Related papers: Asymptotics for the electric field concentration i…
This paper is concerned with the stress concentration phenomenon in elastic composite materials when the inclusions are very closely spaced. We investigate the gradient blow-up estimates for the Lam\'{e} system of linear elasticity with…
We consider an insulated conductivity model with two neighboring inclusions of $m$-convex shapes in $\mathbb{R}^{d}$ when $m\geq2$ and $d\geq3$. We establish the pointwise gradient estimates for the insulated conductivity problem and…
A composite conductive material, which consists of fibers of a high conductivity in a matrix of low conductivity, is discussed. The effective conductivity of the system considered is calculated in Clausius-Mossotti approximation. Obtained…
In this paper we study the boundary gradient estimate of the solution to the insulated conductivity problem with the Neumann boundary data when a convex insulating inclusion approaches the boundary of the matrix domain. The gradient of…
A high-contrast two-phase nonlinear composite material with adjacent inclusions of $m$-convex shapes is considered for $m>2$. The mathematical formulation consists of the insulated conductivity problem with $p$-Laplace operator in…
The electrical {\em dc}-conductivity of disordered, non-interacting electrons is calculated in the asymptotic limit of high lattice dimensions $d\to \infty$. To go beyond the lowest-order contribution in the expansion parameter $1/d$ of the…
We study the electric potential and field produced by disordered distributions of charge to see why clumps of charge do not produce large potentials or fields. The question is answered by evaluating the probability distribution of the…
Conditions at which a quasi-one-dimensional (1D) electron system can be considered as a quantum liquid of impenetrable charged particles are theoretically analyzed. In the presence of an inert, neutralizing background, a motion of…
We present new data for the electrical conductivity of foams in which the liquid fraction ranges from two to eighty percent. We compare with a comprehensive collection of prior data, and we model all results with simple empirical formul\ae.…
Distinguishing an exciton condensate from an excitonic gas or insulator remains a fundamental challenge, as both phases feature bound electron-hole pairs but differ only by the emergence of macroscopic phase coherence. Here, we…
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation.…
Electrons in condensed matter may transition into a variety of broken-symmetry phase states due to electron-electron interactions. Applying diverse mean-field approximations to the interaction term is arguably the simplest way to identify…
An exact solution for electromagnetic wave diffraction at the junction of two-dimensional electron systems (2DES) is obtained and analyzed for electric field polarized along the edge. A special emphasis is paid to the metal-contacted and…
We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of…
Very recent measurements of the electrical conductivity of solid systems AgX - CdX$_2$ (where X$\equiv$Cl,Br) that form large areas of solid solutions, have shown that maximum conductivity occurs for a concentration around 20 mol\% of the…
Non-empty space reading of Maxwell equations as local energy identities explains why a Coulomb field is carried rigidly by electrons in experiments. The analytical solution of the Poisson equation defines the sharp radial shape of charged…
The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…
The quantum dynamics of quasi-one-dimensional ring with varying electron filling factor is investigated in presence of external electric field. The system is modeled within Hubbard Hamiltonian with attractive Coulomb correlation, which…
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 $1-p$,…
Usually the conductivity is quantized as the inverse of the resistivity, \rho=hc/ie^2, \sigma=ie^2/hc and the velocity versus the electric field is linear, v=\mu E where \mu is the mobility of the electrons.However,when the applied electric…