Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs
- Creators
- Kuchment, Peter
- Kunyansky, Leonid A.
Abstract
The theory of classical waves in periodic high contrast photonic and acoustic media leads to the spectral problem - Δu= λ∈u, where the dielectric constant ∈(x) is a periodic function which assumes a large value ∈ near a periodic graph Σ in R^2 and is equal to 1 otherwise. Existence and locations of spectral gaps are of primary interest. The high contrast asymptotics naturally leads to pseudodifferential operators of the Dirichlet-to-Neumann type on graphs and on more general structures. Spectra of these operators are studied numerically and analytically. New spectral effects are discovered, among them the "almost discreteness" of the spectrum for a disconnected graph and the existence of "almost localized" waves in some connected purely periodic structures.
Additional Information
© 2012 A K Peters, Ltd. Work of both authors was partially supported by the NSF Grant DMS-961044 and by a DEPSCoR Grant administered through the ARO. The first author was also partially supported by an NSF EPSCoR Grant. The content of this article does not necessarily reflect the position or the policy of the federal government. The authors express their gratitude to Professors P. Exner, A. Figotin, A. Klein, and Dr. I. Ponomarev for helpful discussions. We are thankful to Professors V. Isakov, S. Molchanov, and Z. Sun for references to literature and to reviewers for important remarks.Additional details
- Eprint ID
- 28743
- Resolver ID
- CaltechAUTHORS:20120111-075338043
- DMS-961044
- NSF
- Army Research Office (ARO) DEPSCoR Grant
- NSF DEPSCoR Grant
- Created
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2012-01-11Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field
- Other Numbering System Name
- Zentralblatt MATH identifier
- Other Numbering System Identifier
- 0930.35112