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A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are…

Analysis of PDEs · Mathematics 2024-10-23 Thomas Rey , Tommaso Tenna

We exhibit some arguments in favour of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the…

Statistical Mechanics · Physics 2013-08-12 Umberto Marini Bettolo Marconi , Andrea Puglisi , Angelo Vulpiani

In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…

Numerical Analysis · Mathematics 2014-03-05 Alessandro Munafo , Jeffrey R. Haack , Irene M. Gamba , Thierry E. Magin

We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but…

Analysis of PDEs · Mathematics 2018-07-02 Christian Klingenberg , Marlies Pirner , Gabriella Puppo

In this article we deduce a mathematical model of Maxwell-Stefan type for a reactive mixture of polyatomic gases with a continuous structure of internal energy. The equations of the model are derived in the diffusive limit of a kinetic…

Analysis of PDEs · Mathematics 2019-11-18 Benjamin Anwasia , Marzia Bisi , Francesco Salvarani , Ana Jacinta Soares

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

Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…

Statistical Mechanics · Physics 2007-05-23 E. Ben-Naim , P. L. Krapivsky

A kinetic model is proposed for rarefied flows of molecular gas with rotational and temperature-dependent vibrational degrees of freedom. The model reduces to the Boltzmann equation for monatomic gas when the energy exchange between the…

Fluid Dynamics · Physics 2022-01-19 Qi Li , Lei Wu

We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the…

Mathematical Physics · Physics 2025-05-27 Marzia Bisi , Maria Groppi , Giorgio Martalò

In the following work, we consider the Boltzmann equation that models a polyatomic gas by representing the microscopic internal energy by a continuous variable I. Under some convenient assumptions on the collision cross-section…

Analysis of PDEs · Mathematics 2022-08-31 Stéphane Brull , Marwa Shahine , Philippe Thieullen

We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…

Statistical Mechanics · Physics 2015-06-24 Pierre-Henri Chavanis

This communication is both a pedagogical note for understanding polyatomic modelling in kinetic theory and a ''cheat sheet'' for a series of corresponding concepts and formulas. We explain, detail and relate three possible approaches for…

Analysis of PDEs · Mathematics 2025-01-31 Marzia Bisi , Thomas Borsoni , Maria Groppi

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability…

Fluid Dynamics · Physics 2023-06-28 Qi Li , Jianan Zeng , Lei Wu

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be…

Fluid Dynamics · Physics 2023-05-24 Praveen Kumar Kolluru , Mohammad Atif , Santosh Ansumali

Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…

Mathematical Physics · Physics 2023-05-01 William Barham , Philip J. Morrison , Eric Sonnendrücker

The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model…

Statistical Mechanics · Physics 2007-08-30 Andres Santos

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…

Statistical Mechanics · Physics 2007-09-23 E. Trizac , A. Barrat , M. H. Ernst

The statistical-physical study of granular matter is essential to understand, from a fundamental point of view, the many different phenomena emerging in these classical many-body systems. Under rapid-flow conditions, granular materials…

Soft Condensed Matter · Physics 2023-10-23 Alberto Megías

The BGK model is a relaxation-time approximation of the celebrated Boltzmann equation, and the Marle model is a direct extension of the BGK model in a relativistic framework. In this paper, we introduce the Marle model for polyatomic gases…

Analysis of PDEs · Mathematics 2024-02-06 Byung-Hoon Hwang

We formulate a generalized self-consistent stochastic quantum kinetic theory for finite-temperature ultracold Bose gases interacting via a generic long-range interaction, applicable to a broad range of systems, by means of Keldysh…

Quantum Gases · Physics 2025-07-28 Nick P. Proukakis , Gerasimos Rigopoulos , Alex Soto