scholarly journals Comments on “Matrix Elements of the Linearized Collision Operator”

1970 ◽  
Vol 13 (8) ◽  
pp. 2202 ◽  
Author(s):  
S. C. Gupta
Keyword(s):  
Collision Operator ◽  
Matrix Elements ◽  
Linearized Collision Operator

Matrix Elements of the Linearized Collision Operator for Multi-temperature Gas-mixtures

1978 ◽  
Vol 33 (4) ◽  
pp. 480-492
Author(s):  
Ulrich Weinert
Keyword(s):  
Collision Operator ◽  
Basis Functions ◽  
Inelastic Collisions ◽  
Matrix Elements ◽  
Flux Vector ◽  
Balance Equations ◽  
Heat Flux Vector ◽  
The Matrix ◽  
Boltzmann Collision Operator ◽  
Linearized Collision Operator

For a multi-component and multi-temperature gas-mixture the matrix elements of the linearized Boltzmann collision operator are investigated for isotropic interaction potentials. The representation by means of Burnett basis functions simplifies the algebraic structure and enables closed expressions for the general results, which can also be used for an investigation of inelastic collisions. For the elastic case those collision terms are given explicitely which appear in the balance equations for mass, momentum, energy and heat flux-vector.

On the Inversion of the Linearized Collision Operator

1981 ◽  
Vol 36 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Ulrich Weinert
Keyword(s):  
Kernel Function ◽  
Inverse Operator ◽  
Integral Kernel ◽  
Collision Operator ◽  
Boltzmann Collision Operator ◽  
Linearized Collision Operator

Abstract Some features are discussed in connection with the representation of the linearized Boltzmann collision operator and its inversion. It is shown that under certain assumptions the inverse operator can be given explicitly as an integral kernel function.

Symmetries of and entropy production by transport in toroidal confinement systems

1998 ◽  
Vol 59 (4) ◽  
pp. 695-706 ◽  
Author(s):  
H. SUGAMA ◽  
W. HORTON
Keyword(s):  
Entropy Production ◽  
Transport Process ◽  
Collision Operator ◽  
Positive Definite ◽  
Anomalous Transport ◽  
The Self ◽  
Entropy Production Rate ◽  
Onsager Symmetry ◽  
Neoclassical Transport ◽  
Linearized Collision Operator

A synthesized formulation of classical, neoclassical and anomalous transport in toroidal confinement systems with electromagnetic fluctuations and large mean flows is presented. The positive-definite entropy production rate and the conjugate flux–force pairs are rigorously defined for each transport process. The Onsager symmetries of the classical and neoclassical transport matrices are derived from the self-adjointness of the linearized collision operator. The linear gyrokinetic equation with given electromagnetic fluctuations determines the anomalous fluxes with the quasilinear anomalous transport matrix, which satisfies the Onsager symmetry.

Kinetic Theory for a Dilute Gas of Particles with Spin. II. Relaxation Coefficients

1968 ◽  
Vol 23 (12) ◽  
pp. 1893-1902
Author(s):  
S. Hess ◽  
L. Waldmann
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Interaction Potential ◽  
Collision Operator ◽  
Dilute Gas ◽  
Order Of Magnitude ◽  
Generalized Boltzmann Equation ◽  
Linearized Collision Operator ◽  
Relaxation Coefficients

The relaxation coefficients to be discussed are given by collision brackets pertaining to the linearized collision operator of the generalized Boltzmann equation for particles with spin. The order of magnitude of various nondiagonal relaxation coefficients which are of interest for the SENFTLEBEN-BEENAKKER effect is investigated. Those nondiagonal relaxation coefficients which are linear in the nonsphericity parameter ε (ε essentially measures the ratio of the nonspherical and the spherical parts of the interaction potential), as well as some diagonal relaxation coefficients are expressed in terms of generalized Omega-integrals.

scholarly journals Higher order slip according to the linearized Boltzmann equation with general boundary conditions

2011 ◽  
Vol 369 (1944) ◽  
pp. 2228-2236 ◽  
Author(s):  
Silvia Lorenzani
Keyword(s):  
Boltzmann Equation ◽  
Collision Operator ◽  
Velocity Slip ◽  
Lattice Boltzmann Methods ◽  
Linearized Boltzmann Equation ◽  
Potential Applications ◽  
Microscale Flows ◽  
Scattering Kernel ◽  
Linearized Collision Operator ◽  
Slip Coefficients

In the present paper, we provide an analytical expression for the first- and second-order velocity slip coefficients by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator and the Cercignani–Lampis scattering kernel of the gas–surface interaction. The polynomial form of the Knudsen number obtained for the Poiseuille mass flow rate and the values of the velocity slip coefficients are analysed in the frame of potential applications of the lattice Boltzmann methods in simulations of microscale flows.

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