Related papers: Approximate Isotropic Cloak for the Maxwell equati…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
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…
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…
Invisibility cloaks of light, which used to be confined to the imagination, have now been turned into a scientific reality, thanks to the enabling theoretical tools of transformation optics and conformal mapping. Inspired by those…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
This paper presents a brand new methodology to deal with isotopic fine structure calculations. By using the Poisson approximation in an entirely novel way, we introduce mathematical elegance into the discussion on the trade-off between…
An elliptical invisible cloak is proposed using a coordinate transformation in the elliptical-cylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
The authors present an impedance-matched reduced version of acoustic cloaking whose mass is in a reasonable range. A layered cloak design with isotropic material is also proposed for the reduced cloak. Numerical calculations from the…
An invisibility cloak that can hide an arbitrary object external to the cloak itself has not been devised before. In this Letter, we introduce a novel way to design a remote cloaking device that makes any object located at a certain…
In this work we theoretically propose scattering cancellation-based cloaks for heat waves that obey the Maxwell-Cattaneo equation. The proposed cloaks possess carefully tailored diffusivity to cancel the dipole scattering from the object…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the {\em cloaked region} (denoted by $\Omega_0$, where the objects inside are…
Coordinate-transformation cloaking is based on the design of a metamaterial shell made of an anisotropic, spatially inhomogeneous "transformation medium" that allows rerouting the impinging wave around a given region of space. In its…
Closed-form expressions were recently derived for depolarization dyadics for truncated spheres and truncated spheroids, and the formalism was extended to truncated ellipsoids. These results were exploited to develop an implementation of the…
The ability to control electromagnetic fields, heat currents, electric currents, and other physical phenomena by coordinate transformation methods has resulted in novel functionalities, such as cloaking, field rotations, and concentration…
The synthesis of non-magnetic 2D dielectric cloaks as proper solutions of an inverse scattering problem is addressed in this paper. Adopting the relevant integral formulation governing the scattering phenomena, analytic and numerical…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
In this paper, we review the methodology of transformation optics, which can construct invisibility cloak through the transformation of coordinates based on the form invariance of Maxwell's equations. Three different ways to define the…