The non-linear macroscopic model of Relativistic Extended Thermodynamics of an ultra-relativistic gas

Francesco Borghero; Sebastiano Pennisi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 1, page 59-68
  • ISSN: 1120-6330

Abstract

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The model for an ultra-relativistic gas is here considered in the framework of Extended Thermodynamics. The closure, satisfying exactly the principles of relativity and of entropy, is obtained by following the approach «at a macroscopic level». Our results are compared with the ones of the kinetic approach.

How to cite

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Borghero, Francesco, and Pennisi, Sebastiano. "The non-linear macroscopic model of Relativistic Extended Thermodynamics of an ultra-relativistic gas." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.1 (2004): 59-68. <http://eudml.org/doc/252416>.

@article{Borghero2004,
abstract = {The model for an ultra-relativistic gas is here considered in the framework of Extended Thermodynamics. The closure, satisfying exactly the principles of relativity and of entropy, is obtained by following the approach «at a macroscopic level». Our results are compared with the ones of the kinetic approach.},
author = {Borghero, Francesco, Pennisi, Sebastiano},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Extended Thermodynamics; Fluid Models; Ultra-relativistic Gas; Entropy Principle; extended thermodynamics; fluid models; ultra-relativistic gas; entropy principle},
language = {eng},
month = {3},
number = {1},
pages = {59-68},
publisher = {Accademia Nazionale dei Lincei},
title = {The non-linear macroscopic model of Relativistic Extended Thermodynamics of an ultra-relativistic gas},
url = {http://eudml.org/doc/252416},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Borghero, Francesco
AU - Pennisi, Sebastiano
TI - The non-linear macroscopic model of Relativistic Extended Thermodynamics of an ultra-relativistic gas
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/3//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 1
SP - 59
EP - 68
AB - The model for an ultra-relativistic gas is here considered in the framework of Extended Thermodynamics. The closure, satisfying exactly the principles of relativity and of entropy, is obtained by following the approach «at a macroscopic level». Our results are compared with the ones of the kinetic approach.
LA - eng
KW - Extended Thermodynamics; Fluid Models; Ultra-relativistic Gas; Entropy Principle; extended thermodynamics; fluid models; ultra-relativistic gas; entropy principle
UR - http://eudml.org/doc/252416
ER -

References

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  1. LIU, I.-S. - MÜLLER, I. - RUGGERI, T., Relativistic thermodynamics of gases. Ann. of Phys., 169, 1986, 191-219. MR846050DOI10.1016/0003-4916(86)90164-8
  2. MÜLLER, I. - RUGGERI, T., Rational Extended Thermodynamics. 2nd ed., Springer Tracts in Natural Philosophy, 37, Springer-Verlag, New York, 1998, 396 pp. Zbl0895.00005MR1632151DOI10.1007/978-1-4612-2210-1
  3. BOILLAT, G. - RUGGERI, T., Moment equations in the kinetic theory of gases and wave velocities. Continuum Mech. Thermodyn., 9, 1997, 205-212. Zbl0892.76075MR1467331DOI10.1007/s001610050066
  4. BOILLAT, G. - RUGGERI, T., Relativistic gas: Moment equations and maximum wave velocity. J. Math. Phys., 40, 1999, 6399-6404. Zbl0962.82060MR1725865DOI10.1063/1.533099
  5. PENNISI, S., Extended Thermodynamics of non degenerate ultrarelativistic gases. Il Nuovo Cimento, 104B, 1989, 273-290. 
  6. PENNISI, S., Soluzioni esatte per la termodinamica estesa di un gas ultrarelativistico. Rend. Sem. Fac. Scienze Univ. Cagliari, 70, 2000, 273-286. 
  7. PENNISI, S., Some considerations on a non-linear approach to extended thermodynamics. Pitagora EditriceBologna, 1987, 259-264. 
  8. GEROCH, R. - LINDBLOM, L., Dissipative relativistic fluid theorie of divergence type. Physical Review D., 41, 1990, 1855-1861. MR1048881DOI10.1103/PhysRevD.41.1855
  9. DREYER, W., Maximisation of the entropy in non-equilibrium. J. Phys. A: Math. Gen., 20, 1987, 6505-6517. Zbl0633.76081MR926398
  10. BOILLAT, G. - RUGGERI, T., Maximum wave velocity in the moments system of a relativistic gas. Continuum Mech. Thermodyn., 11, 1999, 107-111. Zbl0935.76077MR1680244DOI10.1007/s001610050106
  11. BRINI, F. - RUGGERI, T., Maximum velocity for wave propagation in a relativistic rarefied gas. Continuum Mech. Thermodyn., 11, 1999, 331-338. Zbl0946.76084MR1723707DOI10.1007/s001610050128
  12. JÜTTNER, F., Das Maxwellsche Gesetz der Geshwindigkeitsverteilung in der Relativtheorie. Annalen der Physik, 34, 1911, 856-882. JFM42.0981.01
  13. JÜTTNER, F., Die Relativistische Quantentheorie des Idealen Gases. Zeitschrift f. Physik, 47, 1928, 542-566. JFM54.0987.01
  14. PENNISI, S., A family of exact solutions in Relativistic Extended Thermodynamics. Continuum Mech. Thermodyn., 44, 2002, 377-387. Zbl1012.80003MR1920895DOI10.1007/s001610100079
  15. AMENDT, P. - WEITZNER, H., Relativistically covariant warm charged fluid beam modeling. Phys. Fluids, 28, 1985, 949-957. Zbl0586.76203
  16. ANILE, A.M. - PENNISI, S., Fluid models for relativistic electron beams. Continuum Mech. Thermodyn., 1, 1989, 267-282. MR1024193DOI10.1007/BF01125777
  17. PENNISI, S., A fourth order approach to relativistic extended thermodynamics. Continuum Mech. Thermodyn., 11, 1999, 51-71. Zbl0972.80001MR1685026DOI10.1007/s001610050103
  18. PENNISI, S., Relativistic Extended Thermodynamics with 30 independent fields. Atti Sem. Mat. Fis. Univ. Modena, L, 2002, 429-449. Zbl1221.80003MR1958290

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