scholarly journals Hamilton-Jacobi method for molecular distribution function in a chemical oscillator

2013 ◽  
Vol 139 (21) ◽  
pp. 214105 ◽  
Author(s):  
Hiizu Nakanishi ◽  
Takahiro Sakaue ◽  
Jun'ichi Wakou
Keyword(s):  
Distribution Function ◽  
Jacobi Method ◽  
Molecular Distribution ◽  
Molecular Distribution Function ◽  
Chemical Oscillator

A note on Wild's solution of the Boltzmann equation

1954 ◽  
Vol 50 (2) ◽  
pp. 293-297
Author(s):  
Martin J. Klein
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Boltzmann Equation ◽  
Formal Solution ◽  
Relaxation Behaviour ◽  
Integro Differential Equation ◽  
Molecular Distribution ◽  
The Boltzmann Equation ◽  
Molecular Distribution Function ◽  
Velocity Moments

ABSTRACTIt is shown that Wild's formal solution of the Boltzmann integro-differential equation can be used to obtain Maxwell's classical relaxation behaviour of the second velocity moments of the molecular distribution function.

Boundary-value problems in the kinetic theory of gases Part I. Slip flow

1969 ◽  
Vol 36 (1) ◽  
pp. 145-159 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Boundary Value Problems ◽  
Neutron Transport ◽  
Boundary Value ◽  
Slip Flow ◽  
New Method ◽  
Milne Problem ◽  
Molecular Distribution ◽  
Molecular Distribution Function

A new method for treating boundary-value problems in gas-kinetic theory has been developed. The new method has the advantage of reproducing the bulk or asymptotic flow properties accurately whilst giving a realistic description of the behaviour of the molecular distribution function in the neighbourhood of a wall. As an example, the Kramers, or slip-flow, problem is solved for a general specular-diffuse boundary condition and some new expressions for the slip coefficient, flow speed and molecular distribution function at the surface are derived.A brief discussion of the eigenvalue spectrum of the associated Boltzmann equation is given and its physical significance pointed out.Certain analogies between this problem and the Milne problem in neutron transport theory are demonstrated.

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