Related papers: Gradient estimates for the perfect conductivity pr…
The idea of replacing an edgy perfectly conducting boundary by the corresponding interface filled with a dielectric material of extreme complex permittivities, is examined in the present work. A semi-analytical solution to the corresponding…
In this paper we analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. Assuming that the core and shell have circular boundaries that…
The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the…
The paper establishes tight lower bound for effective conductivity tensor $K_*$ of two-dimensional three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed that three materials are mixed with fixed…
Perfect light transmission into a dielectric at the Brewster angle is one of the simplest effects in macroscopic electromagnetism. The common wisdom states that absorption in the dielectric violates Brewster angle and leads to a…
We study the insulated conductivity problem with closely spaced insulators embedded in a homogeneous matrix where the current-electric field relation is the power law $J = |E|^{p-2}E$. The gradient of solutions may blow up as $\varepsilon$,…
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…
In this article, we consider the problem of finding the support of an inhomogenous possibly anisotropic inclusion in a background of constant electric conductivity from the electrical impedance tomography data at the boundary of a bounded…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…
The duality and other symmetry properties of the effective conductivity sigma_e of the classical two-dimensional isotropic randomly inhomogeneous heterophase systems at arbitrary number of phases N are discussed. A new approach for a…
This work concerns the design of perfectly conducting objects that are invisible to an incident transverse magnetic plane wave. The object in question is a finite planar waveguide with a finite periodic array of barriers. By optimizing this…
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth…
We derive exact expressions for so-called ``void'' bounds on the trapping constant $\gamma$ and fluid permeability $k$ for coated-spheres and coated-cylinders models of porous media. We find that in some cases the bounds are optimal, i.e.,…
We consider the initial-boundary value problem in the quarter space for the system of equations of ideal Magneto-Hydrodynamics for compressible fluids with perfectly conducting wall boundary conditions. On the two parts of the boundary the…
We present a ${\Gamma}$-convergence approximation for the total anisotropic length of a partition. This theoretical result gives rise to a numerical method which allows the study of minimal partitions with respect to different anisotropies.…
We compute cosmological perturbations for a generic self-gravitating media described by four derivatively- coupled scalar fields. Depending on the internal symmetries of the action for the scalar fields, one can describe perfect fluids,…
A model of an exact gravity dual of a gapless superconductor is presented in which the condensate is provided by a charged scalar field coupled to a bulk black hole of hyperbolic horizon in asymptotically AdS spacetime. Below a critical…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The…
We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field…