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Abstract
We study the behavior of the spectrum of a family of onedimensional operators with periodic highcontrast coefficients as the period goes to zero, which may represent, e.g., the elastic or electromagnetic response of a twocomponent 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
Original language  English 

Pages (fromto)  7298 
Number of pages  17 
Journal  Multiscale Modeling and Simulation 
Volume  13 
Issue number  1 
Early online date  8 Jan 2015 
DOIs  
Publication status  Published  2015 
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Dive into the research topics of 'Spectral analysis of onedimensional highcontrast elliptic problems with periodic coefficients'. Together they form a unique fingerprint.Projects
 1 Finished

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council