Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910616259657728 |
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| author | Jung, Jae Won Seo, Sung Kyu Kim, Kyungsik |
| author_facet | Jung, Jae Won Seo, Sung Kyu Kim, Kyungsik |
| contents | In this paper, we study the Navier-Stokes equation and the Burgers equation for the dynamical motion of a passive particle with harmonic and viscous forces, subject to an exponentially correlated Gaussian force. As deriving the Fokker-Planck equation for the joint probability density of a passive particle, we find obviously the important solution of the joint probability density by using double Fourier transforms in three-time domains, and the moments from derived moment equation are numerically calculated. As a result, the dynamical motion of a passive particle with respect to the probability density having two variables of displacement and velocity in the short-time domain has a super-diffusive form, whereas the distribution in the long-time domain is obtained to be Gaussian by analyzing only from the velocity probability density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14150 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces Jung, Jae Won Seo, Sung Kyu Kim, Kyungsik Statistical Mechanics In this paper, we study the Navier-Stokes equation and the Burgers equation for the dynamical motion of a passive particle with harmonic and viscous forces, subject to an exponentially correlated Gaussian force. As deriving the Fokker-Planck equation for the joint probability density of a passive particle, we find obviously the important solution of the joint probability density by using double Fourier transforms in three-time domains, and the moments from derived moment equation are numerically calculated. As a result, the dynamical motion of a passive particle with respect to the probability density having two variables of displacement and velocity in the short-time domain has a super-diffusive form, whereas the distribution in the long-time domain is obtained to be Gaussian by analyzing only from the velocity probability density. |
| title | Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2409.14150 |