Nonlinear void-fraction waves in two-phase bubbly flow

It is shown that nonlinear void-fraction waves constitute exact solutions of the two-fluid equations for bubbly flow, if and only if the virtual-mass coefficientm() is a definite function of the void fraction. In the case of spherical bubbles the functional dependence is given bym()=(1/2)(1–a)(1–3). A similar expression was obtained recently by means of an elaborate linear stability analysis of a uniform two-phase flow. It is remarkable that the greater part of the physical quantities of a nonlinear void-fraction wave depends linearly on. The virtual-mass coefficient may be derived directly from a special form of Hamilton's variational principle.

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Zusammenfassung Es wird gezeigt daß nichtlineare Konzentrationswellen exakte Lösungen der Zweifluiden Gleichungen einer Blasenströmung darstellen dann und nur dann, wenn der Koeffizientm() der virtuellen Masse eine bestimmte Funktion der Volumenkonzentration der Blasen ist. Die funktionelle Abhängigkeit ist im Falle kugelförmiger Blasen gegeben durchm()= (1/2)(1–) (1–3). Ein gleicher Ausdruck wurde neulich mittels einer umständlichen linearen Stabilitätsanalysis einer uniformen Zweiphasen-Strömung erhalten. Es ist bemerkenswert daß der größere Teil der physikalischen Größen einer nichtlinearen Konzentrationswelle in linearer Weise von abhängt. Der Koeffizient der virtuellen Masse kann in direkter Weise von einer speziellen Form des Hamiltonschen Variationsprinzips hergeleitet werden.

     

Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Wide-angle one-way wave equations

A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].     

String structures and the index of the Dirac-Ramond operator on orbifolds

We discuss the relationship between string structures and the topological class H ⁴(M,Z) on non-simply connected manifolds. We also investigate to what extent the index formula for the Dirac-Ramond operator detects the class, .Supported by the NSF Grant #84-07109 and by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069On leave from the University of Wroclaw, Wroclaw, Poland     

Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

Sensitivity of hydrodynamic system of the Obukhov type

The paper deals with the regime of advanced Bénard instabilities (described usually by the Lorenz system) in a more general system formulated firstly by Obukhov. It has been shown that triplet co-operation leads to characteristic courses where some new regularities occur.     

Computer-simulated diffraction patterns for metastable austenitic steels

The paper deals with the computer simulation of composite theoretical electron-diffraction patterns for metastable austenitic steels, containing deformation and martensite transformation structures. In many cases generated data can be used for interpretation of experimentally determined diffraction patterns. A few examples are presented which demonstrate that the application of the composite theoretical diffraction patterns may be complicated due to various diffraction effects which can modify the geometry of experimentally obtained diffraction patterns.     

Linear mode conversion of waves near the maxima or minima of the density in a warm magnetized plasma

Behaviour of the h. f. electrostatic waves near the plasma or upper hybrid resonances was studied in the case that these resonances are situated at the maxima or minima of the plasma density. Supposing the parabolic density profile in these regions we obtained the connection formulae for the WKB solutions. In a weakly inhomogeneous magnetoplasma the effect of the parabolic profile manifests itself only in narrow frequency band centred at the resonance frequency corresponding to the extreme value of the density. The whole process can be then described by only two coefficients, viz. the power conversion and power transmission coefficients.