Das Düsenschwellphänomen beim Austritt einer wandhaftenden anorganischen Glasschmelze aus Strangpreßwerkzeugen mit nichtkreisförmigem Öffnungsquerschnitt

Zusammenfassung Eine ausgeprägte Strangaufweitung tritt bei anorganischen Glasschmelzen dann auf, wenn bei schleichender Strömung eine Haftung zwischen der Wand des Matrizenkanals und dem strömenden Medium gegeben ist. Sie rührt dabei von der Umorientierung der Geschwindigkeitsverteilung von einem parabelförmigen zu einem kastenförmigen Profil her.In den experimentellen Untersuchungen konnte festgestellt werden, daß oberhalb einer bestimmten Kanallänge, d. h. bei ausgeprägten Strömungsverhältnissen im Preßwerkzeug die flächenbezogene Strangaufweitung konstant und dabei insbesondere unabhängig von der Profilform etwa 29% beträgt. Daraus wird gefolgert, daß dieser Betrag dem linearen Wert für den zweidimensionalen Fall des unendlich ausgedehnten Spaltes entsprechen muß.In einer theoretischen Analyse wurde die Berechnung dieses Falles ausgehend von der Stokes-Gleichung mit Hilfe der Methode der finiten Elemente durchgeführt. Aus der sich daraus ergebenden Druck- und Geschwindigkeitsverteilung konnte schließlich die Kontur des austretenden Stranges sowie dessen Endhöhe ermittelt werden.Ein Vergleich der experimentell und rechnerisch ermittelten Werte für die Strangaufweitung zeigt dabei eine recht gute Übereinstimmung und bestätigt dadurch auch die weitgehende Unabhängigkeit der flächenbezogenen Aufweitung von der Querschnittsform des Stranges.

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Inorganic glass melts are showing a characteristic die swell, when in the case of slow motion a strong adhesion between the streaming fluid and the wall of the die channel exists. The reason for this phenomenon is the rearrangement of the velocity profile from a parabolic to a box-type design form.The experimental investigations have demonstrated, that above a certain channel length, this means at distinct flow conditions inside the die channel, the value for the extension of the cross-sectional area is constant of about 29%. Particularly it is independent of the shape of the used die profiles. From this result, it is to deduce that this value must correspond to that of the two-dimensional case of the infinite extended slit.In a theoretical analysis the computation of this case was performed, starting from the Stokes-equation by the finite element method. By means of the resulting pressure and velocity distribution, the contour of the emerging rod and its final thickness could be determined.A comparison between experimental and computational results shows good agreement. So the appreciable independence of the magnitude of the die swell from the profile of the extruded rod is confirmed.

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A Fläche - a ^p ,a ^u Knotenpunktsvariablen für Druck bzw. Geschwindigkeit - a, b Seitenlängen des Rechteckprofils - B =L · N ^u Matrix - D Viskositätsmatrix - f Kräftematrix - K Schwerkraftvektor - K ^p ,K ^u Elementdruckmatrix, Elementgeschwindigkeitsmatrix - L Transformationsmatrix für den ebenen Fall - m Kronecker-Symbol für den zweidimensionalen Strömungszustand - N ^p ,N ^u Ansatzfunktionsmatrizen für Druck bzw. Geschwindigkeit - p Preßdruck - R Radius - T Preßtemperatur - t Lastvektor - u = (w, v) Geschwindigkeitsvektor - _A flächenbezogene Strangaufweitung - _R Aufweitung einer linearen QuerschnittsabmessungR - dynamische Viskosität - Dichte - D u/Dt Substantielle Ableitung der Geschwindigkeit nach der Zeit - T Transponierte einer Matrix (oberer Index) Vorgetragen auf der Jahrestagung der Deutschen Rheologischen Gesellschaft in Berlin vom 13.–15. Mai 1985     

On the periodic points of a two-parameter family of maps of the plane

We study the dynamics of a two-parameter family of noninvertible maps of the plane, derived from a model in population dynamics. We prove that, as one parameter varies with the other held fixed, the nonwandering set changes from the empty set to an unstable Cantor set on which the map is topologically equivalent to the shift endomorphism on two symbols. With the help of some numerical work, we trace the genealogies of the periodic points of the family of period 5, and describe their stability types and bifurcations. Among our results we find that the family has a fixed point which undergoes fold, flip and Hopf bifurcations, and that certain families of period five points are interconnected through a codimension-two cusp bifurcation.     

Interaction of an ultrasonic wave with a bubbly mixture

The interaction of an ultrasonic wave with a bubbly two-phase flow is studied both experimentally and theoretically. Brief theoretical reviews of acoustic wave generation by a piston and of the interaction of a plane wave with a single bubble are given. A theory relating ultrasonic wave transmission through a bubbly flow with two-phase flow parameters, notably the bubble size and the volumetric interfacial area, is derived and compared with preliminary data. The theoretical and experimental limitations concerning the application of ultrasonic transmission measurements to the study of bubbly flow are discussed in detail, and recommendations for future work in this area are made.Nomenclature A projected cross-sectional area of a bubble - a bubble radius - a _T emitter radius - c speed of sound - d equivalent bubble diameter - I intensity - I ₀ incident intensity - J ₀ Bessel function of zero order - J ₀ Bessel function of first order - j ₁ spherical Bessel function of the first kind and of order l - k wave number - n _l spherical Bessel function of the second kind (Nishi's notation) - n number of bubbles per unit volume or per unit area - P ₀ pressure amplitude at the emitter; equilibrium pressure in the liquid - p pressure perturbation - r spherical coordinate, radial distance to the x-axis - S total scattering cross-sectional area, surface of the piston - S _i scattering cross-sectional area of the i-th bubble - T transmittance - t time - U complex source strength divided by the source area - W ratio of radial distance from the axis on the emitter surface to the radius of the emitter - x axis coinciding with the direction of propagation of the plane wave; distance between the transducers - void fraction - interfacial area per unit volume - spherical coordinate - ultrasonic wavelength - density - angular frequency     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Reconstructing visible regions from visible segments

An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algorithms operating on polyhedral scenes and in cartography. A special case of reconstruction can be formulated as a graph problem: Determine the faces of a straight-edge planar graph given in terms of its edges. This is accomplished inO(n logn) time using linear space for a graph withn edges, and is worst-case optimal. The graph may have separate components but the components must not contain each other. The general problem of reconstruction is then solved by applying our algorithm to each component in the containment relation.Research of this author is supported by the National Science Foundation under grant no. ECS-8351942, and by the Schlumberger-Doll Research Labs, Ridgefield, Connecticut.     

Extension of a binaural cross-correlation model by contralateral inhibition. I. Simulation of lateralization for stationary signals

Running interaural cross correlation is a basic assumption to model the performance of the binaural auditory system. Although this concept is particularly suited to simulate psychoacoustic localization phenomena, there exist some localization effects which cannot be explained by pure cross correlation. In this paper a model of interaural cross correlation is extended by a "contralateral-inhibition mechanism" and by "monaural detectors" in order to simulate a wide range of psychoacoustic lateralization data. The extended model explains lateralization of pure tones with interaural time differences as well as with interaural level differences. Multiple images are predicted for tones with characteristic combinations of interaural signal parameters and for noise signals with different degrees of interaural cross correlation. The model is also capable of simulating dynamic lateralization phenomena, such as the "law of the first wave front" which is dealt with in a companion paper [Lindemann, J. Acoust. Soc. Am. 80, 1623-1630 (1986)]. The present paper is restricted to a comparison of the model predictions for stationary signals with the results of dichotic listening experiments.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.