Non-dissipative hydrodynamic equations based on a nonlocal collision integral
Journal Title: Journal of Physics and Electronics - Year 2018, Vol 26, Issue 1
Abstract
We consider a slightly non-uniform one-component gas with weak potential interaction. The basis of the investigation is the known kinetic equation in the case of small interaction which is truncated up to the second order of smallness. This equation contains a nonlocal collision integral of the second order in small interaction. In this paper we consider the hydrodynamic stage of the system evolution, and, in contrast to the standard hydrodynamics, we take into account the non-locality of the collision integral. We propose the following set of the reduced description parameters which are the densities of the conserved quantities: the particle number density, the momentum density, and the total energy density. It should be stressed that in contrast to the standard hydrodynamics, the kinetic energy is not conserved, and only the total system energy is conserved if the nonlocal collision integral is used. Definitions of the system velocity and temperature are proposed; it should be stressed that the proposed temperature definition is based on the total system energy rather than on the kinetic one. The hydrodynamics in the leading order in small gradients is investigated, and it is shown that the system one-particle distribution function in the leading-in-gradients order coincides with the Maxwellian one. Particle number density, velocity and temperature time evolution equations (hydrodynamic equations) are derived in the non-dissipative case. The leading-in-interaction orders of the obtained equations coincide with the corresponding equations in the framework of the standard hydrodynamics. The corrections of the first and second order in small interaction are also obtained.
Authors and Affiliations
V. N. Gorev, A. I. Sokolovsky
Keywords
Related Articles
- EP ID EP540502
- DOI 10.15421/331802
- Views 242
- Downloads 0
Electrical characteristics of two-layer structure varistor ceramics–PPTC nanocomposite
Electrical characteristics of experimental two-layer structure based on layers of varistor ceramics and polymer nanocomposite with carbon filler being in thermal contact are studied. A layer of such polymer nanocomposite...
Influence of heat treatment on photoluminescence spectra in ZnS:Mn crystals with hexagonal structure
It has been investigated the influence of heat treatment with the following temperins on the integral photoluminescence spectra and on the individual bands of this spectra. It has been showed the correlation between the...
Effect of thermal treatment on structure and leakage current of Na0.5Bi0.5TiO3 thin films
Na0.5Bi0.5TiO thin films were grown on heated to 200°С Pt/TiO2/SiO2/Si substrates by ex-situ method with high-frequency (13.56 MHz) magnetron deposition. Thermal treatment of the films was carried out at 650°С, 700°С and...
Calculation of nonequilibrium thermodynamic potential of Bose system near the condensation point
Bose system of zero spin particles is considered in the presence of the Bose–Einstein condensate in the vicinity of the phase transition point. The system is investigated in the framework of the Bogolyubov model with the...
Non-dissipative hydrodynamic equations based on a nonlocal collision integral
We consider a slightly non-uniform one-component gas with weak potential interaction. The basis of the investigation is the known kinetic equation in the case of small interaction which is truncated up to the second orde...