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Matem. Mod., 2018, Volume 30, Number 2, Pages 48–80 (Mi mm3939)  

This article is cited in 5 scientific papers (total in 5 papers)

Kinetic Monte Carlo method: mathematical foundations and applications to physics of low-dimensional nanostructures

S. V. Kolesnikov, A. M. Saletsky, S. A. Dokukin, A. L. Klavsyuk

Faculty of Physics, Moscow State University

Abstract: The kinetic Monte Carlo method is essential tool for investigation of atomic and molecular systems. It is applicable for the wide range of problems such as the atomic diffusion, the formation of crystal defects and chemical compounds, the growth and the self-organization of nanostructures. In the present review we consider the basic principles of the kinetic Monte Carlo method and its modern modifications both lattice and non-lattice. The special attention is focused on the self-learning algorithms constructed from different saddle point finding methods and the algorithms for kinetic Monte Carlo acceleration. All methods are illustrated by the actual examples, the most of them are connected with the physics of metal surfaces.

Keywords: kinetic Monte Carlo, self-organization, nanostructures.

Full text: PDF file (1240 kB)
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Received: 03.04.2017

Citation: S. V. Kolesnikov, A. M. Saletsky, S. A. Dokukin, A. L. Klavsyuk, “Kinetic Monte Carlo method: mathematical foundations and applications to physics of low-dimensional nanostructures”, Matem. Mod., 30:2 (2018), 48–80

Citation in format AMSBIB
\Bibitem{KolSalDok18}
\by S.~V.~Kolesnikov, A.~M.~Saletsky, S.~A.~Dokukin, A.~L.~Klavsyuk
\paper Kinetic Monte Carlo method: mathematical foundations and applications to physics of low-dimensional nanostructures
\jour Matem. Mod.
\yr 2018
\vol 30
\issue 2
\pages 48--80
\mathnet{http://mi.mathnet.ru/mm3939}
\elib{https://elibrary.ru/item.asp?id=32497617}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Kolesnikov, A. M. Saletsky, “Electromigration of small vacancy clusters on the (100) copper surface”, JETP Letters, 108:1 (2018), 18–22  mathnet  crossref  crossref  isi  elib  elib
    2. A. G. Syromyatnikov, A. M. Saletsky, A. L. Klavsyuk, “Dependence of the distribution of atomic chain lengths on a vicinal surface on external parameters”, JETP Letters, 107:12 (2018), 766–769  mathnet  crossref  crossref  isi  elib  elib
    3. S. A. Dokukin, S. V. Kolesnikov, A. M. Saletsky, “Diffusion of atomic dimers during the formation of a pt/cu(111) surface alloy”, Mosc. Univ. Phys. Bull., 74:4 (2019), 385–391  crossref  isi
    4. A. G. Syromyatnikov, A. M. Saletsky, A. L. Klavsyuk, “Stability and magnetism on the atomic scale: atom-wide wires on vicinal metal substrate”, J. Magn. Magn. Mater., 510 (2020), 166896  crossref  isi
    5. A. G. Syromyatnikov, S. V. Kolesnikov, A. M. Saletsky, A. L. Klavsyuk, “Formation and properties of metallic atomic chains and wires”, Phys. Usp., 64:7 (2021), 671–701  mathnet  crossref  crossref
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