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Article Dans Une Revue Applied Mathematics and Computation Année : 2022

Resonance scattering in a waveguide with identical thick perforated barriers

Résumé

We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.
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Arxiv 2001.07060 (2020) Delitsyn, Grebenkov [Resonance scattering in a waveguide with identical thick perforated barriers].pdf (361.35 Ko) Télécharger le fichier
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Dates et versions

hal-03805545 , version 1 (10-10-2022)

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Andrey Delitsyn, Denis S Grebenkov. Resonance scattering in a waveguide with identical thick perforated barriers. Applied Mathematics and Computation, 2022, 412, pp.126592. ⟨10.1016/j.amc.2021.126592⟩. ⟨hal-03805545⟩
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