Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces
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.
Keywords
Cite
@article{arxiv.2409.14150,
title = {Dynamical behavior of passive particles with harmonic, viscous, and correlated Gaussian forces},
author = {Jae Won Jung and Sung Kyu Seo and Kyungsik Kim},
journal= {arXiv preprint arXiv:2409.14150},
year = {2024}
}
Comments
10 pages, 5 tables