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arXiv · 1510.00989

Spectral properties of the Neumann-Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system

Kazunori Ando·Yong-Gwan Ji·Hyeonbae Kang·Kyoungsun Kim·Sanghyeon Yu
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Abstract

We first investigate spectral properties of the Neumann-Poincaré (NP) operator for the Lamé system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for Laplace operator. We then show that even if elasto-static NP operator is not compact even on smooth domains, its spectrum consists of eigenvalues which accumulates to two numbers determined by Lamé constants. We then derive explicitly eigenvalues and eigenfunctions on disks and ellipses. We then investigate resonance occurring at eigenvalues and anomalous localized resonance at accumulation points of eigenvalues. We show on ellipses that cloaking by anomalous localized resonance takes place at accumulation points of eigenvalues.

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Kazunori Ando, Yong-Gwan Ji, Hyeonbae Kang, Kyoungsun Kim, Sanghyeon Yu. 2015-10-04. Spectral properties of the Neumann-Poincaré operator and cloaking by anomalous localized resonance for the elasto-static system. https://arxiv.org/abs/1510.00989

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