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We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for…
In an electromagnetic cloak based on a transformation approach, reduced sets of material properties are generally favored due to their easier implementation in reality, although a seemingly inevitable drawback of undesired reflection exists…
We investigate the problem of planar conductivity inclusion with imperfect interface conditions. We assume that the inclusion is simply connected. The presence of the inclusion causes a perturbation in the incident background field. This…
In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters deduced from a geometrical transformation as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we…
We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a…
We design three dimensional electromagnetic cloaks, starting from a small region of complex shape instead of a point. We derive the expression of a transformation matrix describing an objet with a surface of revolution and its associated…
The purpose of this paper is to present a simple micromechanics-based model to estimate the effective thermal conductivity of real-world macroscopically isotropic materials of matrix-inclusion type. The methodology is based on the…
We analyze the simplest problem of electrochemical relaxation in more than one dimension - the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In…
We report on the thermal and electrical properties of hybrid epoxy composites with graphene and boron nitride fillers. The thicknesses, lateral dimensions, and aspect ratios of each filler material were intentionally selected for geometric…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
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…
We introduce a solid material that is itself invisible, possessing identical electromagnetic properties as air (i.e. not a cloak) at a desired frequency. Such a material could provide improved mechanical stability, electrical conduction and…
Nonlinear photomagnetization is a process by which an oscillating electric field induces a static magnetization. We show that all 32 crystallographic point groups admit such spin polarization using circularly polarized electric fields to…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
Generalized beams of light that are made to turn inside out, creating black nodal areas of total destructive interference are described. As an example we experimentally created an elliptical node from a uniformly illuminated elliptical…
Unprecedented material compatibility and ease of integration, in addition to the unique and diverse optoelectronic properties of layered materials have generated significant interest in their utilization in nanophotonic devices. While…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…