1/f noise in random resistor networks: Fractals and percolating systems.

Noise excess on fractals and percolating systems

Percolation-Induced Exponential Scaling in the Large Current Tails of Random Resistor Networks

There is a renewed surge in percolation-induced transport properties of diverse nanoparticle composites (cf. RSC Nanoscience & Nanotechnology Series, Paul O’Brien Editor-inChief). We note in particular a broad interest in nanocomposites exhibiting sharp electrical property gains at and above percolation threshold, which motivated us to revisit the classical setting of percolation in random resi...

Restoration of isotropy on fractals.

We report a new type of restoration of macroscopic isotropy (homogenization) in fractals with microscopic anisotropy. The phenomenon is observed in various physical setups, including diffusions, random walks, resistor networks, and Gaussian field theories. The mechanism is unique in that it is absent in uniform media, while universal in that it is observed in a wide class of fractals. 05.40+j, ...

Random resistor network model of minimal conductivity in graphene.

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the qu...

Comment on " epsilon expansion for the conductivity of a random resistor network"

We present a reanalysis of the renormalization-group calculation to first order in ε=6−d, where d is the spatial dimensionality, of the exponent, t, which describes the behavior of the conductivity of a percolating network at the percolation threshold. If we set t=(d−2)νp+ζ, where νp is the correlation-length exponent, then our result is ζ=1+(ε/42). This result clarifies several previously para...