TY - JOUR

T1 - Series analysis of randomly diluted nonlinear resistor networks

AU - Meir, Yigal

AU - Blumenfeld, Raphael

AU - Aharony, Amnon

AU - Harris, A. Brooks

PY - 1986

Y1 - 1986

N2 - The behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is V=rI±, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance R between pairs of sites separated by the percolation correlation length, scales as p-pc-(±). The exponent (±) was evaluated for 0<±< and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at ±=0, via that of the linear resistance, at ±=1, to the exponent characterizing the singly connected bonds, 3/4(z)1. Our results agree with known results for ±=0 and ±=1, also with recent results for general ± at d=6- dimensions. The second moment R2 was found to diverge as R2 (for all ± and d), indicating a scaling form for the probability distribution of R.

AB - The behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is V=rI±, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance R between pairs of sites separated by the percolation correlation length, scales as p-pc-(±). The exponent (±) was evaluated for 0<±< and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at ±=0, via that of the linear resistance, at ±=1, to the exponent characterizing the singly connected bonds, 3/4(z)1. Our results agree with known results for ±=0 and ±=1, also with recent results for general ± at d=6- dimensions. The second moment R2 was found to diverge as R2 (for all ± and d), indicating a scaling form for the probability distribution of R.

UR - http://www.scopus.com/inward/record.url?scp=0001477922&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.34.3424

DO - 10.1103/PhysRevB.34.3424

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AN - SCOPUS:0001477922

SN - 0163-1829

VL - 34

SP - 3424

EP - 3428

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

IS - 5

ER -