Recurrence procedure for calculating kernels of the nonlinear collision integral of the Boltzmann equation

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

scholarly journals The Chapman?Enskog Solution of the Boltzmann Equation: A Reformulation in Terms of Irreducible Tensors and Matrices

1967 ◽  
Vol 20 (3) ◽  
pp. 205 ◽  
Author(s):  
Kallash Kumar
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Harmonic Oscillator ◽  
Shell Model ◽  
Nuclear Physics ◽  
Collision Integral ◽  
Polar Coordinates ◽  
Irreducible Tensors ◽  
The Boltzmann Equation ◽  
Oscillator Shell

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.

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.

Isotropic matrix elements of the collision integral for the Boltzmann equation

2017 ◽  
Vol 62 (9) ◽  
pp. 1307-1312 ◽  
Author(s):  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. B. Gerasimenko
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Matrix Elements ◽  
Isotropic Matrix ◽  
The Boltzmann Equation

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
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Matrix Elements ◽  
The Boltzmann Equation

Some general properties of the nonlinear collision integral in the Boltzmann equation

2010 ◽  
Vol 55 (10) ◽  
pp. 1400-1410 ◽  
Author(s):  
A. Ya. Ender ◽  
I. A. Ender ◽  
L. A. Bakaleinikov
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
General Properties ◽  
The Boltzmann Equation
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