RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 5, Pages 879–895 (Mi zvmmf10393)  

This article is cited in 2 scientific papers (total in 2 papers)

Discrete spectrum of cranked quantum and elastic waveguides

S. A. Nazarovabc

a St. Petersburg State University, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg, 198504, Russia
b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoi pr. 61, V.O., St. Petersburg, 199178, Russia
c St. Petersburg State Polytechnical University, Politekhnicheskaya ul. 29, St. Petersburg, 195251, Russia

Abstract: The spectrum of quantum and elastic waveguides in the form of a cranked strip is studied. In the Dirichlet spectral problem for the Laplacian (quantum waveguide), in addition to well-known results on the existence of isolated eigenvalues for any angle $\alpha$ at the corner, a priori lower bounds are established for these eigenvalues. It is explained why methods developed in the scalar case are frequently inapplicable to vector problems. For an elastic isotropic waveguide with a clamped boundary, the discrete spectrum is proved to be nonempty only for small or close-to-$\pi$ angles $\alpha$. The asymptotics of some eigenvalues are constructed. Elastic waveguides of other shapes are discussed.

Key words: quantum and elastic waveguides, discrete spectrum, trapped modes, asymptotics of eigenvalues.

Funding Agency Grant Number
Saint Petersburg State University 0.38.237.2014


DOI: https://doi.org/10.7868/S0044466916050173

Full text: PDF file (387 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2016, 56:5, 864–880

Bibliographic databases:

Document Type: Article
UDC: 519.63
Received: 26.01.2015

Citation: S. A. Nazarov, “Discrete spectrum of cranked quantum and elastic waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 879–895; Comput. Math. Math. Phys., 56:5 (2016), 864–880

Citation in format AMSBIB
\Bibitem{Naz16}
\by S.~A.~Nazarov
\paper Discrete spectrum of cranked quantum and elastic waveguides
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 5
\pages 879--895
\mathnet{http://mi.mathnet.ru/zvmmf10393}
\crossref{https://doi.org/10.7868/S0044466916050173}
\elib{http://elibrary.ru/item.asp?id=26068766}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 5
\pages 864--880
\crossref{https://doi.org/10.1134/S0965542516050171}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000377419200013}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84974653329}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10393
  • http://mi.mathnet.ru/eng/zvmmf/v56/i5/p879

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nazarov S.A., “Spectrum of a Problem of Elasticity Theory in the Union of Several Infinite Layers”, Russ. J. Math. Phys., 25:1 (2018), 73–87  crossref  mathscinet  zmath  isi
    2. F. L. Bakharev, S. A. Nazarov, “Asimptotika sobstvennykh chisel dlinnykh plastin Kirkhgofa s zaschemlennymi krayami”, Matem. sb., 210:4 (2019), 3–26  mathnet  crossref  elib
  • Number of views:
    This page:74
    References:18
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019