3.6 A Lower Bound for 3 Finite Speeds in Non-Relativistic 3.4 Specific Form of the

3.5 Pulse Speeds in a Non-Degenerate Gas in Equilibrium 

We recall the discussion of characteristic speeds in Section  2.4 which we apply to the system (23Popup Equation) of field equations. The characteristic equation of this system reads

  equation649

or, by (11Popup Equation):

  equation657

This equation determines the characteristic speeds V, whose maximal value tex2html_wrap_inline3875 is the pulse speed. In the case of moments and for a non-degenerate gas at rest and in equilibrium this equation reads, by (42Popup Equation),

  equation669

tex2html_wrap_inline3879 is the Maxwellian phase density, so that all integrals in (47Popup Equation) are Gaussian integrals, easy to calculate. Weiss [49] has calculated the speeds V for different degrees n of extended thermodynamics. Recall that tex2html_wrap_inline3779, tex2html_wrap_inline3829 range over the values 1 through n . He has made a list of tex2html_wrap_inline3875 which is represented here in Table  1 . tex2html_wrap_inline3875 is normalized in Table  1 by tex2html_wrap_inline3895, the ordinary speed of sound, sometimes called the adiabatic sound speed.

Inspection of Table  1 shows that the pulse speed increases monotonically with the number of moments and there is clearly a suspicion that it may tend to infinity as n goes to infinity. This suspicion will presently be confirmed.



3.6 A Lower Bound for 3 Finite Speeds in Non-Relativistic 3.4 Specific Form of the

image Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
Ingo Müller
http://www.livingreviews.org/lrr-1999-1
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de