Fractional Derivatives Applied to Phase-Space Reconstructions

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.     

Ähnliche Grenzschichtlösungen zweiter Ordnung für Strömungs- und Temperaturgrenzschichten an longitudinal gekrümmten Wänden mit Grenzschichtbeeinflussung

Zusammenfassung Für die inkompressible, stationäre Strömungs- und Temperaturgrenzschicht an longitudinal gekrümmten Wänden mit Grenzschichtbeeinflussung werden unter Berücksichtigung der Glieder zweiter Ordnung, d. h. mit Berücksichtigung der Verdrängung und des metrischen Krümmungseinflusses ähnliche Lösungen angegeben. Die Lösungen erstrecken sich auf Wände, deren Krümmungk proportional zu einer Potenz der Bogenlängex ist. In dieser Familie von Wandkurven sind die Staupunktströmung an einem Zylinder und die Strömungen an Keilen mit gekrümmten Keilflanken eingeschlossen. Dabei ist der Öffnungswinkel des Keils mit dem Krümmungsverlauf der Keilflanken verknüpft.

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Similarity solutions are given for incompressible, steady hydrodynamic and thermal boundary layers on longitudinally curved walls with boundary layer interference considering second order terms i. e. allowing for displacement and metric curvature influence. The solution apply to walls with curvaturek proportional to a power of the arc lengthx. Involved in this family of wall-curves is the stagnation point flow on a cylinder and the flow along wedges with curved walls. Here, the angle of the wedge is connected to the curvature of the wedge-walls.

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Mit Unterstützung der Aerospace Research Laboratories durch das U. S. Air Force European Office of Aerospace Research.     

What are gene patents and why are people worried about them?

This article examines what it means to patent a gene. Numerous ethical concerns have been raised about the effects of such patents on clinical medical practice as well as on research and development. We describe what kinds of inventions are covered by human gene patents, give several examples and summarize the small body of empirical research performed in the US examining the effects of these patents. There is little evidence that early fears about gene patenting placing substantial restraints on research and clinical medicine have come to fruition. Nonetheless, there are areas of concern, and policy makers, physicians and the public should be alert to ensure that the net social benefits of patenting human genes are maintained.     

Experimental visualization of bubble formation from an orifice in microgravity in the presence of electric fields

 The formation of air bubbles injected into a stagnant, isothermal liquid in microgravity through an orifice was studied. The bubbles grew very large in microgravity. They attained a nearly spherical shape and showed pronounced affinity towards coalescence in the absence of electric fields and other perturbations. Under the influence of electric fields, periodic detachment was observed, with bubble sizes larger than in terrestrial conditions. The bubble shape was elongated. After detachment, the bubbles moved away from the electrode at which they formed without coalescing with other bubbles. Experimental data on bubble shape and size at detachment showed good agreement with models. Received: 26 March 2001 / Accepted: 16 August 2001     

Fluid Dynamics at Connections in Paediatric Cardiac Surgery*

The modified Blalock-Taussig shunt is a connection created between the systemic and pulmonary arterial circulations to improve pulmonary perfusion in children with congenital heart diseases. Survival of these patients is critically dependent on blood flow distribution between the pulmonary and systemic circulations, that in turn depends upon the fluid dynamic behaviour of the shunt. Computational fluid dynamics, structural analyses as well as in vitro experiments were carried out to derive a quantitative relationship between the shunt flow and the corresponding pressure drop. While computational fluid dynamics simulations were based on the assumption of rigid wall for the shunt and the arteries, proper distensible conduits were used in the in vitro study and the structural analysis of the anastomosis deformation. The results indicated that the internal pressure combined with wall distensibility modifies the cross-sectional area of the distal anastomosis (between the shunt and the pulmonary artery). This fact affects the pressure drop across the shunt, especially at low pressures. Based on the results from the computational analyses and the in vitro experiments, a relationship between pressure drop and flow in the shunt was obtained, which matches data from clinical measurements.     

