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On spectral properties of Neuman-Poincaré operator and plasmonic resonances in 3D elastostatics. (English) Zbl 1435.35372

The authors consider plasmon resonances and cloaking for the elastostatic system in \(\mathbb{R}^3\) via the spectral theory of the Neumann-Poincaré operator. They first derive the full spectral properties of the Neumann-Poincaré operator for the 3D elastostatic system in the spherical geometry. The spectral result is of significant interest for its own sake, and serves as a highly nontrivial extension of the corresponding 2D study in [K. Ando et al., Eur. J. Appl. Math. 29, No. 2, 189–225 (2018; Zbl 06903421)]. The derivation of the spectral result in 3D involves much more complicated and subtle calculations and arguments than that for the 2D case. Then they consider a 3D plasmonic structure in elastostatics which takes a general core-shell-matrix form with the metamaterial located in the shell. Using the obtained spectral result, they provide an accurate characterisation of the anomalous localised resonance and cloaking associated to such a plasmonic structure.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
74B05 Classical linear elasticity
47A10 Spectrum, resolvent
35B34 Resonance in context of PDEs
74J20 Wave scattering in solid mechanics

Citations:

Zbl 06903421
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References:

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