494 research outputs found
Analysis of surface polariton resonance for nanoparticles in elastic system
This paper is concerned with the analysis of surface polariton resonance for
nanoparticles in linear elasticity. With the presence of nanoparticles, we
first derive the perturbed displacement field associated to a given elastic
source field. It is shown that the leading-order term of the perturbed elastic
wave field is determined by the Neumann-Poinc\'are operator associated to the
Lam\'e system. By analyzing the spectral properties of the aforesaid
Neumann-Poinc\'are operator, we study the polariton resonance for the elastic
system. The results may find applications in elastic wave imaging.Comment: 18 pages, comments are welcom
Surface concentration of transmission eigenfunctions
The transmission eigenvalue problem is a type of non-elliptic and
non-selfadjoint spectral problem that arises in the wave scattering theory when
invisibility/transparency occurs. The transmission eigenfunctions are the
interior resonant modes inside the scattering medium. We are concerned with the
geometric rigidity of the transmission eigenfunctions and show that they
concentrate on the boundary surface of the underlying domain in two senses.
This substantiates the recent numerical discovery in [10] on such an intriguing
spectral phenomenon of the transmission resonance. Our argument is based on
generalized Weyl's law and certain novel ergodic properties of the coupled
boundary layer-potential operators which are employed to analyze the
generalized transmission eigenfunctions.Comment: 25 pages and comments are welcom
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