A parameterization of collisions in the Boltzmann equation by a rotation matrix and Boltzmann collision integral in discrete models of gas mixtures

2001 ◽  
Author(s):  
Vladimir L. Saveliev
Keyword(s):  
Boltzmann Equation ◽  
Gas Mixtures ◽  
Collision Integral ◽  
Rotation Matrix ◽  
Discrete Models ◽  
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.

scholarly journals Mobility of Ions in Gas Mixtures

1973 ◽  
Vol 26 (2) ◽  
pp. 203 ◽  
Author(s):  
RE Robson
Keyword(s):  
Boltzmann Equation ◽  
Gas Mixtures ◽  
Interaction Potentials ◽  
The Boltzmann Equation ◽  
Mobility Of Ions ◽  
Helium Neon

A formula for the mobility of ions in a mixture of neutral gases is obtained as a generalization of an expression previously derived from the Boltzmann equation for ions in a pure gas (Kumar aitd Robson 1973). It is shown that Blanc's law holds only for very specialized situations. Using interaction potentials obtained in a previous work (Robson and Kumar 1973), the mobilities of K + ions in helium-neon mixtures have been calculated and the deviations from Blanc's law are discussed.

scholarly journals Analysis of application and improvement of methods to solve discrete models of Boltzmann equation

Vestnik IGEU ◽  
2021 ◽  
pp. 62-69
Author(s):  
V.P. Zhukov ◽  
A.Ye. Barochkin ◽  
A.N. Belyakov ◽  
O.V. Sizova
Keyword(s):  
Boltzmann Equation ◽  
Discrete Models ◽  
Joint Analysis ◽  
Technological Systems ◽  
Boltzmann Equations ◽  
The Boltzmann Equation ◽  
Reasonable Choice ◽  
Volume Method ◽  
Energy Balances

To describe technological systems using models of Markov chains and discrete models of the Boltzmann equation it is necessary to determine the probabilities of transition of a system from one state to another. An urgent topic of a scientific research is to improve the accuracy of solving the Boltzmann equation by making a reasonable choice of probabilities of transition and admissible areas of their application. The strategy to model and determine the probabilities of transitions is based on the finite volume method, the ratios of the theory of probability and the joint analysis of material and energy balances. Considering the ratios of the theory of probability, the authors have obtained the refined formula for the probabilities of transitions over the cells of the computational space of discrete models of the Boltzmann equations in case of the description of technological systems. Recommendations to choose the area of application of the model are presented. The computational analysis has showed a significant improvement of the quality of forecasting when we implement the proposed dependencies and recommendations. The relative error of calculating the energy of the system is reduced from 8,4 to 2,8 %. The presented calculated dependencies to determine the probabilities of transition and recommendations for their application can be used to simulate various technological processes and improve the quality of their description.

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
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