We consider the balance system of Extended Thermodynamics with 13 Moments in the case of Fermi and Bose gases, for processes not far from equilibrium. In this case, the hyperbolicity of the differential system holds only in a neighborhood of the equilibrium state. The main aim of the paper is to evaluate the hyperbolicity region of the differential system. The knowledge of this region in the state variables is mandatory to check the admissibility of the solutions and the corresponding boundary and Cauchy data in the limit of the approximation considered. The results are obtained through numerical evaluations of the Fermi and Bose integral functions I_n(+/-)(alpha) that appear in the characteristic polynomial. Particular attention is devoted to the completely degenerate case when Fermi gas reaches the 0 K and when the Bose gas is in proximity of the transition temperature T-c . In these limiting cases, the hyperbolicity requirement is lost according to previous results. In the last section we make use of the Maxwellian iteration in order to evaluate the heat conductivity and the viscosity for the degenerate Fermi and Bose gas.

Hyperbolicity in Extended Thermodynamics of Fermi and Bose gases

TROVATO, Massimo
2004-01-01

Abstract

We consider the balance system of Extended Thermodynamics with 13 Moments in the case of Fermi and Bose gases, for processes not far from equilibrium. In this case, the hyperbolicity of the differential system holds only in a neighborhood of the equilibrium state. The main aim of the paper is to evaluate the hyperbolicity region of the differential system. The knowledge of this region in the state variables is mandatory to check the admissibility of the solutions and the corresponding boundary and Cauchy data in the limit of the approximation considered. The results are obtained through numerical evaluations of the Fermi and Bose integral functions I_n(+/-)(alpha) that appear in the characteristic polynomial. Particular attention is devoted to the completely degenerate case when Fermi gas reaches the 0 K and when the Bose gas is in proximity of the transition temperature T-c . In these limiting cases, the hyperbolicity requirement is lost according to previous results. In the last section we make use of the Maxwellian iteration in order to evaluate the heat conductivity and the viscosity for the degenerate Fermi and Bose gas.
File in questo prodotto:
File Dimensione Formato  
Ruggeri Trovato CMT.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 989.99 kB
Formato Adobe PDF
989.99 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/4345
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 26
  • ???jsp.display-item.citation.isi??? 20
social impact