of networks
AU - Chubynsky, M. V.
AU - Thorpe, Michael
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2005/5
Y1 - 2005/5
N2 - We consider resistor networks, which are lattices with bonds represented by conductors and some of the bonds removed. It is known that effective medium theories predict that the effective conductivity of such networks is a linear function of the number of bonds present above the percolation threshold, but exact results for completely random networks deviate from linearity. We show that if instead we take a randomly chosen tree spanning the lattice and then start adding bonds to it at random, the conductivity changes linearly with the number of added bonds and coincides with the effective medium result for a given bond concentration. We also make comparisons with some related models.
AB - We consider resistor networks, which are lattices with bonds represented by conductors and some of the bonds removed. It is known that effective medium theories predict that the effective conductivity of such networks is a linear function of the number of bonds present above the percolation threshold, but exact results for completely random networks deviate from linearity. We show that if instead we take a randomly chosen tree spanning the lattice and then start adding bonds to it at random, the conductivity changes linearly with the number of added bonds and coincides with the effective medium result for a given bond concentration. We also make comparisons with some related models.
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U2 - 10.1103/PhysRevE.71.056105
DO - 10.1103/PhysRevE.71.056105
M3 - Article
AN - SCOPUS:27144497096
VL - 71
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 5
M1 - 056105
ER -