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, w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute for Condensed Matter Physics
2018-03-01
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| Series: | Condensed Matter Physics |
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| Online Access: | https://doi.org/10.5488/CMP.21.13001 |
| _version_ | 1811218320772300800 |
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| author | V.V. Ignatyuk I.M. Mryglod T. Bryk |
| author_facet | V.V. Ignatyuk I.M. Mryglod T. Bryk |
| author_sort | V.V. Ignatyuk |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-12T07:08:40Z |
| format | Article |
| id | doaj.art-d5577316d92d4c8581fdd6f202531be1 |
| institution | Directory Open Access Journal |
| issn | 1607-324X 2224-9079 |
| language | English |
| last_indexed | 2024-04-12T07:08:40Z |
| publishDate | 2018-03-01 |
| publisher | Institute for Condensed Matter Physics |
| record_format | Article |
| series | Condensed Matter Physics |
| spelling | doaj.art-d5577316d92d4c8581fdd6f202531be12022-12-22T03:42:43ZengInstitute for Condensed Matter PhysicsCondensed Matter Physics1607-324X2224-90792018-03-012111300110.5488/CMP.21.13001A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescalesV.V. IgnatyukI.M. MryglodT. BrykA 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.https://doi.org/10.5488/CMP.21.13001nonequilibrium statistical mechanicsstatistical hydrodynamicsclassical fluidsLangevin equationMarkovian processes |
| spellingShingle | V.V. Ignatyuk I.M. Mryglod T. Bryk A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales Condensed Matter Physics nonequilibrium statistical mechanics statistical hydrodynamics classical fluids Langevin equation Markovian processes |
| title | 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_short | 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 |
| topic | nonequilibrium statistical mechanics statistical hydrodynamics classical fluids Langevin equation Markovian processes |
| url | https://doi.org/10.5488/CMP.21.13001 |
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