TY - JOUR

T1 - Nonlinear resistor fractal networks, topological distances, singly connected bonds and fluctuations

AU - Blumenfeld, Rafael

AU - Aharony, Amnon

PY - 1985/6/1

Y1 - 1985/6/1

N2 - We consider a fractal network of nonlinear resistors, with the voltage V behaving as a power of;he current I, V= RIα. The resistance between two points at a distance L is R(L)δ Lξ(α). We prove that ξ(δ) describes the scaling of the topological-chemical distance, while i(m) describes that of the number of singly connected ‘red’ bonds. -For random resistors, y e also consider the width of the resistance distribution, ΔRδ Lξ2(α). Values for ξ and ξ2 are explicitly derived for two model fractals, and ΔR/R is found to grow with L for the Sierpinski gasket and a > 1.612. The relevance of the results to percolation clusters is discussed.

AB - We consider a fractal network of nonlinear resistors, with the voltage V behaving as a power of;he current I, V= RIα. The resistance between two points at a distance L is R(L)δ Lξ(α). We prove that ξ(δ) describes the scaling of the topological-chemical distance, while i(m) describes that of the number of singly connected ‘red’ bonds. -For random resistors, y e also consider the width of the resistance distribution, ΔRδ Lξ2(α). Values for ξ and ξ2 are explicitly derived for two model fractals, and ΔR/R is found to grow with L for the Sierpinski gasket and a > 1.612. The relevance of the results to percolation clusters is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0001470499&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/18/8/008

DO - 10.1088/0305-4470/18/8/008

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AN - SCOPUS:0001470499

SN - 0305-4470

VL - 18

SP - L443-L448

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 8

ER -