相关论文: On a regularized scheme for approximate acoustic c…
We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a…
The concept of an invisibility cloak is a fixture of science fiction, fantasy, and the collective imagination. However, a real device that could hide an object from sight in visible light from absolutely any viewpoint would be extremely…
Carpet cloaking is proposed to hide an object on a dielectric half-space from electromagnetic (EM) detection. A two-dimensional conformal transformation specified by an analytic function is utilized for the design. Only one nonsingular…
Invisibility or cloaking has captured human's imagination for many years. With the recent advancement of metamaterials, several theoretical proposals show cloaking of objects is possible, however, so far there is a lack of an experimental…
The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the conventional inverse scattering problems is that only the…
We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its…
We present a theory for the cloaking of arbitrarily-shaped objects and demonstrate electromagnetic scattering-cancellation through designed homogeneous coatings. First, in the small-particle limit, we expand the dipole moment of a coated…
Fundamental features of rotationally symmetric acoustic cloaks with anisotropic inertia are derived. Two universal relations are found to connect the radial and transverse phase speeds and the bulk modulus in the cloak. Perfect cloaking…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
In this manuscript, we demonstrate the design and experimental proof of an optical cloaking structure which multi-directionally conceals a perfectly electric conductor (PEC) object from an incident plane wave. The dielectric modulation…
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive…
Recently, it was shown that an infinite perfectly conducting (PEC) cylinder can be nearly perfectly cloaked from normally incident electromagnetic waves using a single-layer homogeneous dielectric cladding. Here we study the electromagnetic…
In the analysis of the $h$-version of the finite-element method (FEM), with fixed polynomial degree $p$, applied to the Helmholtz equation with wavenumber $k\gg 1$, the $\textit{asymptotic regime}$ is when $(hk)^p C_{\rm sol}$ is…
A near-perfect, non-singular cylindrical invisibility cloak with diamond cross section is achieved by a two-step coordinate transformation. A small line segment is stretched and then blown up into a diamond space, and finally the cloak…
Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in (Gustafson and Sj\"oberg 2010) and (Bernland, Luger and Gustafson 2011). These bounds apply to a wide class of linear passive systems such as…
By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural…
We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…