1. |
On simulation methods for the Boltzmann equation |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 141-154
Reinhard Illner,
Helmut Neunzert,
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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
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2. |
Oscillating Maxwellians: Exact solutions for the Boltzmann equation |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 155-173
H. Cornille,
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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
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3. |
Calculation of the number densities in an extended kinetic theory of gas mixtures |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 175-187
V.C. Boffi,
G. Spiga,
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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
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4. |
Steady gas flows past bodies at small Knudsen numbers |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 189-199
Yoshio Sone,
K. Aoki,
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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
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5. |
On the relaxation of the heavy-particle velocity averages of a Rayleigh gas |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 201-211
Leonardo Ferrari,
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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
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6. |
Existence of global solutions for the space inhomogeneous Enskog equation |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 213-221
Carlo Cercignani,
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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
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7. |
New results on the Boltzmann equation in unbounded domains |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 223-230
G. Toscani,
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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
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8. |
Generalized Hamiltonians, functional integration and statistics of continuous fluids and plasmas |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 231-251
H. Tasso,
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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
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9. |
Dimension of the universal attractor describing the periodically driven Sine-Gordon equations |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 253-265
Jean-Michel Ghidaglia,
Roger Temam,
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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
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10. |
Standing and travelling waves for nonlinear wave equations |
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Transport Theory and Statistical Physics,
Volume 16,
Issue 2-3,
1987,
Page 267-277
Alan Weinstein,
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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
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