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Spectral properties of the Neumann-Poincar\'e operator and cloaking by anomalous localized resonance for the elasto-static system
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We first investigate spectral properties of the Neumann-Poincar\'e (NP) operator for the Lam\'e 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 Lam\'e 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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Spectral properties of Neumann-Poincare operator and anomalous localized resonance in elasticity beyond quasi-static limit
For a spherical elastic inclusion, the paper gives explicit finite-frequency eigenvalues and eigenfunctions of the Neumann-Poincaré operator and constructs core-shell metamaterials whose anomalous resonances cloak sou...
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