scholarly journals On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2382
Author(s):  
Andrey Saveliev
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Magnetic Fields ◽  
Kinetic Theory ◽  
Charged Particles ◽  
Kinetic Theory Of Gases ◽  
The Boltzmann Equation ◽  
Ideal Magnetohydrodynamics ◽  
Complex Valued

In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields.

On the Theory of Determining the Transport Characteristics of Gas Mixtures

2020 ◽  
Vol 992 ◽  
pp. 823-827
Author(s):  
I.V. Anisimova ◽  
A.V. Ignat'ev
Keyword(s):  
Mass Transfer ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Potential Energy ◽  
Uniform Convergence ◽  
Transport Coefficient ◽  
Collision Term ◽  
Kinetic Theory Of Gases ◽  
The Boltzmann Equation ◽  
Improper Integrals

The paper considers the identification of properties of real gases and creation of nanomaterials on the basis of molecular and kinetic theory of gases, namely the Boltzmann equation. The collision term of the Boltzmann equation is used in the algorithm for the identification of transport properties of media. The article analyses the uniform convergence of improper integrals in the collision term of the Boltzmann equation depending on the conditions for the connection between the kinetic and potential energy of interacting molecules. This analysis allows to soundly identify the transport coefficient in macro equations of heat and mass transfer.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

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.

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