Computation of nonlinear functionals in particle methods

We consider the numerical computation of nonlinear functionals of distribution functions approximated by point measures. Two methods are described and estimates for the speed of convergence as the number of points tends to infinity are given. Moreover, numerical results for the entropy functional are presented.     

Analysis of ink flow in a mimeograph printer based on the mechanics of fluid-filled poroelastic solids

Summary To understand some main ink flow mechanisms in a mimeograph printer, the continuum mechanics theory of fluid-saturated porous solids is applied to analyze the ink flow through screens and a printing master, which are modeled by a fluid-filled poroelastic single layer. The layer is assumed to be pressed by a press roller from below and to be subjected from above to the hydrodynamic lubrication pressure induced between a printing drum and an ink roller. Nonlinear elasticity of the layer and dependence of the permeability on its deformation are taken into account. The numerical results show some important results: e.g., squeezing-out of the ink from the layer by the layer compaction by the press roller plays an important role, especially for the case where the compression duration is small in comparison with the characteristic time of the ink-filled poroelastic layer.     

The Valve Metal Character of Zirconium as inferred from anode potential measurements in mineral acid solutions

A study on the value metal character of Zr in 0.1 M solutions of H₂SO₄, HNO₃, and H₃PO₄ has been performed using the anode potential as the primary variable in galvanostatic, potentiostatic, and capacity measurements. A method of surface pre-treatment, which suppresses both O₂ evolution and metal dissolution, has been described. Kinetic parameters of oxide growth have been calculated. The results indicate that:

• (i) the high field approximation is applicable following an exponential law, and
• (ii) the height and activation distance of the energy barrier for ion transport through the oxide phase (Verwey model) are the same three acids.

Measurements have been also made on the dielectric breakdown of oxide, and this occurs at potentials above 200 V. Direct capacity measurements give similar results as those based on reciprocal capacity calculated from galvanostatic experiments. It is concluded that the dominant anodic oxide species is ZrO₂ having a dielectric constant of 25. Open circuit potential measurements show that Zr is spontaneously oxidized in the three acids.     

A route to chaos in a nonlinear oscillator with delay

Summary The paper presents an analysis of the transition from regular to chaotic motion in a Van der Pol-Duffing's oscillator with delay after a Hopf bifurcation. The conditions for the occurrence of the Hopf bifurcation have been determined by means of the approximate method. For the parameters near the bifurcation point a computer simulation of the vibrating system had been performed and the evolution of the system from regular motion to chaos has been analysed at the decrease of the value of the dimensionless damping coefficient.With 2 Figures     

Investigation of the flow in the impeller-side space of rotary pumps with superimposed throughflow for the determination of axial force and frictional torque

Summary The subject of the present theoretical and experimental work is laminar flow processes in the gap between a rotating disc and a stationary wall. A report is given of the creation of suitable computational methods for determining the pressure gradient and velocity field in the impeller-side space of specifically slow-working rotary pumps in the process of conveying very viscous media with Newton properties, given temperature-dependent viscosity. The exposition is based on the abstract model conception of parallel radial gaps, the resultant frictional torques and the axial forces being determined for the case of a superimposed throughflow. On the one hand, the basis of the computations is an implicit difference method, and on the other an asymptotic computational method which leads to success via disturbance estimates in conjunction with similarity transformations, and approaches the difference method in accuracy while being relatively simple to handle and requiring little expenditure of time. On the basis of the computational results, experiments are conducted using a suitable experimental set-up, which answer the question concerning the efficiency and area of validity of the computational model.Notation c _p specific heat capacity - f _ax axial force - m moment of rotation - p pressure - q throughflow parameter - r radius - r, ,z coordinates - s gap width - u, v, w velocities - volume flow - angular velocity - viscosity - thermal conductivity - density - material parameter - a external - i internal - w wall With 7 Figures     

The incorporation of yield surface distortion into a unified constitutive model,part 2: Predictive capabilities

Summary The MATMOD-4V-DISTORTION model has been derived [1] with the intent of improving the MATMOD-4V model by adding the capability to predict distortions of small strain offset yield surfaces. This model is compared against a variety of experimental data to verify its behavior. Model simulations are compared with experimental data for proportional and nonproportional prestress histories and the effect of yield definition is also investigated. Finally, the same model which predicts a flattening of the yield surface in space is used to predict a rotation of the yield surface in ₁-₂ coordinates.With 9 Figures     

