General Spherical Harmonic Tensors in the Boltzmann Equation

1966 ◽  
Vol 7 (8) ◽  
pp. 1453-1458 ◽  
Author(s):  
Tudor Wyatt Johnston
Keyword(s):  
Boltzmann Equation ◽  
Spherical Harmonic ◽  
The Boltzmann Equation

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

Inelastic collision integral approximation of the Boltzmann equation

1976 ◽  
Vol 16 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Pierre Ségur ◽  
Joëlle Lerouvillois-Gaillard
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Power Series ◽  
Spherical Harmonic ◽  
Inelastic Collision ◽  
Collision Integral ◽  
Spherical Harmonic Expansion ◽  
Square Root ◽  
Integral Approximation ◽  
The Boltzmann Equation

A study is made of the inelastic collision integral of the Boltzmann equation using scattering probability formalism. The collision operators are expanded in a power series in the square root of the ratio of masses.Furthermore, a spherical harmonic expansion is made of all the operators so obtained. These developments are valid whatever the shape of the distribution function of the particles.

The Boltzmann Equation and the H Theorem (1872–1875)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Transport Phenomena ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
H Theorem ◽  
Irreversible Evolution

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.

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