January 29:  Ed Spiegel, Department of Astronomy, Columbia University

Continuum Equations for Rarefied Gases
  

  Kirchhoff, who participated in the early development of the fluid dynamical equations, used them to study the propagation of sound waves. In the last century, it was found that his results for the phase speeds and the damping lengths of the waves were in disagreement with experiment when the mean free paths of the particles in the gas were longer than the acoustic wave lengths.

  One source of this problem is in the iterative character of the usual Chapman-Enskog development. For long mean free paths, the Navier-Stokes equations may be repaired by excluding the iterative steps from their derivation. The fluid equations that are then extracted from kinetic theory lead to phase speeds that agree with experimental results. But the damping lengths from the augmented N-S equations still do not agree with those from experiments in the long mean free path limit. Rational approximations of the leading terms of the fluid equations may repair this fault, provided attention is paid to the role of time in the dynamics, but they lack a certain inevitability. The acausal aspect of the standard fluid equations also is removed. Astrophysical topics that may relate to these issues will be mentioned as time permits.