Waves in a thin and periodically oscillating medium

Rita Ferreira; M. Luísa Mascarenhas

doi:10.1016/j.crma.2008.03.007

Waves in a thin and periodically oscillating medium

Rita Ferreira^*, M. Luísa Mascarenhas

^*Corresponding author for this work

Computer, Electrical and Mathematical Science and Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language	English (US)
Pages (from-to)	579-584
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	9-10
DOIs	https://doi.org/10.1016/j.crma.2008.03.007
State	Published - May 1 2008

ASJC Scopus subject areas

Mathematics(all)

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abstract = "We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).",

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AU - Ferreira, Rita

AU - Mascarenhas, M. Luísa

PY - 2008/5/1

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N2 - We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

AB - We study the asymptotic behavior of the spectrum of an elliptic operator with periodically oscillating coefficients, in a thin domain, with vanishing Dirichlet conditions. Two cases are treated: the case where the periodicity of the oscillations and the thickness of the domain have the same order of magnitude and the case where the oscillations have a frequency much greater than the thickness of the domain. A physical motivation can be to understand the behavior of the probability density associated to the wave function of a particle confined to a very thin domain, with periodically varying characteristics. To cite this article: R. Ferreira, M.L. Mascarenhas, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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SN - 1631-073X

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ER -

Waves in a thin and periodically oscillating medium

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