- 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
of related papers
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