scholarly journals Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals. I. Scattering by phonons, antiferromagnons, and helimagnons

2020 ◽  
Vol 102 (21) ◽  
Author(s):  
J. Amarel ◽  
D. Belitz ◽  
T. R. Kirkpatrick
Keyword(s):  
Exact Solution ◽  
Boltzmann Equation ◽  
Low Temperature ◽  
Transport Coefficients ◽  
The Boltzmann Equation

Fick's First Law Correction by an exact solution of the boltzmann equation

1987 ◽  
Vol 12 (3) ◽  
pp. 105-112 ◽  
Author(s):  
D. Straub ◽  
R. Graue ◽  
F. Heitmeir ◽  
P. Nebendahl ◽  
Th. K. Wurst
Keyword(s):  
Exact Solution ◽  
Boltzmann Equation ◽  
The Boltzmann Equation

Nonlinear transport coefficients and plane Couette flow of a viscous, heat-conducting gas between two plates at different temperatures

1987 ◽  
Vol 65 (9) ◽  
pp. 1090-1103 ◽  
Author(s):  
Byung Chan Eu ◽  
Roger E. Khayat ◽  
Gert D. Billing ◽  
Carl Nyeland
Keyword(s):  
Boltzmann Equation ◽  
Couette Flow ◽  
Transport Coefficients ◽  
Heat Conducting ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
Plane Couette Flow ◽  
The Boltzmann Equation ◽  
Viscous Heat ◽  
Different Temperatures

By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the interfacial interaction between the surface and the gas molecule. The nonlinear transport coefficients employed in the generalized hydrodynamic equations are obtained from the Boltzmann equation by means of the modified-moment method. The profiles calculated are in agreement with the Liu–Lees theory as long as the boundary values are in agreement. It is found that the viscous-heating effect has a significant influence on the temperature and velocity profiles. The nonlinearity of transport coefficients also has significant effects on the profiles as the Knudsen and Mach numbers increase.

Zur näherungsweisen Berechnung der elektrischen Leitfähigkeit eines Plasmas

1973 ◽  
Vol 28 (9) ◽  
pp. 1454-1458
Author(s):  
H. Schirmer ◽  
I. Stober
Keyword(s):  
Electrical Conductivity ◽  
Exact Solution ◽  
Boltzmann Equation ◽  
Approximate Formula ◽  
The Boltzmann Equation

In order to calculate the electrical conductivity of a plasma an approximate formula has been derived which is based on an improvement of the expression corresponding to a Lorentzian gas. The deviation from the exact solution (which is based on the Boltzmann equation of a plasma) is in most cases lower than 5% and will exceed this deviation only in exceptional cases.The calculations have been performed for xenon and neon.

A multi-term spherical harmonic expansion of the Boltzmann equation for application to low-temperature collisional plasmas

2019 ◽  
Vol 26 (10) ◽  
pp. 103506 ◽  
Author(s):  
S. B. Swanekamp ◽  
P. F. Ottinger ◽  
P. E. Adamson ◽  
J. L. Giuliani ◽  
Tz. B. Petrova ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Low Temperature ◽  
Spherical Harmonic ◽  
Spherical Harmonic Expansion ◽  
The Boltzmann Equation
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