摘要:

The purpose of this talk is to give a comparative discussion of some simulation procedures for the Boltzmann equation in terms of rigour and numerical effort. The methods under consideration are the algorithms suggested by Bird [7] and Nanbu [9] respectively, and a modification o f the Nanbu procedure suggested by Babovsky [2]. The procedures are applied to and compared by means of a shock wave problem.

ISSN:0041-1450    

DOI:10.1080/00411458708204655

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

For two classes of non linear Boltzmann equations, when the particles are of the Maxwell type and external forces are present, we present explicit distributions solutions. First, for the homogeneous one dimensional Kac model for which momentum conservation has been dropped, we include linear velocity forces and uniform source terms. Second, for the homogeneous and inhomogeneous Boltzmann equations of dimension d > 1, for which both energy and momentum conservations hold, we include either spatially dependent forces or velocity forces plus uniform sources. For both classes there exist examples of distributions which relax towards oscillating Maxwellians and other towards absolute Maxwellians. We give the complete proofs for the Kac model and present results for the d > 1 dimensional models.

ISSN:0041-1450    

DOI:10.1080/00411458708204656

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Analytical and numerical results for the number densities p. (t) (j=l,2,—,N) of a N-component gas mixture, including removal and self-generation effects, are presented, especially for N=2 and N=3. The dynamics of the mixture considered is also illustrated by curves describing the physical behaviour of the single p. versus t.

ISSN:0041-1450    

DOI:10.1080/00411458708204657

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Steady gas flows at small Knudsen numbers around arbitrary bodies (Asymptotic behavior for small Knudsen numbers of the solution of time-independent boundary value problems of the Boltzmann equation over a general domain) are considered when the Reynolds number of the system is of the order of unity. The generalized slip flow theory developed for the Boltzmann-Krook-Welander equation is extended for the standard Boltzmann equation. From the result, the effect of gas rarefaction on the flow (the relation between Boltzmann and hydrodynamic systems) is clarified, and several features of the force on a closed body in the gas are derived.

ISSN:0041-1450    

DOI:10.1080/00411458708204658

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The relaxation of the most important heavy-particle velocity averages of a Rayleigh gas is studied both exactly in the Maxwell model and, by using the approximate theory based on the usual Fokker-Planck equation, in the Rayleigh limit. It is pointed out that this usual (approximate) kinetic equation yields, in the Maxwell model, the exact relaxation of the heavy-particle mean velocity, and a very good description of the relaxation of the heavy-particle mean square speed, irrespectively of the fact that in several physical situations the same kinetic equation cannot correctly describe the relaxation of the heavy-particle velocity distribution. It is found, moreover, that in certain situations the heavy-particle mean-square velocity components relax, in the approximate theory, in an unphysical way, unless an appropriate limitation on the initial heavy-particle mean velocity is imposed.

ISSN:0041-1450    

DOI:10.1080/00411458708204659

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The Enskog equation for a gas of hard smooth spheres is written under the assumption that correlations are negligible but space separation of the spheres at the moment of collision is not.

ISSN:0041-1450    

DOI:10.1080/00411458708204660

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We give some new results on the Cauchy problem for the full non-linear Boltzmann equation in unbounded domains when the initial values are ”small“. Then we prove a global existence theorem for the full Broadwell model in all space when the initial data are ”large“.

ISSN:0041-1450    

DOI:10.1080/00411458708204661

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Generalized Hamiltonian formalism including generalized Poisson brackets and Lie-Poisson brackets is presented in Sec. II. Gyroviscous magnetohydrodynamics is treated as a relevant example in Euler and Clebsch variables. Section III is devoted to a short review of functional integration containing the definition and a discussion of ambiguities and methods of evaluation. The main part of the contribution is given in Sec. IV, where some of the content of the previous sections is applied to Gibbs statistics of continuous fluids and plasmas. In particular, exact fluctuation spectra are calculated for relevant equations in fluids and plasmas.

ISSN:0041-1450    

DOI:10.1080/00411458708204662

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

In this work we give a rigorous and explicit bound of the fractal dimension of the universal attractor describing the long time behavior of the damped Sine-Gordon equation driven by a time-periodic force. The dependence of the dimension in terms of the physical quantities is provided.

ISSN:0041-1450    

DOI:10.1080/00411458708204663

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The aim of this talk will be to present results, many of them obtained jointly with A. Floer, on the existence and stability of standing and traveling wave solutions for nonlinear equations of Schrödinger and Klein-Gordon type. Emphasis will be placed on situations other than the flat, spatially homogeneous ones which have usually been studied in the past; in particular, equations with a potential or with spherical geometry will be considered. The relation between the hamiltonian structures for waves and particles will be discussed.

ISSN:0041-1450    

DOI:10.1080/00411458708204664

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor