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.

     

Drag on an elliptic cylinder in a fluid particle suspension

An elliptic cylinder is performing oscillations parallel to either of the principal axes of the cross-sectional ellipse in a fluid particle suspension. The stream function governing the flow and the velocity components are determined in terms of Mathieu functions. The drag on the cylinder is evaluated and expressed in terms of two parametersK andK. The effects of the variation of the frequency parameter, eccentricity parameter and relaxation time parameter on the drag parametersK, K is studied numerically.     

A finitely convergent “row-action” method for the convex feasibility problem

We present a modification of the Cyclic Subgradient Projection (CSP) method by Censor and Lent, which solves the convex feasibility problem in a finite number of steps when a Slater type condition holds, while preserving its row-action properties. A linear rate of convergence for the CSP method is established assuming the same hypothesis.Research partially supported by CNPq, under Grant No. 301699/81.     

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)].     

Every 8-uniform 8-regular hypergraph is 2-colorable

As is well known, Lovász Local Lemma implies that everyd-uniformd-regular hypergraph is 2-colorable, providedd 9. We present a different proof of a slightly stronger result; everyd-uniformd-regular hypergraph is 2-colorable, providedd 8.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

Planning systems and artificial intelligence

Traditional O.R. systems are compared with problem solving in Artificial Intelligence via Expert Systems. The discussion centers on explicit knowledge representation. The general aspects are illustrated by two planning systems:

1. LESP 2: A learning system for inspection plan generation
2. IDA: A system for finding functions and solutions in construction

     

Periodic solutions of nonlinear integral equations

The existence of a continuous periodic solution of the system

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