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Creators/Authors contains: "Furia, Alexander"

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  1. ; (, Journal of Mathematical Physics)
    We consider the asymptotic analysis of the resonances of the scalar Helmholtz equation corresponding to a bounded scatterer with a periodic index of refraction and small period size ϵ. When the homogenized resonance is simple, we derive an explicit formula for the first order corrections to the limiting resonances. For scatterers with boundary that has a flat part of rational normal, the first order corrections are not unique and depend on the interaction of the boundary of the scatterer with the microstructure. In this case the resonances converge only O(ϵ) in general. For smooth domains with no flat parts, the resonances converge o(ϵ), but the convergence is nonetheless sub-quadratic. 
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    Free, publicly-accessible full text available April 1, 2026