Related papers: Series, Index and Threshold for Random 2D Composit…
In a Monte Carlo study the conductivity of two-dimensional random stick systems is investigated from the percolation threshold up to ten times the percolation threshold density. We propose a model explicitly depending on the stick density…
We study macroscopic electrical or thermal conductivity of a composite made of straight or coiled nanowires suspended in poorly conducting medium. We assume that volume fraction of the wires is so large that spaces occupied by them overlap,…
In 1892, Lord Rayleigh estimated the effective conductivity of rectangular arrays of disks and proved, by means of the Eisenstein summation, that the lattice sum $S_2$ is equal to $\pi$ for the square array. Further, it became clear that…
We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the…
We discuss the optical conductivity of several non-interacting two-dimensional (2D) semiconducting systems focusing on gapped Dirac and Schr\"odinger fermions as well as on a system mixing these two types. Close to the band-gap, we can…
Recently, quantum corrections to optical conductivity of disordered metals up to the UV region were observed. Although this increase of conductivity with frequency, also called anti-Drude behaviour, should disappear at the electron…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
Superconductivity was originally observed in 3D metals caused by an effective attraction between electrons mediated by the electron-phonon interaction. Since then there has been a lot of work on 2D conductors including the possibility of…
A new algorithm for the derivation of low-density expansions has been used to greatly extend the series for moments of the pair-connectedness on the directed square lattice near an impenetrable wall. Analysis of the series yields very…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
Films made from random nanowire arrays are an attractive choice for electronics requiring flexible transparent conductive films. However, thus far there has been no unified theory for predicting their electrical conductivity. In particular,…
We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable $\mathcal{D}$ (space-time dimensionality) provide a regular way to derive analytical representations of loop…
We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…
In this article we compare solutions to elliptic problems having rapidly oscillated conductivity (permeability, etc) coefficient with solutions to corresponding homogenized problems obtained from two-scale extensions of the initial…
We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of $N$ identical two-level systems undergoing collective…
Let $d_S$ denote the arithmetic density of a subset $S \subseteq \mathbb N$. We derive a power series in $q\in \mathbb C$, $|q|<1$, with co\"efficients related to integer partitions and integer compositions, that yields $1/d_S$ in the limit…
By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…
We consider the problem of decomposing a piecewise constant function on the circle into a sum of indicator functions of closed circular disks in the plane, whose number and location are not a priori known. This represents a situation where…
A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the…
In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regularizes two-dimensional generalized Eisenstein series for all…