Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 228, Pages 58–84
DOI: https://doi.org/10.36535/0233-6723-2023-228-58-84 (Mi into1227) 		 
Spontaneous clustering in Markov chains. IV. Clustering in turbulent environments

V. V. Uchaikina, V. A. Litvinovb

a Ulyanovsk State University
b Barnaul Law Institute of the Ministry of Internal Affairs of the Russian Federation
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DOI: https://doi.org/10.36535/0233-6723-2023-228-58-84
Abstract: In the fourth part of the review, we discuss mathematical models of clustering that describe the behavior of impurity particles (markers, tags, etc.) in a turbulent environment. Along with the classical approach (Smoluchowski, Richardson), we describe statistical models used in computer modeling of processes (the Neyman–Scott and Metropolis models and Markov chains). Some aspects of the processes of local accumulation and gravitational sedimentation of particles in a turbulent environment are discussed. The last section is devoted to the concept of a representative sample, which is important in natural and numerical experiments.
The first part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 220. — P. 125–144.
The second part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 221. — P. 128–147.
The third part: Itogi Nauki Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. — 2023. — 222. — P. 115–133.
Keywords: turbulence, Markov chain, power spectrum, radial function, numerical modeling
Funding agency Grant number
Russian Science Foundation 23-79-30017
Ministry of Science and Higher Education of the Russian Federation 075-15-2021-581
This work was supported by the Russian Science Foundation (project No. 23-79-30017) and the Ministry of Higher Education and Science of the Russian Federation (project No. 075-15-2021-581).
Document Type: Article
UDC: 519.2:531/534
MSC: 65P40
Language: Russian
Citation: V. V. Uchaikin, V. A. Litvinov, “Spontaneous clustering in Markov chains. IV. Clustering in turbulent environments”, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 228, VINITI, Moscow, 2023, 58–84
Citation in format AMSBIB
\Bibitem{UchLit23}
\by V.~V.~Uchaikin, V.~A.~Litvinov
\paper Spontaneous clustering in Markov chains. IV. Clustering in turbulent environments
\inbook Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 228
\pages 58--84
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1227}
\crossref{https://doi.org/10.36535/0233-6723-2023-228-58-84}
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