Relaxation Rate Spectrum of the Linearized Boltzmann Equation for Hard Sphere

1969 ◽  
Vol 12 (11) ◽  
pp. 2306 ◽  
Author(s):  
C. C. Yan
Keyword(s):  
Boltzmann Equation ◽  
Relaxation Rate ◽  
Hard Sphere ◽  
Linearized Boltzmann Equation

Discrete relaxation modes for a hard-sphere gas

1968 ◽  
Vol 46 (21) ◽  
pp. 2463-2469 ◽  
Author(s):  
M. Rahman ◽  
M. K. Sundaresan
Keyword(s):  
Boltzmann Equation ◽  
Discrete Spectrum ◽  
Hard Sphere ◽  
Spherically Symmetric ◽  
Symmetric State ◽  
Elementary Method ◽  
Linearized Boltzmann Equation ◽  
Relaxation Modes

The discrete spectrum of a linearized Boltzmann equation for a hard-sphere gas is studied, and the results of Kuščer and Williams (1967) for a spherically symmetric state are rederived by a more elementary method. Extension is made to nonisotropic states, and it is shown that the discrete spectrum is empty for [Formula: see text].

Continuum eigenfunctions for a hard-sphere gas

1968 ◽  
Vol 46 (20) ◽  
pp. 2287-2290 ◽  
Author(s):  
M. Rahman ◽  
M. K. Sundaresan
Keyword(s):  
Integral Equation ◽  
Boltzmann Equation ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Singular Integral ◽  
Hard Sphere ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Fredholm Equations ◽  
Linearized Boltzmann Equation

The singular integral equation resulting from the linearized Boltzmann equation for a hard-sphere gas in the continuous region is reduced to two Fredholm equations of first and second kinds using the theory of singular integral equations with Cauchy-type singularities.

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