Approximate cloaking for the full wave equation via change of variables: The Drude–Lorentz model
نویسندگان
چکیده
This paper concerns approximate cloaking by mapping for a full, but scalar wave equation, when one allows for physically relevant frequency dependence of the material properties of the cloak. The paper is a natural continuation of [20], but here we employ the Drude-Lorentz model in the cloaking layer, that is otherwise constructed by an approximate blow up transformation of the type introduced in [10]. The central mathematical problem translates into the analysis of the effect of a small inhomogeneity in the context of a non-local full wave equation.
منابع مشابه
Approximate Cloaking for the Full Wave Equation via Change of Variables
We study, in the context of the full wave equation, an approximate cloaking scheme, that was previously considered for the Helmholtz equation [8], [17]. This cloaking scheme consists in a combination of an absorbing layer with an anisotropic layer, obtained by so-called transformation optics. We give optimal bounds for the visibility that tend to zero as a certain regularization parameter appro...
متن کاملApproximate Cloaking for the Full Wave Equation via Change of Variables | SIAM Journal on Mathematical Analysis | Vol. 44, No. 3 | Society for Industrial and Applied Mathematics
We study, in the context of the full wave equation, an approximate cloaking scheme that was previously considered for the Helmholtz equation [R. V. Kohn, D. Onofrei, M. S. Vogelius, and M. I. Weinstein, Comm. Pure Appl. Math., 63 (2010), pp. 973–1016, H.-M. Nguyen and M. S. Vogelius, Arch. Ration. Mech. Anal., 203 (2011), pp. 769–807]. This cloaking scheme consists in a combination of an absorb...
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1. Overview 2 2. Electromagnetic waves 3 2.1. Approximate cloaking via change of variables 3 2.1.1. Cloaking for the Helmholtz equation 3 2.1.2. Full range estimates for the degree of invisibility 4 2.1.3. Perfect cloaking for the Helmholtz equation 4 2.2. Electrical impedance tomography 5 2.3. Generalized impedance boundary conditions 5 2.3.1. The Helmholtz equation 6 2.3.1. The time harmonic ...
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