BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids

BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids

A chain of kinetic equations for non-equilibrium one-particle, two-particle and s-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydr...

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Бібліографічні деталі
Дата:2016
Автори: Yukhnovskii, I.R., Hlushak, P.A., Tokarchuk, M.V.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики конденсованих систем НАН України 2016
Назва видання:Condensed Matter Physics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/156560
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids / I.R. Yukhnovskii, P.A. Hlushak, M.V. Tokarchuk // Condensed Matter Physics. — 2016. — Т. 19, № 4. — С. 43705: 1–18. — Бібліогр.: 51 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1565602019-06-19T01:26:11Z BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids Yukhnovskii, I.R. Hlushak, P.A. Tokarchuk, M.V. A chain of kinetic equations for non-equilibrium one-particle, two-particle and s-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with non-equilibrium distribution function of collective variables that satisfies generalized Fokker-Planck equation. On the basis of the method of collective variables, a scheme of calculation of non-equilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of collective variables is proposed. Contributions of short- and long-range interactions between particles are separated, so that the short-range interactions (for example, the model of hard spheres) are described in the coordinate space, while the long-range interactions — in the space of collective variables. Short-ranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres. Запропоновано ланцюжок кiнетичних рiвнянь для нерiвноважних одночастинкової, двочастинкової i sчастинкової функцiй розподiлу частинок з урахуванням нелiнiйних гiдродинамiчних флуктуацiй. Використовується метод нерiвноважного статистичного оператора Зубарєва з проектуванням. Нелiнiйнi гiдродинамiчнi флуктуацiї описуються нерiвноважною функцiєю розподiлу колективних змiнних, що задовольняє узагальнене рiвняння Фоккера-Планка. На основi методу колективних змiнних запропоновано спосiб розрахунку нерiвноважної структурної функцiї розподiлу колективних змiнних та їх гiдродинамiчних швидкостей (вище гаусового наближення), що мiстяться в узагальненому рiвняннi Фоккера-Планка для нерiвноважної функцiї розподiлу колективних змiнних. При цьому роздiленi вклади вiд короткодiючих i далекодiючих взаємодiй мiж частинками, що привело до того, що короткодiючi взаємодiї (наприклад, модель твердих сфер) описуються в координатному просторi, а далекодiючi — у просторi колективних змiнних. Короткодiюча складова розглядається як базисна, якiй вiдповiдає ланцюжок рiвнянь ББГКI для моделi твердих сфер. 2016 Article BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids / I.R. Yukhnovskii, P.A. Hlushak, M.V. Tokarchuk // Condensed Matter Physics. — 2016. — Т. 19, № 4. — С. 43705: 1–18. — Бібліогр.: 51 назв. — англ. 1607-324X PACS: 74.40.Gh, 05.70.L, 64.70.F DOI:10.5488/CMP.19.43705 arXiv:1612.07219 http://dspace.nbuv.gov.ua/handle/123456789/156560 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description A chain of kinetic equations for non-equilibrium one-particle, two-particle and s-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev non-equilibrium statistical operator with projection is used. Nonlinear hydrodynamic fluctuations are described with non-equilibrium distribution function of collective variables that satisfies generalized Fokker-Planck equation. On the basis of the method of collective variables, a scheme of calculation of non-equilibrium structural distribution function of collective variables and their hydrodynamic speeds (above Gaussian approximation) contained in the generalized Fokker-Planck equation for the non-equilibrium distribution function of collective variables is proposed. Contributions of short- and long-range interactions between particles are separated, so that the short-range interactions (for example, the model of hard spheres) are described in the coordinate space, while the long-range interactions — in the space of collective variables. Short-ranged component is regarded as basic, and corresponds to the BBGKY chain of equations for the model of hard spheres.
format Article
author Yukhnovskii, I.R.
Hlushak, P.A.
Tokarchuk, M.V.
spellingShingle Yukhnovskii, I.R.
Hlushak, P.A.
Tokarchuk, M.V.
BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
Condensed Matter Physics
author_facet Yukhnovskii, I.R.
Hlushak, P.A.
Tokarchuk, M.V.
author_sort Yukhnovskii, I.R.
title BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
title_short BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
title_full BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
title_fullStr BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
title_full_unstemmed BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
title_sort bbgky chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids
publisher Інститут фізики конденсованих систем НАН України
publishDate 2016
url http://dspace.nbuv.gov.ua/handle/123456789/156560
citation_txt BBGKY chain of kinetic equations, non-equilibrium statistical operator method and collective variable method in the statistical theory of non-equilibrium liquids / I.R. Yukhnovskii, P.A. Hlushak, M.V. Tokarchuk // Condensed Matter Physics. — 2016. — Т. 19, № 4. — С. 43705: 1–18. — Бібліогр.: 51 назв. — англ.
series Condensed Matter Physics
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AT hlushakpa bbgkychainofkineticequationsnonequilibriumstatisticaloperatormethodandcollectivevariablemethodinthestatisticaltheoryofnonequilibriumliquids
AT tokarchukmv bbgkychainofkineticequationsnonequilibriumstatisticaloperatormethodandcollectivevariablemethodinthestatisticaltheoryofnonequilibriumliquids
first_indexed 2023-05-20T17:49:44Z
last_indexed 2023-05-20T17:49:44Z
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