Related papers: Optimal Estimates for the Electric Field in Two-Di…
In the perfect conductivity problem of composites, the electric field may become arbitrarily large as $\varepsilon$, the distance between the inclusions and the matrix boundary, tends to zero. The main contribution of this paper lies in…
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of order $\varepsilon$ apart. The solution $u$ represents the electric potential. In dimensions $n \ge 3$ it is an open problem to find…
We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We…
This paper deals with the field enhancement, that is, the gradient blow-up, due to presence of a bow-tie structure of perfectly conducting inclusions in two dimensions. The bow-tie structure consists of two disjoint bounded domains which…
We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field $|J|$. We prove that the conductivity…
In this paper, we consider very high concentration of electric field in between infinitely many circular perfect conductors arranged closely in two rows. In stiff fiber-reinforced composite, shear stress concentrations occur in between…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the…
A field excited by an emitter can be enhanced due to presence of closely located inclusions. In this paper we consider such field enhancement when inclusions are disks of the same radii, and the emitter is of dipole type and located in the…
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…
This paper presents a rigorous mathematical analysis of transverse electromagnetic (EM) field concentration between two adjacent obstacles within the framework of the quasi-static approximation. We investigate three degenerate conductivity…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We…
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…
If two conducting or insulating inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between inclusions tends to zero, resulting in high concentration of stress in between two inclusions.…
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…
In this paper, we investigate the gradient estimates for solutions to the perfect conductivity problem with two closely spaced perfect conductors embedded in a homogeneous matrix, modeled by $p$-Laplacian elliptic equations. We first prove…
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The approximations are computationally efficient in the sense the…
A field in a homogeneous medium can be amplified or enhanced by inserting closely located perfectly conducting inclusions into the medium. In this paper precise quantitative estimates for such enhancement are derived when the given field is…
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…