BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Linear-in-gradients hydrodynamic equations for a system with small
  interaction
DTSTART;VALUE=DATE-TIME:20181204T084500Z
DTEND;VALUE=DATE-TIME:20181204T090500Z
DTSTAMP;VALUE=DATE-TIME:20260518T020156Z
UID:indico-contribution-14@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Vyacheslav Gorev (National Mining University)\nThe s
 ystem under consideration is a one-component weakly non-uniform gas with s
 mall potential interaction. The investigation is based on the kinetic equa
 tion in the case of small interaction with a nonlocal collision integral [
 1]. In [2] it is shown that the system kinetic energy is not conserved on 
 the basis of the nonlocal collision integral. So the system temperature sh
 ould be defined on the basis on the total system energy rather than the ki
 netic one. The following hydrodynamic equations are obtained up to the fir
 st order in small gradients and the second order in small interaction:\n\n
 $ \\frac{{\\partial n}}{{\\partial t}} =  - n\\frac{{\\partial {\\upsilon 
 _n}}}{{\\partial {x_n}}} - {\\upsilon _n}\\frac{{\\partial n}}{{\\partial 
 {x_n}}}\, \\quad \\frac{{\\partial {\\upsilon _n}}}{{\\partial t}} =  - {\
 \upsilon _l}\\frac{{\\partial {\\upsilon _n}}}{{\\partial {x_l}}} + \\left
 [ { - \\frac{T}{{nm}} - \\frac{1}{m}V\\left( {k = 0} \\right) + } \\right.
  $\n\n$ \\left. { + \\frac{1}{{2{\\pi ^2}mT}}\\left( {A + \\frac{B}{3}} \\
 right)} \\right]\\frac{{\\partial n}}{{\\partial {x_n}}} + \\left[ { - \\f
 rac{1}{m} - \\frac{n}{{4{\\pi ^2}m{T^2}}}\\left( {A + \\frac{B}{3}} \\righ
 t)} \\right]\\frac{{\\partial T}}{{\\partial {x_n}}}\, $\n\n$ \\frac{{\\pa
 rtial T}}{{\\partial t}} = \\left[ { - \\frac{2}{3}T + \\frac{n}{{9{\\pi ^
 2}T}}\\left( {A + \\frac{B}{2}} \\right)} \\right]\\frac{{\\partial {\\ups
 ilon _n}}}{{\\partial {x_n}}} - {\\upsilon _n}\\frac{{\\partial T}}{{\\par
 tial {x_n}}}\, $\n\n$ A = \\int\\limits_0^\\infty  {dk} {k^2}{V^2}\\left( 
 k \\right)\, \\quad B = \\int\\limits_0^\\infty  {dk{k^3}V\\left( k \\righ
 t)\\frac{{\\partial V\\left( k \\right)}}{{\\partial k}}} $\n\nwhere $n$ i
 s the particle number density\, $\\upsilon_l$ is the velocity\, $T$ is the
  temperature\, and $V(k)$ is the Fourier transform of the system pair pote
 ntial. In fact\, these equations are non-dissipative hydrodynamic equation
 s and in the leading-in-interaction order they coincide with corresponding
  equations in the framework of standard hydrodynamics. The obtained equati
 ons may be a basis for the investigation of the system dissipative hydrody
 namics and system kinetic coefficients. \n\n[1] A.I. Akhiezer and S.V. Pel
 etminsky\, Methods of Statistical Physics\, Oxford\, Pergamon Press\, 1981
 \, 376 p.\n[2] V.N. Gorev and A.I. Sokolovsky\, Visnik Dnipropetrovs'kogo 
 Universitetu. Seria Fizika\, radioelektronika\, 25\, issue 24\, 14 (2017).
 \n\nhttps://indico.bitp.kiev.ua/event/2/contributions/14/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/14/
END:VEVENT
END:VCALENDAR