Related papers: Homogenization Techniques for Periodic Structures
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of integral type featuring contributions of bulk and interfacial…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
This is a concise review of holographic superconductors and superfluids. We highlight some predictions of the holographic models and the emphasis is given to physical aspects rather than to the technical details, although some references to…
We discuss the applicability of holographically patterned polymers, polymer dispersed liquid crystals, and nanoparticle-polymer composites as optical elements for cold neutrons. Requirements concerning the spacing, thickness or strength of…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective…
Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
A rigorous homogenization theory of metamaterials -- artificial periodic structures judiciously designed to control the propagation of electromagnetic waves -- is developed. All coarse-grained fields are unambiguously defined and effective…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such…
A general homogenization procedure for periodic electromagnetic structures, when applied to layered media with asymmetric lattice cells, yields an effective tensor with magnetoelectric coupling. Accurate results for transmission and…
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…
We derive, by means of variational techniques, a limiting description for a class of integral functionals under linear differential constraints. The functionals are designed to encode the energy of a high-contrast composite, that is, a…
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets…