Enhanced near-cloak by FSH lining

Liu, Hongyu; Sun, Huaijiang

doi:10.1016/j.matpur.2012.06.001

Cited by 45 publications

(45 citation statements)

References 34 publications

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“…On the other hand, there are many researchers have considered another methods, called the small-inclusion-blowup construction, which regularized the singular medium which was induced by the one-point-blowup construction for the perfect cloaking. The small-inclusion-blowup method was studied by many researchers: [5,26] for the conductivity model, [1,4,11,25,28,29,30,31] for the acoustic model, [6,7,8,12] for the Maxwell model and [23] for the Lamé model. In [24], the authors also pointed out that the truncation of singularity construction and the small-inclusion construction are equivalent.…”

Section: Introductionmentioning

confidence: 99%

Nearly cloaking for the elasticity system with residual stress

Lin

2017

ASY

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The nearly cloaking via transformation optics approach for the isotropic elastic wave fields is considered. This work extends the study of the nearly cloaking scheme to the elasticity system with residual stress in R N for N = 2, 3, which is an anisotropic elasticity system. It is worth to mention that there are no minor symmetric properties for the elastic tensor with residual stress and this system is invariant under a coordinate transformation. Therefore, we think the elasticity system residual stress model is more natural than the isotropic elasticity system in designing the elastic cloaking medium in the physical sense. In addition, the main difficulty of treating this problem lies in the fact that there are no layer potential theory for the residual stress system. Instead, we will derive suitable elliptic estimates for the elasticity system residual stress by comparing with the Lamé system to achieve desired results.

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Section: Introductionmentioning

confidence: 99%

Nearly cloaking for the elasticity system with residual stress

Lin

2017

ASY

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“…To close this introduction, let us mention that in recent years, different ways of devising negative material and invisibility cloaking are proposed. For instance, we can cite, among many other relevant works, the following mathematical works on cloaking with negative refractive index materials and the invisibility cloaking for different types of waves by Greenleaf et al , Vogelius et al , Ammari et al and Liu et al…”

Section: Introductionmentioning

confidence: 99%

“…To close this introduction, let us mention that in recent years, different ways of devising negative material and invisibility cloaking are proposed. For instance, we can cite, among many other relevant works, the following mathematical works [26][27][28][29][30][31][32][33][34][35][36][37][38] The rest of the paper is organized as follows. In Section 2, we state the main results.…”

Section: Introductionmentioning

confidence: 99%

A cluster of many small holes with negative imaginary surface impedances may generate a negative refraction index

Alsaedi

Ahmad

Challa

et al. 2015

Math Methods in App Sciences

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We deal with the scattering of an acoustic medium modeled by an index of refraction n varying in a bounded region Ω of double-struckR3 and equal to unity outside Ω. This region is perforated with an extremely large number of small holes Dm's of maximum radius a, a << 1, modeled by surface impedance functions. Precisely, we are in the regime described by the number of holes of the order M:=O(aβ − 2), the minimum distance between the holes is d ∼ at, and the surface impedance functions of the form λm∼λm,0a−β with β > 0 and λm,0 being constants and eventually complex numbers. Under some natural conditions on the parameters β,t, and λm,0, we characterize the equivalent medium generating approximately the same scattered waves as the original perforated acoustic medium. We give an explicit error estimate between the scattered waves generated by the perforated medium and the equivalent one, respectively, as a→0. As applications of these results, we discuss the following findings: If we choose negative‐valued imaginary surface impedance functions, attached to each surface of the holes, then the equivalent medium behaves as a passive acoustic medium only if it is an acoustic metamaterial with index of refraction $\tilde {n}(x)=‐n(x),\; x \in \upOmega $ñ(x)=−n(x),x∈Ω and $\tilde {n}(x)=1,\; x \in \mathbb {R}^{3}\setminus {\overline {\upOmega }}$ñ(x)=1,x∈R3∖Ω¯. This means that with this process, we can switch the sign of the index of the refraction from positive to negative values. We can choose the surface impedance functions attached to each surface of the holes so that the equivalent index of refraction $\tilde {n}$ñ is $\tilde {n}(x)=1,\; x \in \mathbb {R}^{3}$ñ(x)=1,x∈R3. This means that the region Ω modeled by the original index of refraction n is approximately cloaked. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Approximate cloaking with lossy layer can be used to hide both passive bodies and active sources for electromagnetic scattering [15,22,23], and also for acoustic scattering [24]. Special coatings can also be used to enhance cloaking for systems governed by Helmholtz equation [25,26].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Scattering by Approximately Cloaked Dielectric Cylinder

Zamel¹,

El-Diwany²,

El‐Hennawy³

2014

PIER B

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Abstract-In cloaking, a body is hidden from detection by surrounding it by a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden 2D or cylindrical body into a line. Some components of the electrical parameters of the cloaking material (ε, µ) are required to have infinite or zero value at the boundary of the hidden object. In order to eliminate the zero or infinite values of the electrical parameters, approximate cloaking can be used by transforming the cylindrical body virtually into a small cylinder rather than a line, but this produces some scattering. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. In this work, the scattering pattern, and the backscattering cross section against the frequency for cloaked dielectric cylinder are studied for both transverse magnetic (TM z ) and transverse electric (TE z ) polarizations of the incident plane wave for different transformed body radii.

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Enhanced near-cloak by FSH lining

Cited by 45 publications

References 34 publications

Nearly cloaking for the elasticity system with residual stress

Nearly cloaking for the elasticity system with residual stress

A cluster of many small holes with negative imaginary surface impedances may generate a negative refraction index

Electromagnetic Scattering by Approximately Cloaked Dielectric Cylinder

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