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Honeycomb-lattice Minnaert bubbles
(2018)SAM Research ReportThe aim of this paper is to rigorously show the existence of a Dirac dispersion cone in a bubbly honeycomb phononic crystal comprised of bubbles of arbitrary shape. The main result is an asymptotic formula for the quasi-periodic Minnaert resonance frequencies close to the symmetry points K in the Brilloun zone. This shows the linear dispersion relation of a Dirac cone. Our findings in this paper are illustrated in the case of circular ...Report -
Subwavelength resonances of encapsulated bubbles
(2018)SAM Research ReportThe aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance ...Report -
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