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Spectral analysis of one-dimensional high-contrast elliptic problems with periodic coefficients


Reference:

Cherednichenko, K., Cooper, S. and Guenneau, S., 2015. Spectral analysis of one-dimensional high-contrast elliptic problems with periodic coefficients. Multiscale Modeling and Simulation, 13 (1), pp. 72-98.

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    Official URL:

    http://dx.doi.org/10.1137/130947106

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    Abstract

    We study the behavior of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent, e.g., the elastic or electromagnetic response of a two-component composite medium. Compared to the standard operators with moderate contrast, they exhibit a number of new effects due to the underlying nonuniform ellipticity of the family. The effective behavior of such media in the vanishing period limit also differs notably from that of multidimensional models investigated thus far by other authors, due to the fact that neither component of the composite forms a connected set. We then discuss a modified problem, where the equation coefficient is set to a positive constant on an interval that is independent of the period. Formal asymptotic analysis and numerical tests with finite elements suggest the existence of localized eigenfunctions (``defect modes''), whose eigenvalues are situated in the gaps of the limit spectrum for the unperturbed problem. Read More: http://epubs.siam.org/doi/10.1137/130947106

    Details

    Item Type Articles
    CreatorsCherednichenko, K., Cooper, S. and Guenneau, S.
    DOI10.1137/130947106
    Related URLs
    URLURL Type
    http://epubs.siam.org/journal/mmsubtPublisher
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code42128

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