Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces

Jae Won Jung; Sung Kyu Seo; Kyungsik Kim

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arXiv · 2409.14150

Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces

Jae Won Jung·Sung Kyu Seo·Kyungsik Kim

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Abstract

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.

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Jae Won Jung, Sung Kyu Seo, Kyungsik Kim. 2024-09-21. Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces. https://arxiv.org/abs/2409.14150

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