Related papers: Conductivity exponents at the percolation threshol…
The surface discharge of electrified dielectrics at high humidity is considered. The percolative nature of charge transport in electrets is established. Particular attention is given to the phenomena of adsorption and nucleation of…
Based on a recent proposal [O.P. Sushkov, Phys. Rev. B 64, 155319 (2001)], we relate the quantum conductance through a sample in which electrons are strongly correlated to the persistent current of a large ring, composed of the sample and a…
Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\sigma_1$ and $\sigma_2$ with the probabilities $p$ and $1-p$,…
The conductance through a semi-infinite one-dimensional wire, partly embedded in a superconducting bulk electrode, is studied. When the electron-electron interactions within the wire are strongly repulsive, the wire effectively decouples…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Conduction in bulk polycrystalline high-T$_c$ superconductors with relatively high critical currents has been shown to be percolative. This phenomenon is due to weak links at grain boundaries. These weak links are the major limiting factor…
We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find…
The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models…
A vast class of disordered conducting-insulating compounds close to the percolation threshold is characterized by nonuniversal values of transport critical exponents. The lack of universality implies that critical indexes may depend on…
We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
This paper concerns optimal gradient estimates of solutions for the perfect conductivity problem with closely spaced interfacial boundaries. The problem arises from composite material. Our estimates exhibit different blow up rates of the…
Algebraic expressions are found for the effective conductivities of some infinite tessellations composed of conducting square, triangular, or hexagonal tiles. A tessellation is further characterized by the number N of different colors…
Iterative construction of a Sierpinski carpet or sponge is shown to be a critical phenomenon analogous to uncorrelated percolation. Critical exponents are derived or calculated (by random walks over the carpet or sponge at infinite…
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…
The magnetic flux trapping in type-II superconductor containing fractal clusters of a normal phase, which act as pinning centers, is considered. The critical current distribution for an arbitrary fractal dimension of the boundaries of the…
We consider the critical temperature for superconductivity, defined via the linear BCS equation. We prove that at weak coupling the critical temperature for a sample confined to a quadrant in two dimensions is strictly larger than the one…
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical simulations based on the…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few…