相关论文: Tight Bounds on the Effective Complex Permittivity…
The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider…
Electromagnetic materials with a uniaxial effective permittivity tensor, characterized by its transverse ($\epsilon_\perp$) and axial ($\epsilon_\parallel$) components, play a central role in the design of advanced photonic and…
The purpose of this paper is to set out optimal gradient estimates for solutions to the isotropic conductivity problem in the presence of adjacent conductivity inclusions as the distance between the inclusions goes to zero and their…
Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex…
The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous dielectric particles. Two factors of anisotropy are taken into account, the shape of…
Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light--matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical…
This paper deals with bounds satisfied by the effective non-symmetric conductivity of three-dimensional composites in the presence of a strong magnetic field. On the one hand, it is shown that for general composites the antisymmetric part…
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…
To derive bounds on the strain and stress response of a two-component composite material with viscoelastic phases, we revisit the so-called analytic method (Bergman 1978), which allows one to approximate the complex effective tensor,…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
An analytical model is presented for a rectangular lattice of isotropic scatterers with electric and magnetic resonances. Each isotropic scatterer is formed by putting appropriately 6 $\Omega$-shaped perfectly conducting particles on the…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…
A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant,…
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct…
Two different formalisms for the homogenization of composite materials containing ellipsoidal inclusions based on Bruggeman's original formula for spherical inclusions can be found in the literature. Both approximations determine the…
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbitrary large. We establish both the pointwise upper bound and…