Resistance fluctuations in randomly diluted networks

Percolation of diffusional creep: a new universality class

We study the percolation aspects of diffusional "Coble" creep on heterogeneous grain boundary networks, assuming free grain boundary sliding. A novel percolation threshold is obtained for the honeycomb lattice when two representative types of grain boundaries are randomly distributed, p(cc)=0.5416+/-0.0036. The creep viscosity diverges near the percolation threshold with power-law exponents t=1.69+/-0.09 and s=1.88+/-0.12, different from the standard conduction and rigidity percolation exponents. The moments of both the force and flux distributions all conform to finite-size scaling at p(cc), but with new exponents. These new scaling behaviors seen in the creeping system are proposed to arise from the unique coupling of both force and flux balances in the network.

Models for correlated multifractal hypersurfaces

We discuss and implement computer approximations of fractal and multifractal hypersurfaces. These hypersurfaces consist of reconstructions of a stochastic process in the real space from randomly distributed variables in the discrete wavelet domain. The synthetic surfaces have the usual fractional Brownian motion as a particular case, and inherit the correlation structure of these fractals. We first introduce the one-dimensional version of these surfaces that obey a weak self-affine symmetry. This symmetry appears in the wavelet domain as a condition on the second moments of the probability distributions of the wavelet coefficients. Then we use these relations to define the fractals and multifractals in d dimensions. Finally, we concentrate on the generation of samples of these hypersurfaces.

Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution

We study the multifractal moments of the current distribution in randomly diluted resistor networks near the percolation threshold. When an external current is applied between two terminals x and x(') of the network, the lth multifractal moment scales as M((l))(I)(x,x(')) approximately equal /x-x'/(psi(l)/nu), where nu is the correlation length exponent of the isotropic percolation universality class. By applying our concept of master operators [Europhys. Lett. 51, 539 (2000)] we calculate the family of multifractal exponents [psi(l)] for l>or=0 to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.

Scaling law of resistance fluctuations in stationary random resistor networks

In a random resistor network we consider the simultaneous evolution of two competing random processes consisting in breaking and recovering the elementary resistors with probabilities W(D) and W(R). The condition W(R)>W(D)/(1+W(D)) leads to a stationary state, while in the opposite case, the broken resistor fraction reaches the percolation threshold p(c). We study the resistance noise of this system under stationary conditions by Monte Carlo simulations. The variance of resistance fluctuations <deltaR2> is found to follow a scaling law |p-p(c)|(-kappa(0)) with kappa(0) = 5.5. The proposed model relates quantitatively the defectiveness of a disordered media with its electrical and excess-noise characteristics.