HARMONIC SOLUTIONS OF SOME SECOND-ORDER NONLINEAR EQUATIONS UNDER A PERIODIC FORCE

In this paper we prove some theorems on the existence of harmonic solutions of somesecond-order nonlinear equations under a periodic force.These theorems extend relevantresults in refs.[1]-[8].     

The mixed mode brittle fracture criteria in siliding mode fracture

It is well-known that the present mixed mode brittle fracture criteria are all theopening mode fracture criterion.We consider that mixed mode brittle fracture of slidingmode fracture exists too.Hence we propose three criteria of mixed mode brittle fracture ofsliding mode fracture;:the radial shearing stress criterion,the maximum shearing stresscriterion and the distortional strain-energy-density criterion.Thus,we can overall explainthe phenomena of brittle fracture in the structural elements with cracks.     

Two-phase heat transfer correlation for multi-component mixtures in the saturated flow-boiling regime

Investigations of two-phase heat transfer in the saturated flow-boiling region for multi-component mixtures has led to a proposed new correlation for the heat transfer coefficient where heat transfer of boiling is simply expressed in terms of the boiling number. This correlation was tested against the existing data on forced convective boiling heat transfer reported in the literature, giving satisfactory results; the correlation should, however, be tested further against wider data on convective heat transfer coefficients in multicomponent systems. The present lack of such data should be remedied.     

Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

Pulsierende Druckströmung hochpolymerer Schmelzen im kreisförmigen Kanal

Zusammenfassung Es werden theoretische und experimentelle Untersuchungen pulsierender Strömungen viskoelastischer Flüssigkeiten in einem kreisförmigen Kanal durchgeführt. Unter Voraussetzung einer eindimensionalen, isothermen und vollentwickelten Strömung in Anwesenheit sinusförmiger Druckgradientenschwankungen wird für die rheologische Zustandsgleichung von Bird-Carreau eine asymptotische Lösung erzielt. Die Ergebnisse weisen darauf hin, daß sowohl die relative Amplitude der Ausstoßschwankungen als auch die relative Änderung des mittleren Ausstoßes sich in einer allgemeinen Form darstellen läßt, die bezüglich der Temperatur und der relativen Amplitude der Druckgradientenschwankungen invariant ist. Die theoretischen Ergebnisse werden mit experimentellen Daten für ein Polyethylen niederer Dichte verglichen. Dabei wird eine gute Übereinstimmung der Theorie mit dem Experiment festgestellt.

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Theoretical and experimental studies were carried out on the pulsating flow of viscoelastic liquids through a circular channel. By assuming the flow to be one-dimensional, isothermal, and fully developed and the Bird-Carreau constitutive equation to be applicable, an asymptotic solution was found. The results obtained indicate that both the relative amplitude of pulsation of the output and the relative change in the average output may be presented in a generalized form that is independent of the relative amplitude of the pressure pulsations and temperature. The theoretical results were verified experimentally for a low-density polyethylene. Good agreement was found between the theory and the experimental data.

     

Performance of a small air-lift pump

Pumping of liquids using two-phase flow has been examined experimentally in small air-lift pumps with 12—19 mm bore plexiglass tubes. An air injection system was devised to create and maintain ‘perfect’ slug flow in the vertical riser tube. An equation has been derived, based on momentum conservation considerations, which correlates well with the measurements obtained. Slip variation, or liuid holdup, between the two phases and the formation of the ‘entrance’ section part of the pump (suction pipe) were taken into consideration. Unlike its predecessors, this equation predicts the reversal in the pump performance curve observed experimentally.     

The effect of magnetic fields and boundary conditions on the Couette flow of nematics

The paper discusses the theory of Couette flow of a nematic liquid crystal. The apparent viscosity, orientation and velocity profiles are computed forp-azoxyanisole as functions of shear rate and magnetic field for symmetric and asymmetric molecular alignments at the boundaries and for different relative radii of the cylinders. For symmetric homeotropic boundary condition an azimuthal field exhibits a threshold analogous to a Freedericksz transition. An expression is also derived for the Freedericksz threshold in the hydrostatic case.     

Precise lattice parameter measurements in CsCl-Br solid solutions between room temperature and 90°K by powder x-ray diffraction

Solid solutions of CsCl-Br in five different concentrations were prepared in sealed quartz tubes by heating the mixture to 1123°K for 6–8 hr and quenching to room temperature. X-ray diffractograms were taken at eight different temperatures between room temperature and 90°K for these solid solutions using the YPC50NM powder diffractometer and a continuous flow cryostat. The observed lattice parameters for each sample at each temperature obtained from the powder diffractograms were then extrapolated to give the true lattice parameters using the least square method with Nelson-Riley extrapolation scheme. The values of the true lattice parameters at each concentration and at each temperature were tabulated and the results discussed. It is shown that the lattice parameters vs temperature for some concentrations exhibit an anomalous behaviour. Contribution No. 691     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.