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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, Issue 4, Pages 86–99 (Mi vuu298)  

This article is cited in 8 scientific papers (total in 8 papers)

MECHANICS

Bifurcation of the nanostructures induced by ion bombardment

A. N. Kulikov, D. A. Kulikov, A. S. Rudyi

P. G. Demidov Yaroslavl State University, Yaroslavl, Russia
Full-text PDF (196 kB) Citations (8)
References:
Abstract: We consider ion-bombardment-induced processes for formation of periodic structures. As a mathematical model, we have chosen the generalized two-dimensional Kuramoto–Sivashinsky equation which is equivalent to the equation obtained by Bradley–Harper. The jagged relief obtained due to ionic bombardment can be explained from a mathematical point of view as local bifurcations of flat profile involving an exchange of stabilities.
To describe the above relief asymptotic formulas are obtained. The bifurcation theory method for problems with infinite dimensional phase space is used to study nonlinear boundary value problem. In particular, we use normal form building which springs from Krylov–Bogolyubov method of averaging.
Keywords: ion bombardment, periodic nanostructures, Kuramoto-Sivashinsky equation, local bifurcations, normal forms.
Received: 29.06.2011
Document Type: Article
UDC: 517.956.4
MSC: 37H20
Language: Russian
Citation: A. N. Kulikov, D. A. Kulikov, A. S. Rudyi, “Bifurcation of the nanostructures induced by ion bombardment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 4, 86–99
Citation in format AMSBIB
\Bibitem{KulKulRud11}
\by A.~N.~Kulikov, D.~A.~Kulikov, A.~S.~Rudyi
\paper Bifurcation of the nanostructures induced by ion bombardment
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 4
\pages 86--99
\mathnet{http://mi.mathnet.ru/vuu298}
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  • https://www.mathnet.ru/eng/vuu/y2011/i4/p86
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    Abstract page:392
    Full-text PDF :208
    References:66
    First page:1
     
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