Thermal gradient effects on the vibration of prestressed rectangular plates

Summary The effect of a thermal gradient on the transverse vibration of a prestressed rectangular plate is investigated by the method of matched asymptotic expansions. This class of heated plate is characterised by changing its Young's modulus with temperature. Analytical results for the eigenvalues are presented for fully-clamped and fully-hinged rectangular plates when the bending rigidity is small compared to the in-plane loading. To leading order in (where ² denotes the normalized bending rigidity), the eigenvalues of an ideal membrane are obtained, independent of thermal effects.Thermal gradient effects occur in the first order correction of eigenvalues for a clamped plate while the eigenvalues of a hinged plate are affected by thermal gradient only to second order. In particular, Schneider's results are recovered when thermal gradient effects are absent.Nomenclature W' bending deflection - D(x) flexural rigidity - D ₀ reference flexural rigidity - x',y' rectangular co-ordinate - E modulus of elasticity - E ₁ reference modulus of elasticity - t' time - h' height of plate - a' length of plate - b' width of plate - T temperature - T ₀ reference temperature - slope of variation ofE withT - parameter - L characteristic length - N ₀ characteristic in-plane force - m mass per unit area - characteristic frequency - outer solution - inner solution - small parameter     

Stromdichte- und Magnetfeldverteilung bei einer Anordnung aus Platten und vielen parallelen Stromleitern

Übersicht Die vorliegende Arbeit befaßt sich mit der gesamten Stromdichte- und Magnetfeldverteilung in vielen flachen leitenden Platten konstanter Permeabilität, die bei einer Anordnung aus diesen Platten und vielen parallelen stromführenden Leitern angeordnet in mehreren Lagen entsteht. Unter Anwendung der Maxwellschen Differentialgleichungen und durch Einführung des Vektorpotentials werden allgemeine Gleichungen für die Komponenten der magnetischen Induktion im zweidimensionalen Feldraum aufgestellt. Die Stromdichteverteilung in den leitenden Platten, in denen Wirbelströme entstehen, wird aus dem Vektorpotential hergeleitet. Zunächst werden die Platten unendlich lang angenommen und die entsprechenden Gleichungen in Integralform aufgestellt, für deren Lösung die Gauss-Laguerresche Methode angewandt wird. Dann werden die Platten beiderseits durch Eisenwände begrenzt, womit die Gleichungen unter Berücksichtigung der Randbedingungen in Summenform ausgedrückt werden.

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Distribution of current and magnetic field density in flat conductive plates in an array composed from plates and many parallel conductors

Contents In the present research work the overall distribution of current and magnetic field density in many flat plates of constant magnetic permeability has been investigated, which applies to an array composed from the flat plates and many parallel conductors installed in many layers. Use of Maxwell's differential equations and vector potential results in general equations for the components of magnetic density in two dimensional field space. The distribution of current density in the conductive plates, where eddy currents are taken into account, is obtained from the vector potential. Initially the flat plates are considered being of infinite length, and with appropriate arrangement of the boundary conditions, the model applies to flat plates limited to both sides by iron partitions. Examples are given for both cases, where for the plates of infinite length the Gauss-Laguerre method is applied.

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Liste der Symbole A Vektorpotential - B Magnetische Induktion - I ₁ Stromstärke eines Leiters - N ₁ Anzahl der parallelen Leiter - N ₂ Anzahl der parallelen Platten - Permeabilität des Plattenmaterials - _r Relative Permeabilitätskonstante des Plattenmaterials - Leitfähigkeit - b Breite des Hauptstreukanals - i Stromdichte der Platten samt Wirbelströme - h ₁ Höhe der Leiter - a ₁ Breite der Leiterlagen - a Plattendicke - s Breite des Nebenstreukanals - c Abstand der letzten Platte von der Eisenwand - g Plattenhöhe - x, z, , Dimensionen - Q, K Integrationskonstanten - k ganze Zahl     

The Blasius problem formulated as a free boundary value problem

Summary In the present paper we point out that the correct way to solve the Blasius problem by numerical means is to reformulate it as free boundary value problem. In the new formulation the truncated boundary (instead of infinity) is the unknown free boundary and it has to be determined as part of the numerical solution. Taking into account the partial inavariance of the mathematical model at hand with respect to a stretching group we define a non-iterative transformation method. Further, we compare the improved numerical results, obtained by the method in point, with analytical and numerical ones. Moreover, the numerical results confirm that the question of accuracy depends on the value of the free boundary. Therefore, this indicates that boundary value problems with a boundary condition at infinity should be numerically reformulated as free boundary value problems.     

A combinatorial study of the rigidity of planar structures

Summary A combinatorial method is presented for examining the rigidity of planar structures. In this approach, an expansion process is used for the formation of a statically determinate substructure, known as a -tree of a structure. The algorithm of Lováz and Yemini, and the method of Sugihara are employed for the recognition of the elementary subgraphs, during this process.With 4 Figures