Stochastic solution of the Boltzmann equation for thermal electrons in an attractive Coulombic potential

1969 ◽  
Vol 3 (3) ◽  
pp. 377-385
Author(s):  
M. J. Bell ◽  
M. D. Kostin
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Diffusion Approximation ◽  
Stochastic Method ◽  
Free Electrons ◽  
The Boltzmann Equation ◽  
Stochastic Solution ◽  
Positive Ion ◽  
Fokker Planck

A stochastic method has been employed to investigate the distribution function of free electrons in gases in the field of a positive ion. Stochastic results have been obtained for several pressures and for both large (Langevin) and small ions, and the results have been compared with the solutions of the diffusion approximation and Pitaevskii's Fokker—Planck approximation to the Boltzmann equation.

scholarly journals A Fokker–Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases

2017 ◽  
Vol 168 (5) ◽  
pp. 1031-1055 ◽  
Author(s):  
J. Mathiaud ◽  
L. Mieussens
Keyword(s):  
Boltzmann Equation ◽  
Prandtl Number ◽  
Polyatomic Gases ◽  
The Boltzmann Equation ◽  
Fokker Planck

INCLUSION OF FLOW TERMS IN THE CARTESIAN TENSOR EXPANSION OF THE BOLTZMANN EQUATION

1963 ◽  
Vol 41 (11) ◽  
pp. 1776-1786 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Flow Velocity ◽  
Velocity Space ◽  
Pressure Tensor ◽  
Moment Equations ◽  
Ionized Gas ◽  
The Boltzmann Equation ◽  
Integrated Distribution Function ◽  
Boltzmann's Equation

The Cartesian tensor expansion of Boltzmann's equation as given by Johnston (1960) is extended to include terms denoting gradients in flow velocity. The expansion is performed in intrinsic velocity space. The gradient velocity terms yield a linear contribution to the tensor (f2) part of the angle-integrated distribution function from which the zero-trace pressure tensor is calculable. It is shown that the standard moment equations are obtained by further integration over the magnitude of velocity. For the case of a completely ionized gas, collisional terms are inserted appropriately.

Die Methode der Korrelationsfunktion in der Theorie der Supraleitung

1966 ◽  
Vol 21 (11) ◽  
pp. 1842-1849 ◽  
Author(s):  
Gerhart Lüders
Keyword(s):  
Correlation Function ◽  
Transition Temperature ◽  
Boltzmann Equation ◽  
Concentration Dependence ◽  
Diffusion Approximation ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
The Boltzmann Equation ◽  
Paramagnetic Impurities ◽  
Method Of Correlation

The method of correlation function is extended to the case of paramagnetic impurities. The BOLTZMANN equation is obtained and subsequently applied to a derivation of the concentration dependence of the transition temperature, of the linearized GINZBURG—LANDAU equation, and of the diffusion approximation.

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.

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