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- W2676136729 abstract "The present work deals with propagation of acoustic waves in periodic media. Thesemedia have particularly interesting properties since the spectrum associated with theunderlying wave operator in such media has a band-gap structure: there exist intervals offrequences for which monochromatic waves do not propagate. Moreover, by introducinglinear defects in this kind of media, one can create guided modes inside the bands offorbidden frequences. In this work we show that it is possible to create such guidedmodes in the case of particular periodic media of grid type: more precisely, the periodicdomain in question is R2 minus an infinite set of rectangular obstacles periodically spacedin two orthogonal directions (the distance between two neighbour obstacles being ),which is locally perturbed by diminishing the distance between two columns of obstacles.The results are extended to the 3D case.This work has a theoretical and a numerical aspect. From the theoretical point of view theanalysis is based on the fact that, being small, the spectrum of the operator associatedwith our problem is close to the spectrum of a problem posed on a graph which is ageometric limit of the domain as tends to 0. However, for the limit graph the spectrumcan be computed explicitly. Then, we study the spectrum of the non-limit operatorusing asymptotic analysis. Theoretical results are illustrated by numerical computationsobtained with a numerical method developed for study of periodic media: this method isbased on the reduction of the initial (linear) eigenvalue problem posed in an unboundeddomain to a non-linear problem posed in a bounded domain (using the exact Dirichletto-Neumann operator)." @default.
- W2676136729 created "2017-06-30" @default.
- W2676136729 creator A5058125566 @default.
- W2676136729 date "2016-07-07" @default.
- W2676136729 modified "2023-09-24" @default.
- W2676136729 title "Open periodic waveguides : Theory and computation" @default.
- W2676136729 hasPublicationYear "2016" @default.
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