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

8 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

General Mathematics
Applied Mathematics

Keywords

Approximate cloaking
Drude–Lorentz model
Small inhomogeneity
Wave equation

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10.1016/j.matpur.2016.03.012

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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.",

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AU - Vogelius, Michael S.

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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 - Drude–Lorentz model

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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