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Half-space boundary Kramers' problem about isothermal sliding of moderate dense gas with accomodation boundary conditions along a flat firm surface is solving. The new method of the solution of boundary problems of the kinetic theory is…

Mathematical Physics · Physics 2014-12-31 A. V. Latyshev , A. D. Kurilov

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

In the present work the classical problem of the kinetic theory of gases (the Smoluchowsky' problem about temperature jump in rarefied gas) is considered. The rarefied gas fills half-space over a flat firm surface. logarithmic gradient of…

Mathematical Physics · Physics 2014-11-05 A. V. Latyshev

A new kinetic model is proposed where the equilibrium distribution with bounded support has a range of velocities about two average velocities in 1D. In 2D, the equilibrium distribution function has a range of velocities about four average…

Fluid Dynamics · Physics 2023-08-15 Shashi Shekhar Roy , S. V. Raghurama Rao

Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the…

Physics Education · Physics 2019-09-24 Lior M. Burko

The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the…

Soft Condensed Matter · Physics 2014-11-10 Andrés Santos

A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…

Statistical Mechanics · Physics 2022-04-13 M. Mayo , J. Javier Brey , M. I. García de Soria , P. Maynar

We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplified, 1…

Analysis of PDEs · Mathematics 2012-06-22 Yves Bourgault , Damien Broizat , Pierre-Emmanuel Jabin

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…

Analysis of PDEs · Mathematics 2024-01-09 Niclas Bernhoff

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially non-trivial velocity distributions. In this paper, moment equations for the bulk velocities,…

Mathematical Physics · Physics 2023-10-20 Evan Habbershaw , Ryan S. Glasby , Jeffrey R. Haack , Cory D. Hauck , Steven M. Wise

We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex…

Analysis of PDEs · Mathematics 2018-03-13 I-Kun Chen , Chun-Hsiung Hsia , Daisuke Kawagoe

An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…

Statistical Mechanics · Physics 2025-09-08 C. Dalitz , E. H. de Groot

We study the thermodynamical properties of a one-dimensional gas with one-dimensional gravitational interactions, and placed in a uniform mass background. Periodic boundary conditions are implemented as a modification of the potential…

Statistical Mechanics · Physics 2017-02-22 Pankaj Kumar , Bruce N. Miller , Dan Pirjol

In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an approximation of the Boltzmann equation, the…

Analysis of PDEs · Mathematics 2022-03-30 Marlies Pirner , Sandra Warnecke

The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state…

Statistical Mechanics · Physics 2009-11-11 Kim Hyeon-Deuk

The kinetic theory for a fluid of hard spheres which undergo endothermic and/or exothermic reactions with mass transfer is developed. The exact balance equations for concentration, density, velocity and temperature are derived. The Enskog…

Statistical Mechanics · Physics 2007-05-23 James F. Lutsko

The contribution of sliding-induced, atomic-scale instabilities to the kinetic friction force is investigated by molecular dynamics. For this purpose, we derive a relationship between the kinetic friction force $F_{\rm k}$ and the…

Statistical Mechanics · Physics 2009-11-10 Martin Aichele , Martin H. Muser

The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of…

Plasma Physics · Physics 2017-03-07 A. V. Latyshev , S. Sh. Suleymanova

We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is…

Mathematical Physics · Physics 2007-05-23 S. Bastea , R. Esposito , J. L. Lebowitz , R. Marra