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

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 2008
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by POCI/MAT/60587/2004, by FCT-Plurianual (CMA) and by SFRH/BD/25573/2005. The authors thank M. Bendsœ for suggesting the problem, D. Krejcˇirík and D. Borisov for having pointed out some references, and CMAF for the hospitality.

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2008.03.007

Cite this

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title = "Waves in a thin and periodically oscillating medium",

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).",

author = "Rita Ferreira and Mascarenhas, {M. Lu{\'i}sa}",

note = "Funding Information: This research was supported by POCI/MAT/60587/2004, by FCT-Plurianual (CMA) and by SFRH/BD/25573/2005. The authors thank M. Bends{\oe} for suggesting the problem, D. Krejcˇir{\'i}k and D. Borisov for having pointed out some references, and CMAF for the hospitality.",

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AU - Ferreira, Rita

AU - Mascarenhas, M. Luísa

N1 - Funding Information: This research was supported by POCI/MAT/60587/2004, by FCT-Plurianual (CMA) and by SFRH/BD/25573/2005. The authors thank M. Bendsœ for suggesting the problem, D. Krejcˇirík and D. Borisov for having pointed out some references, and CMAF for the hospitality.

PY - 2008/5

Y1 - 2008/5

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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DO - 10.1016/j.crma.2008.03.007

M3 - Article

AN - SCOPUS:43049088408

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9-10

ER -

Waves in a thin and periodically oscillating medium

Abstract

Bibliographical note

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