98-481 Kuchment P., Kunyansky L.

Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs (1852K, PostScript, gzipped and uuencoded) Jul 1, 98

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Abstract. Propagation of classical waves in periodic high contrast photonic and acoustic media is considered in this preprint. The high contrast asymptotics naturally leads to spectral problems for pseudo-differential operators of the Dirichlet-to-Neumann type on graphs and on more general structures. Spectra of these operators are studied numerically and analytically. Existence and locations of spectral gaps are of primary interest. New spectral effects are discovered. Among them "almost discreteness" of the spectrum in the case of a disconnected graph and existence of "almost localized" waves in some connected purely periodic structures.

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