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This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of…

Statistical Mechanics · Physics 2008-05-24 Boris V. Alexeev

Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…

Statistical Mechanics · Physics 2007-05-23 A. N. Gorban , I. V. Karlin

The two-dimensional, periodic Lorentz gas, is the dynamical system corresponding with the free motion of a point particle in a planar system of fixed circular obstacles centered at the vertices of a square lattice in the Euclidian plane.…

Analysis of PDEs · Mathematics 2012-07-26 Emanuele Caglioti , François Golse

Whereas the original Boltzmann's $H$-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity…

Soft Condensed Matter · Physics 2021-06-09 Alberto Megías , Andrés Santos

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal…

Plasma Physics · Physics 2019-02-05 Jean-Maxime Orlac'H , Vincent Giovangigli , Tatiana Novikova , Pere Roca

We propose two models of the Boltzmann equation (BGK and Fokker-Planck models) for rarefied flows of diatomic gases in vibrational non-equilibrium. These models take into account the discrete repartition of vibration energy modes, which is…

Classical Physics · Physics 2020-07-16 J. Mathiaud , Luc Mieussens

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…

Statistical Mechanics · Physics 2009-11-10 Bertrand Lods , Giuseppe Toscani

The Borgnakke-Larsen model, widely used in rarefied flow predictions, serves as the mainstream energy-exchange kernel for polyatomic gases. However, it lacks integrability and does not guarantee detailed balance, limiting theoretical…

Computational Physics · Physics 2026-04-02 Sha Liu , Ningchao Ding , Ming Fang , Hao Jin , Rui Zhang , Congshan Zhuo , Chengwen Zhong

The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…

Analysis of PDEs · Mathematics 2023-07-21 Niclas Bernhoff

A covariant Fokker-Planck type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the…

Statistical Mechanics · Physics 2010-11-19 Guillermo Chacón--Acosta , Gilberto M. Kremer

A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…

Plasma Physics · Physics 2009-10-31 R. A. Treumann

In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and…

Analysis of PDEs · Mathematics 2013-06-20 Stéphane Brull , Pierre Charrier , Luc Mieussens

A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…

Quantum Physics · Physics 2026-04-24 Dalaver H. Anjum , Shahid Nawaz , Muhammad Saleem

In the present contribution, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of…

Plasma Physics · Physics 2011-03-07 Benjamin Graille , Thierry E. Magin , Marc Massot

In this study, we investigate the linear transport of neutral system within the framework of relativistic kinetic theory. Under the relaxation time approximation, we obtain an iterative solution to the relativistic Boltzmann equation in…

General Relativity and Quantum Cosmology · Physics 2025-04-22 Long Cui , Xin Hao , Liu Zhao

The simulation of rarefied gas flow based on the Boltzmann equation is challenging, especially when the gas mixtures have disparate molecular masses. In this paper, a computationally tractable kinetic model is proposed for monatomic gas…

Fluid Dynamics · Physics 2024-03-12 Qi Li , Jianan Zeng , Lei Wu

We investigate numerically a recent BGK-type model for a multi-component mixture of monatomic gases, undergoing a reversible bimolecular chemical reaction. The model replaces each collisional term of the Boltzmann equation with a relaxation…

Statistical Mechanics · Physics 2026-02-23 Giorgio Martalò , Ana Jacinta Soares , Romina Travaglini

The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while…

Analysis of PDEs · Mathematics 2026-01-30 Gaofeng Wang , Weike Wang , Tianfang Wu

Using relativistic kinetic theory, we study spherically symmetric, static equilibrium configurations of a collisionless Maxwell-Boltzmann gas with non-standard self-interactions, modelled by an effective one--particle force. The resulting…

Astrophysics · Physics 2009-11-10 Alexander Balakin , Roberto A. Sussman , Winfried Zimdahl

We consider the existence of steady rarefied flows of polyatomic gas between two parallel condensed phases, where evaporation and condensation processes occur. To this end, we study the existence problem of stationary solutions in a…

Analysis of PDEs · Mathematics 2025-03-18 Ki-Nam Hong , Marwa Shahine , Seok-Bae Yun