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

Rafael Blumenfeld, Amnon Aharony

Research output: Contribution to journalLetterpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)L443-L448
JournalJournal of Physics A: Mathematical and General
Volume18
Issue number8
DOIs
StatePublished - 1 Jun 1985

Fingerprint

Dive into the research topics of 'Nonlinear resistor fractal networks, topological distances, singly connected bonds and fluctuations'. Together they form a unique fingerprint.

Cite this