Approximate cloaking for the full wave equation via change of variables: The Drude–Lorentz model

Hoai Minh Nguyen; Michael S. Vogelius

doi:10.1016/j.matpur.2016.03.012

Approximate cloaking for the full wave equation via change of variables: The Drude–Lorentz model

Hoai Minh Nguyen, Michael S. Vogelius

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 is to analyze the effect of a small inhomogeneity in the context of this non-local full wave equation.

Original language	English (US)
Pages (from-to)	797-836
Number of pages	40
Journal	Journal des Mathematiques Pures et Appliquees
Volume	106
Issue number	5
DOIs	https://doi.org/10.1016/j.matpur.2016.03.012
State	Published - Nov 1 2016

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Approximate cloaking
Drude–Lorentz model
Small inhomogeneity
Wave equation

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10.1016/j.matpur.2016.03.012

Cite this

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abstract = "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 is to analyze the effect of a small inhomogeneity in the context of this non-local full wave equation.",

keywords = "Approximate cloaking, Drude–Lorentz model, Small inhomogeneity, Wave equation",

author = "Nguyen, {Hoai Minh} and Vogelius, {Michael S.}",

note = "Funding Information: The authors would like to thank Michael Weinstein for introducing them to the Drude–Lorentz model, and for related discussions. The work of H-M. Nguyen was partially supported by NSF grant DMS-1201370 and by the Alfred P. Sloan Foundation . The work of M.S. Vogelius was partially supported by NSF grant DMS-1211330 , and by the NSF IR/D program while serving at the National Science Foundation. Publisher Copyright: {\textcopyright} 2016 Elsevier Masson SAS",

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AU - Vogelius, Michael S.

N1 - Funding Information: The authors would like to thank Michael Weinstein for introducing them to the Drude–Lorentz model, and for related discussions. The work of H-M. Nguyen was partially supported by NSF grant DMS-1201370 and by the Alfred P. Sloan Foundation . The work of M.S. Vogelius was partially supported by NSF grant DMS-1211330 , and by the NSF IR/D program while serving at the National Science Foundation. Publisher Copyright: © 2016 Elsevier Masson SAS

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N2 - 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 is to analyze the effect of a small inhomogeneity in the context of this non-local full wave equation.

AB - 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 is to analyze the effect of a small inhomogeneity in the context of this non-local full wave equation.

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KW - Small inhomogeneity

KW - Wave equation

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Approximate cloaking for the full wave equation via change of variables: The Drude–Lorentz model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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