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11.
The aim of this work is to derive sharp quantitative estimates of the qualitative convergence results developed by Li et al. (2015) for regularized full- and partial-cloaks through transformation optics approach. Let Γ0 be a compact set in ?3 and Γδ be a δ-neighborhood of Γ0 for δ∈?+. Γδ represents the virtual domain used for the blow-up construction. By incorporating suitably designed lossy layers, it is shown that if the generating set Γ0 is a generic curve, then one would have an approximate full-cloak within δ2 to the perfect full-cloak, whereas if Γ0 is the closure of an open subset on a flat surface, then one would have an approximate partial-cloak within δ to its perfect counterpart. The estimates derived are independent of the contents being cloaked; that is, the cloaking devices are capable of nearly cloaking an arbitrary content. Furthermore, as a significant by-product, our argument allows the relaxation of the convexity requirement on Γ0 by Li et al. (2015), which is critical for the Mosco convergence argument therein. 相似文献
12.
In this paper, we first design a coordinate transformation and derive the anisotropic material parameters of the quadrilateral thermal cloak according to the transformation thermodynamics principle. Then, since the derived parameters are inherently anisotropic, we eliminate its anisotropy by considering the effective medium theory and use a layered structure of metamaterials composed of only two isotropic materials to design the cloak device. Finally, we simulate the performance of a perfect and layered thermal cloak by the finite element method. To the best of our knowledge, this is the first work to design and simulate the performance of this quadrilateral thermal cloak by the finite element method(FEM). 相似文献
13.
Sébastien Guenneau Alexander Movchan Natasha Movchan 《Journal of Computational and Applied Mathematics》2010,234(6):1962-2309
We analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform [H. Chen, C.T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Appl. Phys. Lett. 91 (2007) 183518]. We find that whereas a single coated inclusion is acoustically neutral at any frequency, an array of them might display some stop bands. More precisely, an array of freely vibrating coated voids is always neutral, whereas an array of clamped coated inclusions might display a zero frequency stop band. Interestingly, an array of radially symmetric coated inclusions behaves as local Helmholtz resonators, for which the eigenfield within each cloak is obtained in closed form, leading to a frequency estimate associated with the lower edge of the low frequency stop band. A finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source. 相似文献
14.
The method of designing electromagnetic invisible cloaks
is usually based on the form-invariance of Maxwell's equations in
coordinate transformation. The exterior boundary of a cylindrical
invisible cloak is unchanged and the interior boundary is extended
from that of a point to that of a cylindrical region in coordination
transformation. This transformation process makes perfect cloaks,
but it causes singularity in the constitutive material parameters of
cloaks. This singularity makes the cloaks impossible to realize
in practice. In order to remove this singularity, this paper sets
a small cylindrical region replacing a point in the space
transformation. The cylindrical region is so small that it does not
affect the invisibility effects, but it can remove the singularity for
material parameters. Full wave simulations based on the finite element
method were used to verify the designed cloaks. 相似文献