摘要:

The Cauchy Problem for the relativistic Vlasov–Maxwell equations is studied in two dimensions. The Cauchy data E0, B0of the fields, and the initial density f0of the plasma, are assumed to be smooth and to decay at infinity, and are to satisfy the usual constraints. When this data is restricted to be cylindrically symmetric, the v –support of the plasma density is shown to be bounded on every bounded time interval. However, a shock could still presumably be formed at very large times.

ISSN:0041-1450    

DOI:10.1080/00411458808230876

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

In its simplest form the kinetic equation of plasma is the one-dimensional Vlasov-Poisson systemThis system describes the motion of a plasma in one space dimension under the electrostatic approximation of zero magnetic field. The function f is the phase space distribution function (for electrons), f0is the initial distribution and b is the fixed background distribution of opposite charge. In this paper we develop a discrete approximation to (1.1). The system is first discretized in x and v, but not in t and the trajectories of (1.1) are approximated by the trajectories of this discretized problem. Time discretization is then introduced and the space discretized system is approximated by the space-time discretization which then becomes the final approximation to (1.1).

ISSN:0041-1450    

DOI:10.1080/00411458808230877

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Exact analytic solutions are given for certain classic linear transport problems describing particle flow in a statistical medium. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two state homogeneous Markov process. The problems treated, in both rod and planar geometry, are: (1) the halfspace albedo problem; (2) the halfspace emissivity problem; (3) the infinite medium Green's function problem; and (4) the halfspace Hilne problem.

ISSN:0041-1450    

DOI:10.1080/00411458808230878

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Some one-dimensional boundary value problems of the kinetic theory of gases can be solved analytically in closed form when the Boltzmann collision operator is replaced a simple kinetic model such as the linear BGK (Bhatnagar-Gross-Krook) model. Such are the slip-flow and the diffusion slip problems. Analytical solutions were obtained by Wiener-Hopf or singular eigenfunctions expansions methods in the sixties and seventies. Here, a Cauchy integral method of solution, developed for radiative transfer problems, is applied to the slip-flow problem and to the diffusion slip problem for a binary gas mixture (with A. Latyshev1). In the CI method, which can handle Wiener-Hopf integral equations with exponentially or non-exponentially decreasing kernels, the Wiener-Hopf equation is recast into a singular integral equation of the Cauchy type, by an inverse Laplace transformation. The latter equation is solved by a classical method of reduction to a boundary value problem in the complex plane (i.e. a Riemann-Hilbert problem). The equivalence between our solutions and other other analytical representations is discussed.

ISSN:0041-1450    

DOI:10.1080/00411458808230879

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A unified description of the polarization matrix describing the polarization of an electromagnetic beam for both the classical and quantum cases is given. Properties of parameters which are independent of the representation of the Pauli matrices are emphasized. It is noted that in the quantum case a completely polarized beam can arise from a density matrix corresponding to a pure or mixed state. Similarly an incoherent beam can also arise from mixed or pure states.

ISSN:0041-1450    

DOI:10.1080/00411458808230880

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458808230881

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A Conference on Mathematical Problems in the Kinetic Theory of Gases, the fifth in a series of meetings on kinetic theory held at Oberwolfach every three years since 1976, convened May 8–14, 1988. Each of the previous meetings has been discussed in a Conference Report published in this journal.1,2,3,4The first four meetings were organized jointly by Helmut Neunzert of Kaiserslautern and Donald Pack of Glasgow, while Carlo Cercingnani of Milano was added to the organizing committee for the current symposium.

ISSN:0041-1450    

DOI:10.1080/00411458808230882

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458808230883

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458808230884

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor