Matrix elements and kernels of the collision integral in the Boltzmann equation

2011 ◽  
Vol 56 (4) ◽  
pp. 452-463 ◽  
Author(s):  
A. Ya. Ender ◽  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova
2017 ◽  
Vol 62 (9) ◽  
pp. 1307-1312 ◽  
Author(s):  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. B. Gerasimenko

1967 ◽  
Vol 20 (3) ◽  
pp. 205 ◽  
Author(s):  
Kallash Kumar

The Chapman-Enskog method of solving the Boltzmann equation is presented in a simpler and more efficient form. For this purpose all the operations involving the usual polynomials are carried out in spherical polar coordinates, and the Racah-Wigner methods of dealing with irreducible tensors are used throughout. The expressions for the collision integral and the associated bracket expressions of kinetic theory are derived in terms of Talmi coefficients, which have been extensively studied in the harmonic oscillator shell model of nuclear physics.


2016 ◽  
Vol 61 (4) ◽  
pp. 486-497 ◽  
Author(s):  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. Ya. Ender ◽  
I. A. Ender

2017 ◽  
Vol 62 (8) ◽  
pp. 1148-1155 ◽  
Author(s):  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. B. Gerasimenko

1976 ◽  
Vol 16 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Pierre Ségur ◽  
Joëlle Lerouvillois-Gaillard

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.


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