Top

Meccanica

Published in:

01-04-2013

On the hyperbolicity of a model with 30 moments for ultrarelativistic gases

Authors: F. Borghero, F. Demontis, S. Pennisi

Published in: Meccanica | Issue 3/2013

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of moments, is present in literature. Here we exploit equations determining wave speeds for the model with 30 independent fields. We find interesting results; for example, the whole system for their determination can be split in some independent subsystems, some wave speeds are expressed by square roots of rational numbers, but not all of them. Moreover these wave speeds for the macroscopic model are the same of those in the kinetic model.

previous article Centreline velocity decay characterisation in low-velocity jets downstream from an extended conical diffuser

next article Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Eckart C (1940) The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluids. Phys Rev 58:919 ADSCrossRef

Müller I, Ruggeri T (1998) Rational extended thermodynamics, 2nd edn. Springer, New York, Berlin Heidelberg MATHCrossRef

Cattaneo C (1948–1949) Sulla conduzione del calore. Atti Semin Mat Fis Univ Modena 3:83 MathSciNet

Müller I (1966) Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien. Dissertation. Aachen

Israel W (1976) Non stationary irreversible thermodynamics: a causal relativistic theory. Ann Phys (NY) 100:341 MathSciNetCrossRef

Liu IS, Müller I, Ruggeri T (1986) Relativistic thermodynamics of gases. Ann Phys (NY) 169:191 ADSCrossRef

Boillat G, Ruggeri T (1999) Maximum wave velocity in the moments system of a relativistic gas. Contin Mech Thermodyn 11:107 MathSciNetADSMATHCrossRef

Boillat G, Ruggeri T (1997) Moment equations in the kinetic theory of gases and wave velocities. Contin Mech Thermodyn 9:205 MathSciNetADSMATHCrossRef

Boillat G, Ruggeri T (1999) Relativistic gas: moment equations and maximum wave velocity. J Math Phys 40:6399 MathSciNetADSMATHCrossRef

10.

Müller I (1999) Speeds of propagation in classical and relativistic extended thermodynamics. Living reviews in relativity. Max-Planck-Institute for Gravitational Physics, Albert Einstein Institute, Potsdam

11.

Borghero F, Demontis F, Pennisi S (2004) An exact macroscopic extended model with many moments for ultrarelativistic gases. In: Proceedings of WASCOM 2003, 12th conference on waves and stability in continuous media. Word Scientific, Singapore, pp 94–101 CrossRef

12.

Borghero F, Pennisi S (2004) The nonlinear macroscopic model of relativistic extended thermodynamics of an ultrarelativistic gas. Rend Mat Acc Lincei 9:59–68 MathSciNet

13.

Banach Z, Larecki W (2002) Evolution of central moments for a general relativistic Boltzmann equation: the closure by entropy maximization. Rev Math Phys 14:469–510 MathSciNetMATHCrossRef

14.

Montanaro A (2011) On piezothermoelastic plates subject to prescribed boundary temperature. Meccanica 46(2):371–381 MathSciNetCrossRef

15.

Singh LP, Husain A, Singh M (2011) A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics. Meccanica 46(2):437–445 MathSciNetCrossRef

16.

Lembo M (2011) Geometry of constraint manifolds and wave propagation in internally constrained elastic bodies. Meccanica 46(4):651–669 MathSciNetCrossRef

17.

Ezzat MA, El-Karamany AS (2011) Two-temperature theory in generalized magneto-thermoelasticity with two relaxation times. Meccanica 46(4):785–794 MathSciNetCrossRef

18.

Ishak A, Yacob NA, Bachock N (2011) Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition. Meccanica 46(4):795–801 MathSciNetCrossRef

19.

Demontis F, Pennisi S (2007) On a further condition in the macroscopic extended model for ultrarelativistic gases. Ann Univ Ferrara, Sez VII, Sci Mat 53:51–64 MathSciNetMATHCrossRef

20.

Müller I (2008) Extended thermodynamics—a theory of symmetric hyperbolic field equations. Appl Math 53(5):469–484 MathSciNetMATHCrossRef

21.

Müller I (2008) Entropy and energy—an universal competition. Entropy 10(4):462–476 MathSciNetADSMATHCrossRef

22.

Friedrichs KO (1954) Symmetric hyperbolic linear differential equations. Commun Pure Appl Math 8:345 MathSciNetCrossRef

23.

Friedrichs KO, Lax PD (1971) Systems of conservation equations with a convex extension. Proc Nat Acad Sci USA 68:1686 MathSciNetADSMATHCrossRef

24.

Friedrichs KO (1974) On the laws of relativistic electromagnetic fluid dynamics. Commun Pure Appl Math 27:749 MathSciNetADSMATHCrossRef

25.

Strumia A (1988) Wave propagation and symmetric hyperbolic systems of conservation laws with constrained field variables. II. Symmetric hyperbolic systems with constrained fields. Nuovo Cimento B 101:19 MathSciNetADSCrossRef

Title: On the hyperbolicity of a model with 30 moments for ultrarelativistic gases
Authors: F. Borghero
F. Demontis
S. Pennisi
Publication date: 01-04-2013
Publisher: Springer Netherlands
Published in: Meccanica / Issue 3/2013
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-012-9617-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2013

Experimental methodology for the tappet characterization of timing system in I.C.E.

Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition

Centreline velocity decay characterisation in low-velocity jets downstream from an extended conical diffuser

Load and rheometric unit for the test of magnetorheological fluid

Steady state thermal and mechanical stresses of a poro-piezo-FGM hollow sphere

Effects of the moving speed of a rigid stamp on contact behaviors of anisotropic materials based on real fundamental solutions

Premium Partners