Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble
We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→0, 1/v→∞ (z→∞), and d 3 (1/v)=const (d 3 z=const)). For this purpose, we use the Kirkwood-Salsburg equations. We prove that, in the Boltzmann-Enskog limit, solutions of these equations exist and the limit distrib...
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| Дата: | 1997 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1997
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4990 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511182951022592 |
|---|---|
| author | Petrina, E. D. Petrina, D. Ya. Петрина, Е. Д. Петрина, Д. Я. Петрина, Е. Д. Петрина, Д. Я. |
| author_facet | Petrina, E. D. Petrina, D. Ya. Петрина, Е. Д. Петрина, Д. Я. Петрина, Е. Д. Петрина, Д. Я. |
| author_sort | Petrina, E. D. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:22:11Z |
| description | We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→0, 1/v→∞ (z→∞), and d 3 (1/v)=const (d 3 z=const)). For this purpose, we use the Kirkwood-Salsburg equations. We prove that, in the Boltzmann-Enskog limit, solutions of these equations exist and the limit distribution functions are constant. By using the cluster and compatibility conditions, we prove that all distribution functions are equal to the product of one-particle distribution functions, which can be represented as power series in z=d 3 z with certain coefficients. |
| first_indexed | 2026-03-24T03:08:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4990 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:08:50Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2a/7fa9c922752cef959be3381ee892f62a.pdf |
| spelling | umjimathkievua-article-49902020-03-18T21:22:11Z Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble О существовании равновесных состояний систем упругих шаров в пределе Больцмана - Энскога Petrina, E. D. Petrina, D. Ya. Петрина, Е. Д. Петрина, Д. Я. Петрина, Е. Д. Петрина, Д. Я. We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→0, 1/v→∞ (z→∞), and d 3 (1/v)=const (d 3 z=const)). For this purpose, we use the Kirkwood-Salsburg equations. We prove that, in the Boltzmann-Enskog limit, solutions of these equations exist and the limit distribution functions are constant. By using the cluster and compatibility conditions, we prove that all distribution functions are equal to the product of one-particle distribution functions, which can be represented as power series in z=d 3 z with certain coefficients. Вивчаються рівноважні стани систем пружних куль в границі Больцмана- Енскога, коли (d→0, 1/v→∞ (z→∞), d 3 (1/v)=const (d 3 z=const)). Для цього використовуються рівняння Кірквуда- Зальцбурга. Доведено, що в границі Больцмана - Енскога існують розв'язки цих рівнянь, і граничні функції розподілу сталі. Використовуючи умову узгодженості і кластерності, доведено, що всі функції розподілу дорівнюють добутку одночастинкових, які в свою чергу можна подати степеневим рядом від z=d 3 z з певними коефіцієнтами. Institute of Mathematics, NAS of Ukraine 1997-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4990 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 1 (1997); 112–121 Український математичний журнал; Том 49 № 1 (1997); 112–121 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4990/6679 https://umj.imath.kiev.ua/index.php/umj/article/view/4990/6680 Copyright (c) 1997 Petrina E. D.; Petrina D. Ya. |
| spellingShingle | Petrina, E. D. Petrina, D. Ya. Петрина, Е. Д. Петрина, Д. Я. Петрина, Е. Д. Петрина, Д. Я. Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title | Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title_alt | О существовании равновесных состояний систем
упругих шаров в пределе Больцмана - Энскога |
| title_full | Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title_fullStr | Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title_full_unstemmed | Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title_short | Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble |
| title_sort | existence of equilibrium states of systems of hard spheres in the boltzmann-enskog limit within the frame work of the grand canonical ensemble |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4990 |
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