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Waves in slowly varying band-gap media
[article]
2016
arXiv
pre-print
This paper is concerned with the asymptotic description of high-frequency waves in locally periodic media. A key issue is that the Bloch-dispersion curves vary with the local microstructure, giving rise to hidden singularities associated with band-gap edges and branch crossings. We describe an asymptotic approach for overcoming this difficulty, and take a first step by studying in detail the simplest case of 1D Helmholtz waves. The method entails matching adiabatically propagating Bloch waves,
arXiv:1612.03895v1
fatcat:rbq5qmrt5nafvnhorutrate4d4