Conductivity exponent and backbone dimension in 2-d percolation

Conductivity Exponent and Backbone Dimension in 2-d Percolation

We present high statistics simulations for 2-d percolation clusters in the “bus bar” geometry at the critical point, for site and for bond percolation. We measured their backbone sizes and electrical conductivities. For all sets of measurements we find large corrections to scaling, most of which do not seem to be described by single powers. Using single power terms for the corrections to scalin...

Resistance of Feynman diagrams and the percolation backbone dimension.

We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-...

Spectral dimension and conductivity exponent of the percolating cluster

Fractal Dimension, Walk Dimension and Conductivity Exponent of Karst Networks around Tulum

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension df , conductivity exponent μ̃ and walk dimension dw are estimated using real space renormalization and numerical simulat...

PRECISE DETERMINATION OF THE CONDUCTIVITY EXPONENT OF 3D PERCOLATION USING “PERCOLA” JEAN-MARIE NORMAND and HANS

Percolation [1] is the simplest model for a random medium and is applied to describe porous media, gelation, mixtures of electrical conductors, and many other disorder dominated situations. It is defined on a lattice by occupying with probability p randomly and independently either the sites or the bonds with conductors. If one considers that locally current can only flow between conductors tha...