Surface spectra of discrete Laplacians

E. Korotyaev, K. Ryadovkin, N. Saburova

Research outputpeer-review

Abstract

It is well known that the spectra of Laplacians on periodic graphs consist of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We consider Laplacians on periodic graphs with boundaries. Under some conditions on the boundary the spectrum of the Laplacian has the so-called surface part, i.e., the spectrum corresponding to waves localized near the boundary. The surface spectrum is of particular interest due to its connection with the study of thermal transport, propagation of electromagnetic and acoustic waves. In this work we describe this spectrum.

Original languageEnglish
Title of host publicationProceedings of the International Conference Days on Diffraction, DD 2018
EditorsA.Ya. Kazakov, A.P. Kiselev, L.I. Goray, O.V. Motygin
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages182-186
Number of pages5
ISBN (Electronic)9781728103136
DOIs
Publication statusPublished - 29 Nov 2018
EventInternational conference Days on Diffraction-2018 - St Petersburg
Duration: 4 Jun 20188 Jun 2018

Publication series

NameProceedings of the International Conference Days on Diffraction, DD 2018

Conference

ConferenceInternational Conference on Days on Diffraction (DD)
CountryRussian Federation
CitySt Petersburg
Period4/06/188/06/18

Scopus subject areas

  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Computational Mathematics
  • Astronomy and Astrophysics
  • Radiation

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    Korotyaev, E., Ryadovkin, K., & Saburova, N. (2018). Surface spectra of discrete Laplacians. In A. Y. Kazakov, A. P. Kiselev, L. I. Goray, & O. V. Motygin (Eds.), Proceedings of the International Conference Days on Diffraction, DD 2018 (pp. 182-186). [8553356] (Proceedings of the International Conference Days on Diffraction, DD 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2018.8553356