Related papers: Asymptotics for the electric field concentration i…
We study the perfect conductivity problem with closely spaced perfect conductors embedded in a homogeneous matrix where the current-electric field relation is the power law $J=\sigma|E|^{p-2}E$. The gradient of solutions may be arbitrarily…
A heterogeneous medium of constituents with vastly different mechanical properties, whose inhomogeneities are in close proximity to each other, is considered. The gradient of the solution to the corresponding problem exhibits singular…
In composite material, the stress may be arbitrarily large in the narrow region between two close-to-touching hard inclusions. The stress is represented by the gradient of a solution to the Lam\'{e} system of linear elasticity. The aim of…
We study the insulated conductivity problem which involves two adjacent convex insulators embedded in a bounded domain. It is known that the gradient of solutions may blow up as the distance between the two inclusions tends to zero.…
The perfect conductivity problem concerns optimal bounds for the magnitude of an electric field in the presence of almost touching perfect conductors. This reduces to obtaining gradient estimates for harmonic functions with Dirichlet…
We consider the Lam\'{e} system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow…
In high-contrast composite materials, the electric (or stress) field may blow up in the narrow region between inclusions. The gradient of solutions depend on $\epsilon$, the distance between the inclusions, where $\epsilon$ approaches to…
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 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…
Spatial fluctuations of the local electric field induced by a constant applied electric field in composite media are studied analytically and numerically. It is found that the density of states for the fields exhibit sharp peaks and abrupt…
This paper studies field concentration between two nearly touching conductors separated by imperfect low-conductivity interfaces, modeled by Robin boundary conditions. It is known that for any sufficiently small interfacial bonding…
The electrical conductivity is calculated for regular inhomogeneous two component isotropic medium in which droplets of one phase with conductivity sigma_2 are embedded in another, with conductivity sigma_1. An expression is formulated…
We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region…
In this paper, we are concerned with the gradient estimate of the electric field due to two nearly touching dielectric inclusions, which is a central topic in the theory of composite materials. We derive accurate quantitative…
Coulomb drag is a process whereby the repulsive interactions between electrons in spatially separated conductors enable a current flowing in one of the conductors to induce a voltage drop in the other. If the second conductor is part of a…
An expression for the electrical conductivity at the core of a magnetar is derived using Boltzmann kinetic equation with the relaxation time approximation. The rates for the relevant scattering processes, e.g., electron-electron and…
In high-contrast elastic composites, it is vitally important to investigate the stress concentration from an engineering point of view. The purpose of this paper is to show that the blowup rate of the stress depends not only on the shape of…
Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $\nu_T = 1$. We find that the phase boundary between the interlayer…
The heterogeneity of composite leads to the extra charge concentration at the boundaries of different phases that results essentially nonzero effective electric susceptability. The relation between tensors of effective electric…
When perfectly conducting or insulating inclusions are closely located, stress which is the gradient of the solution to the conductivity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important…