We investigate in a quantitative way the plasmon resonance at eigenvalues and the essential spectrum (the accumulation point of eigenvalues) of the Neumann–Poincaré operator on smooth domains. We ...first extend the symmetrization principle so that the single layer potential becomes a unitary operator from H−1/2 onto H1/2. We then show that the resonance at the essential spectrum is weaker than that at eigenvalues. It is shown that anomalous localized resonance occurs at the essential spectrum on ellipses, and cloaking due to anomalous localized resonance does occur on ellipses like on the core-shell structure considered in 19. It is shown that cloaking due to anomalous localized resonance does not occur at the essential spectrum on three dimensional balls.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The purpose of this paper is to investigate the spectral nature of the Neumann–Poincaré operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral ...resolution of the operator is derived, which shows, in particular, that it admits only the absolutely continuous spectrum; no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution of the plasmon resonance at the absolutely continuous spectrum.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We prove in a mathematically rigorous way the asymptotic formula of Flaherty and Keller on the effective property of densely packed periodic elastic composites with hard inclusions. The proof is ...based on the primal–dual variational principle, where the upper bound is derived by using the Keller-type test functions and the lower bound by singular functions made of nuclei of strain. Singular functions are solutions of the Lamé system and capture precisely singular behavior of the stress in the narrow region between two adjacent hard inclusions.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We consider the spectral structure of the Neumann–Poincaré operators defined on the boundaries of thin domains of rectangular shape in two dimensions. We prove that as the aspect ratio of the domains ...tends to ∞, or equivalently, as the domains get thinner, the spectra of the Neumann–Poincaré operators are densely distributed in −1/2, 1/2, the interval which contains the spectrum of Neumann–Poincaré operators.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a ...layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a critical radius, CALR does not take place, and for sources located inside the critical radius satisfying certain conditions, CALR does take place as the loss parameter goes to zero.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The aim of this paper is to provide an original method of constructing very effective near-cloaking structures for the conductivity problem. These new structures are such that their first Generalized ...Polarization Tensors (GPT) vanish. We show that this in particular significantly enhances the cloaking effect. We then present some numerical examples of Generalized Polarization Tensors vanishing structures.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The aim of this paper is to extend the method of Ammari et al. (Commun. Math. Phys.,
2012
) to scattering problems. We construct very effective near-cloaking structures for the scattering problem at ...a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This paper concerns the spectral properties of the Neumann–Poincaré operator on two- and three-dimensional bounded domains which are invariant under either rotation or reflection. We prove that if ...the domain has such symmetry, then the domain of definition of the Neumann–Poincaré operator is decomposed into invariant subspaces defined as eigenspaces of the unitary transformation corresponding to rotation or reflection. Thus, the spectrum of the Neumann–Poincaré operator is the union of those on invariant subspaces. In two dimensions, an
m
-fold rotationally symmetric simply connected domain
D
is realized as the
m
th-root transform of a domain, say
Ω
. We prove that the spectrum on one of invariant subspaces is the exact copy of the spectrum on
Ω
. It implies in particular that the spectrum on the transformed domain
D
contains the spectrum on the original domain
Ω
counting multiplicities. We present a matrix representation of the Neumann–Poincaré operator on the
m
-fold rotationally symmetric domain using the Grunsky coefficients. We also discuss some examples including lemniscates,
m
-star shaped domains and the Cassini oval.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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