Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Waves in slowly varying band-gap media   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, captured by a multiple-scale
Wentzel-Kramers-Brillouin (WKB) approximation, with complementary
multiple-scale solutions spatially localised about dispersion singularities.
Within the latter regions the Bloch wavenumber is nearly critical; this allows
their homogenisation, following the method of high-frequency homogenisation
(HFH), over a naturally arising scale intermediate between the periodicity
(wavelength) and the macro-scale. Analogously to a classical turning-point
analysis, we show that close to a spatial band-gap edge the solution is an Airy
function, only that it is modulated on the short scale by a standing-wave Bloch
eigenfunction. By carrying out the asymptotic matching between the WKB and HFH
solutions we provide a detailed description of Bloch-wave reflection from a
band gap. Finally, we implement the asymptotic theory for a layered medium and
demonstrate excellent agreement with numerical computations.

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The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th