S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017), 2065–2078; Comput. Math. Math. Phys., 57:12 (2017), 2017

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 12, Pages 2065–2078
DOI: https://doi.org/10.7868/S0044466917120031 (Mi zvmmf10654)

This article is cited in 12 scientific papers (total in 12 papers)

Generalized Boltzmann-type equations for aggregation in gases

S. Z. Adzhiev^a, V. V. Vedenyapin^bc, Yu. A. Volkov^bc, I. V. Melikhov^a

^a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
^b RUDN University, Moscow, Russia
^c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Full-text PDF (405 kB) Citations (12)

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DOI: https://doi.org/10.7868/S0044466917120031

Abstract: The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker–Döring-type equation). The transition to a continuum description is performed.

Key words: aggregation, coalescence-fragmentation equations, Boltzmann equation, Becker–Döring equations, principle of detailed balance, conservation laws, Fokker–Planck-type equation.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation
Russian Academy of Sciences - Federal Agency for Scientific Organizations	1.3.1

Received: 31.05.2016
Revised: 12.03.2017

English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 12, Pages 2017–2029
DOI: https://doi.org/10.1134/S096554251712003X

Bibliographic databases:

Document Type: Article

UDC: 519.634

Language: Russian

Citation: S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017), 2065–2078; Comput. Math. Math. Phys., 57:12 (2017), 2017–2029

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Linking options:

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This publication is cited in the following 12 articles:

V. V. Vedenyapin, D. A. Kogtenev, “O vyvode i svoistvakh uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2023, 020, 18 pp.
S. Z. Adzhiev, V. V. Vedenyapin, I. V. Melikhov, “Kinetic aggregation models leading to morphological memory of formed structures”, Comput. Math. Math. Phys., 62:2 (2022), 254–268
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Properties of the Vlasov-Maxwell-Einstein equations and their application to the problems of general relativity”, Gravit. Cosmol., 26:2 (2020), 173–183
V. Vedenyapin, N. Fimin, V. Chechetkin, “The system of Vlasov-Maxwell-Einstein-type equations and its nonrelativistic and weak relativistic limits”, Int. J. Mod. Phys. D, 29:1 (2020), 2050006
S. Z. Adzhiev, V I. Melikhov , V. V. Vedenyapin, “On the H-theorem for the Becker-Doring system of equations for the cases of continuum approximation and discrete time”, Physica A, 553 (2020), 124608
S. Z. Adzhiev, Ya. G. Batishcheva, V. V. Vedenyapin, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, M. A. Negmatov, Yu. N. Orlov, N. N. Fimin, V. M. Chechetkin, “S.K. Godunov and kinetic theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences”, Comput. Math. Math. Phys., 60:4 (2020), 610–614
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties”, Nanosyst.-Phys. Chem. Math., 10:5 (2019), 549–563
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Equation of Vlasov–Maxwell–Einstein type and transition to a weakly relativistic approximation”, Comput. Math. Math. Phys., 59:11 (2019), 1816–1831
Victor V. Vedenyapin, Nikolai N. Fimin, Valeriy M. Chechetkin, “DERIVATION OF VLASOV-MAXWELL-EINSTEIN EQUATION AND ITS CONNECTION WITH COSMOLOGICAL LAMBDA-TERM”, Bulletin of the MSRU (Physics and Mathematics), 2019, no. 2, 24
Sergey Adzhiev, Janina Batishcheva, Igor Melikhov, Victor Vedenyapin, “Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem”, Physics, 1:2 (2019), 229
V. V. Vedenyapin, I. S. Pershin, “Uravnenie Vlasova–Maksvella–Einshteina i lyambda Einshteina”, Preprinty IPM im. M. V. Keldysha, 2019, 39–17
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Ob uravnenii Vlasova–Maksvella–Einshteina i ego nerelyativistskikh i slaborelyativistskikh analogakh”, Preprinty IPM im. M. V. Keldysha, 2018, 265, 30 pp.

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

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