TY - JOUR

T1 - Mathematical Modeling of Nonequilibrium Processes at the Department of Physical Mechanics, St. Petersburg State University. Part 1. Modeling of Processes in Gases, Liquids, and Solids

AU - Morozov, V.A.

AU - Khantuleva, T.A.

AU - Yakovlev, A.B.

N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Morozov, V.A.; St. Petersburg State UniversityRussian Federation; эл. почта: v.morozov@spbu.ru Адрес для корреспонденции: Khantuleva, T.A.; St. Petersburg State UniversityRussian Federation; эл. почта: t.khantuleva@spbu.ru Адрес для корреспонденции: Yakovlev, A.B.; St. Petersburg State UniversityRussian Federation; эл. почта: a.b.yakovlev@spbu.ru

PY - 2024/10

Y1 - 2024/10

N2 - Abstract: Here, we provide an overview of research dedicated to modeling nonequilibrium processes in gases, liquids, and solids conducted by the staff of the Department and Laboratory of Physical Mechanics, St. Petersburg State University from its founding in 1986 until 2023 inclusive. The main attention is paid to several important results: (i) the creation of an adsorption-layer model to describe the movement of aircraft in near space and the upper layers of the atmosphere; (ii) theoretical and experimental substantiation of the general approach to modeling high-speed and fast-flowing processes in various media; (iii) application of the indicated general approach to the study of shock-induced wave processes in a solid. The need for an integro-differential form of transport equations for nonequilibrium processes is substantiated in detail. The time evolution of the system, which results from the interaction of structural elements of the medium at the mesolevel, is shown to be described by cybernetic methods developed by A. L. Fradkov using the theory of control of adaptive systems with feedback. Other results are presented rather briefly. © Pleiades Publishing, Ltd. 2024. ISSN 1063-4541, Vestnik St. Petersburg University, Mathematics, 2024, Vol. 57, No. 3, pp. 283–306. Pleiades Publishing, Ltd., 2024. Russian Text The Author(s), 2024, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2024, Vol. 11, No. 3, pp. 419–454.

AB - Abstract: Here, we provide an overview of research dedicated to modeling nonequilibrium processes in gases, liquids, and solids conducted by the staff of the Department and Laboratory of Physical Mechanics, St. Petersburg State University from its founding in 1986 until 2023 inclusive. The main attention is paid to several important results: (i) the creation of an adsorption-layer model to describe the movement of aircraft in near space and the upper layers of the atmosphere; (ii) theoretical and experimental substantiation of the general approach to modeling high-speed and fast-flowing processes in various media; (iii) application of the indicated general approach to the study of shock-induced wave processes in a solid. The need for an integro-differential form of transport equations for nonequilibrium processes is substantiated in detail. The time evolution of the system, which results from the interaction of structural elements of the medium at the mesolevel, is shown to be described by cybernetic methods developed by A. L. Fradkov using the theory of control of adaptive systems with feedback. Other results are presented rather briefly. © Pleiades Publishing, Ltd. 2024. ISSN 1063-4541, Vestnik St. Petersburg University, Mathematics, 2024, Vol. 57, No. 3, pp. 283–306. Pleiades Publishing, Ltd., 2024. Russian Text The Author(s), 2024, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2024, Vol. 11, No. 3, pp. 419–454.

KW - adsorption layer

KW - mesolevel

KW - modeling

KW - nonequilibrium process

KW - transport equations

UR - https://www.mendeley.com/catalogue/66e0cb51-6b7a-3b8e-b522-08346b8c12cb/

U2 - 10.1134/s1063454124700146

DO - 10.1134/s1063454124700146

M3 - статья

VL - 57

SP - 283

EP - 306

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -