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
M3 - מאמר
AN - SCOPUS:0001477922
VL - 34
SP - 3424
EP - 3428
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
SN - 1098-0121
IS - 5
ER -