摘要:

We consider two types of transport equations. One with a nonlinear diffusion term and no absorption, the other with a linear diffusion and a nonlinear absorption. Invariance under homothetie transformations leads to the self similar solutions but questions should be raised about their physical character, their stability, the choice of the arbitrary parameter sometimes left in the reduced equation, etc.

ISSN:0041-1450    

DOI:10.1080/00411458708204665

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The general statistical properties of the Zwanzig projection operator are discussed. In particular it is shown that the mean value of the memory effects contained in the evolution equations generated by the projection operator are always zero. The results are applied to the nonlinear three-wave interaction in a plasma. Simple evolution equations for the mean number of photons of the interacting waves are derived.

ISSN:0041-1450    

DOI:10.1080/00411458708204666

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

It is shown that in anonviscous barotropic compressible fluidfilling an unbounded region, perturbations to the rest state propagate with a finite speed even if they may besingularat a fixed point.

ISSN:0041-1450    

DOI:10.1080/00411458708204667

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We develop the variational method of elliptic systems for the stability analysis of the flow of an inviscid incompressible liquid film with an interface We consider the flow of an inviscid incompressible liquid film covering a circular cylinder which rotates about its axis. The film may be either outside or inside the cylinder but in either case there is an interface between the liquid and the ambient gas on which surface tension exists. The purpose of this work is to present a method for analyzing the stability of such a flow using the variational technique of elliptic systems. Even though the individual results, employed in the analysis, are standard, their combination in this method may be somewhat novel and applicable to similar stability problems. The details of the physical interpretation of our results are given elsewhere ([1]) and here we shall only concentrate on presenting the proof of the stability analysis.

ISSN:0041-1450    

DOI:10.1080/00411458708204668

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

There is a growing interest in the use of orthogonal and conformal mapping methods for the solution of flow problems in two and three dimensions. Here, the non-linear integral equations of Symm and Theodorsen have turned out to be fruitful starting points for further generalizations, exploiting Fast Fourier Transforms. The discretized equations not only offer a means for the construction of boundary fitted coordinates, but also permit the introduction of analytic expansion techniques in the study of problems that otherwise would be completely dominated by insight obtained from numerical calculations alone.

ISSN:0041-1450    

DOI:10.1080/00411458708204669

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

In this paper some new results concerning magnetdhydrodynamic (MHD) equations with the Hall current (HC) term in the Ohm's law are presented. For the cylindrical pinch of a compressible HC fluid, it is found that for large time and long wave length the solution to the governing equations exhibits the behavior of solitons as in the case of an ideal MHD model. In some special cases, the HC model appears to be tetter posed. An open question is whether a simple toroidal equilibrium of an HC fluid with resistivity and viscosity exists. The answer to this question is affirmative if the prescribed velocity on the boundary has a small norm. Furthermore, the equilibrium is also linearly and nonlinearly stable.

ISSN:0041-1450    

DOI:10.1080/00411458708204670

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We analyze a system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field. We demonstrate that the solution to this system tends to a time asymptotic state which is of space-time separable form, (t)f(x). Furthermore, f(x) is independent of the initial conditions and (t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects as radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

ISSN:0041-1450    

DOI:10.1080/00411458708204671

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The problem of current drive by electromagnetic waves at the lower hybrid frequency in a magnetically confined plasma in the presence of a d.c. electric field is considered. A one-dimensional model collision operator is used which allows an analytic solution of the problem that includes a self-consistent treatment of runaways. The kinetic equation is solved in general, and general expressions for the absorbed power, the driven current and the current drive efficiency are given. The case in which the current driven by the waves and that driven by the electric field flow in the same direction is worked out and discussed in detail. It is shown that in general the presence of runaways tends to enhance the influence of the electric field on the current drive efficiency.

ISSN:0041-1450    

DOI:10.1080/00411458708204672

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Numerical solutions of the spectrum of ideal compressible Magnetohydrodynamics are given for an inhomogeneous plasma slab embedded in a constant vertical gravitational field and in a force free sheared horizontal magnetic field. Discrete normal mode solutions with frequencies below the cusp continuum on the one hand and with frequencies above the cusp continuum and below the Alfvén continuum on the other hand are computed for various strengths of the magnetic field and their properties are discussed.

ISSN:0041-1450    

DOI:10.1080/00411458708204673

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We study instability caused by aliasing error with repect to both the viscous Burgers' equation and the incompressible magnetohydrodynamic equations. “Soft” and “hard” breakdowns are predicted to occur in tokamak simulations. Nonlinear stability criteria can be formulated, but it seems preferable to use numerical schemes that are not prone to these breakdowns, notably EPIC.

ISSN:0041-1450    

DOI:10.1080/00411458708204674

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor