we introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. these kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. we construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

Water flooding is a well-known secondary mechanism for improving oil recovery. Conventional approach to evaluate the performance of a water flooding process (e.g. breakthrough and post breakthrough behavior) is to establish a reliable geological reservoir model, upscale it, and then perform flow simulations. To evaluate the uncertainty in the breakthrough time or post breakthrough behavior, thi...

Percolation theory is of interest in problems of phase transitions in condensed matter physics, and in biology and chemistry. More recently, concepts of percolation theory have been invoked in studies of color deconfinement at high temperatures in Quantum Chromodynamics. In the present paper we briefly review the basic concept of percolation theory, exemplify its application to the Ising model,...

Many modern nanostructured materials and doped polymers are morphologically too complex to be interpreted by classical percolation theory. Here, we develop the concept of a hierarchical percolating (percolation-within-percolation) system to describe such complex materials and illustrate how to generalize the conventional percolation to double-level percolation. Based on Monte Carlo simulations,...

In this paper, we discuss the basic elements of percolation theory, beginning with the physical motivation for the abstraction and the essentials of the bond model on the LD square lattice. The critical phenomenon is introduced, a fundamental concept in percolation theory. We then describe the general use of percolation theory to analyze physical phenomena. We examine one such application in de...

Given ω ≥ 1, let Z2(ω) be the graph with vertex set Z 2 in which two vertices are joined if they agree in one coordinate and differ by at most ω in the other. (Thus Z2(1) is precisely Z .) Let pc(ω) be the critical probability for site percolation in Z2(ω). Extending recent results of Frieze, Kleinberg, Ravi and Debany, we show that limω→∞ ωpc(ω) = log(3/2). We also prove analogues of this resu...