A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions,...
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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2018
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157045 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales / V.V. Ignatyuk, I.M. Mryglod, T. Bryk // Condensed Matter Physics. — 2018. — Т. 21, № 1. — С. 13001: 1–14. — Бібліогр.: 35 назв. — англ. |
Репозитарії
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irk-123456789-1570452019-06-20T01:28:35Z A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales Ignatyuk, V.V. Mryglod, I.M. Bryk, T. A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the “overdamped” regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane. Запропоновано простий анзац для дослiдження автокореляцiйних функцiй швидкостей (АФШ) флюїду на рiзних часових промiжках, що базується на ефективному пересумуваннi безмежних ланцюгових дробiв на основi фiзично обгрунтованого припущення про збiжнiсть часiв релаксацiї ядер вищих порядкiв, якi мають суто кiнетичну природу. Отриманi в рамках такого анзацу АФШ порiвнюються з результатами маркiвського наближення для вiдповiдних функцiй пам’ятi. Показано, що хоча в передемпферованому режимi обидва пiдходи дають дуже близькi результати на малих та промiжних часах, лише метод пересумовування дробiв веде до появи степеневих законiв у поведiнцi АФШ на великих часах, що не спостерiгається при описi динамiки флюїду скiнченним числом колективних мод. На основi аналiзу сингулярностей спектральних функцiй на комплекснiй площинi частот отриманi явнi вирази для оцiнки часiв переходу вiд кiнетичного етапу еволюцiї флюїду до гiдродинамiчного режиму. 2018 Article A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales / V.V. Ignatyuk, I.M. Mryglod, T. Bryk // Condensed Matter Physics. — 2018. — Т. 21, № 1. — С. 13001: 1–14. — Бібліогр.: 35 назв. — англ. 1607-324X PACS: 05.20.Jj, 47.10.-g, 47.11.-j DOI:10.5488/CMP.21.13001 arXiv:1712.02593 http://dspace.nbuv.gov.ua/handle/123456789/157045 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 simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed.
The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption
about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin.
The VAFs obtained within our approach are compared with the results of the Markovian approximation for
memory kernels. It is shown that although in the “overdamped” regime both approaches agree to a large extent
at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the
VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions
for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities
of spectral functions in the complex frequency plane. |
| format |
Article |
| author |
Ignatyuk, V.V. Mryglod, I.M. Bryk, T. |
| spellingShingle |
Ignatyuk, V.V. Mryglod, I.M. Bryk, T. A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales Condensed Matter Physics |
| author_facet |
Ignatyuk, V.V. Mryglod, I.M. Bryk, T. |
| author_sort |
Ignatyuk, V.V. |
| title |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| title_short |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| title_full |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| title_fullStr |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| title_full_unstemmed |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| title_sort |
simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2018 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157045 |
| citation_txt |
A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales / V.V. Ignatyuk, I.M. Mryglod, T. Bryk // Condensed Matter Physics. — 2018. — Т. 21, № 1. — С. 13001: 1–14. — Бібліогр.: 35 назв. — англ. |
| series |
Condensed Matter Physics |
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