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A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific heat ratio and is described by one discrete Boltzmann equation (DBE).…

Soft Condensed Matter · Physics 2017-11-22 Chuandong Lin , Aiguo Xu , Guangcai Zhang , Kaihong Luo , Yingjun Li

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

In this paper, for the first time a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy…

comp-gas · Physics 2009-10-22 H. J. Bussemaker , M. H. Ernst , J. W. Dufty

A recent solution of the inelastic Boltzmann equation that applies for strong dissipation and takes into account non-equipartition of energy is used to derive an explicit expression for the thermal diffusion factor. This parameter provides…

Statistical Mechanics · Physics 2009-11-11 Vicente Garzo

The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a…

General Relativity and Quantum Cosmology · Physics 2008-11-26 A. L. Garcia-Perciante , A. Sandoval-Villalbazo , L. S. Garcia-Colin

We analyze a volumetric formulation of lattice Boltzmann for compressible thermal fluid flows. The velocity set is chosen with the desired accuracy, based on the Gauss-Hermite quadrature procedure, and tested against controlled problems in…

Soft Condensed Matter · Physics 2015-05-18 M. Sbragaglia , K. Sugiyama

Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation. The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation…

Statistical Mechanics · Physics 2015-06-05 Gilberto M. Kremer

In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…

Analysis of PDEs · Mathematics 2018-11-05 Andrea Tosin , Mattia Zanella

We present a novel method to solve the spatially homogeneous and isotropic relativistic Boltzmann equation. We employ a basis set of orthogonal polynomials dynamically adapted to allow for emergence of chemical non-equilibrium. Two time…

Numerical Analysis · Mathematics 2015-06-19 Jeremiah Birrell , Jon Wilkening , Johann Rafelski

Hydrodynamic equations for a binary mixture of inelastic hard spheres are derived from the Boltzmann kinetic theory. A normal solution is obtained via the Chapman-Enskog method for states near the local homogeneous cooling state. The mass,…

Soft Condensed Matter · Physics 2009-11-07 Vicente Garzó , J. W. Dufty

We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities…

Statistical Mechanics · Physics 2009-11-11 T. S. Biro , G. Kaniadakis

The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including…

In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…

Analysis of PDEs · Mathematics 2023-05-24 Laurent Boudin , Bérénice Grec , Milana Pavić-Čolić , Srboljub Simić

Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only…

Statistical Mechanics · Physics 2022-07-01 Petr Vágner , Michal Pavelka , Jürgen Fuhrmann , Václav Klika

Relativistic kinetic theory is applied to the study of the balance equations for relativistic multicomponent mixtures, comparing the approaches corresponding to Eckart's and Landau-Lifshitz's frames. It is shown that the concept of particle…

General Relativity and Quantum Cosmology · Physics 2019-07-18 A. R. Sagaceta-Mejía , A. Sandoval-Villalbazo , J. H. Mondragón-Suárez

Many features of granular media can be modeled by a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations accounting for dissipation…

Statistical Mechanics · Physics 2007-05-23 V. Garzo , J. W. Dufty

A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…

Classical Physics · Physics 2015-05-20 Domingo J. Louis-Martinez

The balance equations for thermodynamic quantities are derived from the nonlocal quantum kinetic equation. The nonlocal collisions lead to molecular contributions to the observables and currents. The corresponding correlated part of the…

Statistical Mechanics · Physics 2018-06-19 Klaus Morawetz

We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is…

Analysis of PDEs · Mathematics 2025-09-03 Seung-Yeon Cho , Byung-Hoon Hwang , Myeong-Su Lee , Seok-Bae Yun

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement…

Statistical Mechanics · Physics 2016-11-23 J. Javier Brey , P. Maynar , M. I. García de Soria