Evaluation of creep damage behavior of nickel-base directionally solidified superalloys with different crystallographic orientations

A crystallographic creep damage constitutive model is developed for nickel-base directionally solidified superalloys. The rates of material degradation and grain boundary void growth are considered. The governing parameters are determined from the creep test data of single crystals and directionally solidified superalloys with a crystallographic orientation. A finite element program is used to analyze the creep damage behavior of nickel-base directionally solidified superalloys for different crystallographic orientations. The results depend on the number of grains modelled and compare well with the experimental data.     

Determination of column-buckling criteria using vibratory data

A mathematical model is presented which describes a nondestructive testing procedure for determining buckling criteria for structures. The procedure requires identification of the structure's support boundary conditions using vibration data. Column-buckling experiments are presented which validate the model. The results illustrate the feasibility of using such models to predict the buckling load for structures whose support boundary conditions are not known in advance of service.     

Fatigue-life prediction using local stress-strain concepts

A cumulative-damage approach for predicting fatigue-crack initiation in engineering structures subjected to random loading is outlined. This procedure is based on the assumption that if the stresses and strains at the critical location in a structure can be related to the cyclic stress-strain properties of smooth laboratory specimens, the crack-initiation life in the structure will be the same as the specimen. A flow diagram, indicating the steps required for implementing this procedure on a high-speed digital computer, is discussed in detail.     

A study of the shear viscosity of human whole saliva

Summary A model R-18 Weissenberg Rheogoniometer operating in the continuous shear mode was used to generate shear viscosity vs. shear rate data on male and female human whole saliva. These data were found to accurately follow the Sisko model, , whereµ is the shear viscosity at shear rate is the asymptotic shear viscosity at infinite shear rate, andK andn are constants. Data were collected on the effects of food, coffee, caffeine, and aspirin as functions of time. Studies were also made on the effects of emotional stress, donor sex and age.The saliva viscosity increased with time and then decreased to the basal value for most ingested materials. Emotional stress was found to elevate the saliva viscosity. On the other hand, no significant difference was found between the average saliva viscosities of male and female groups. Also, no significant effect of donor age was detected.

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Zusammenfassung Mit Hilfe eines Weissenberg-Rheogoniometers (Typ R-18) wurden bei stationärem Betrieb Scherviskositätskurven in Abhängigkeit von der Schergeschwindigkeit für den Speichel von Männern und Frauen gemessen. Man fand, daß sich die Meßwerte hinreichend genau durch ein Sisko-Modell, , beschreiben lassen, woµ die Scherviskosität bei der Schergeschwindigkeit die asymptotische Scherviskosität bei unendlich großer Schergeschwindigkeit sowieK undn weitere Konstanten bedeuten. Diese Messungen verfolgten die Wirkung von Nahrung, Kaffee, Coffein und Aspirin als Funktion der Zeit. Untersucht wurde weiterhin der Einfluß von emotionaler Spannung, sowie Geschlecht und Alter der Spender.Die Speichelviskosität stieg bei den meisten eingenommenen Stoffen mit der Zeit zuerst an, um danach wieder auf den Normalwert abzusinken. Ebenso fand man, daß emotionale Spannung eine Viskositätserhöhung hervorruft. Dagegen wurden bei Gruppen von Männern und Frauen keine signifikanten Unterschiede gefunden, und ebenso wurde kein gesicherter Einfluß des Alters festgestellt.

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With 4 figures and 6 tables     

Some theorems in the theory of small deformations superimposed on a finite deformation of a hyperelastic material of grade 2

The equations for small deformations superimposed on large deformations of a hyperelastic material of grade 2 are formulated and applied to derive a basic integral relation that is used to establish generalized Betti, Clapeyron, work and energy theorems. Theorems of minimum and complementary energy are deduced essentially from an energy criterion of super-stability, and these are used to prove uniqueness of solutions to the static and dynamic, mixed incremental boundary value problems. These results use a certain generalized kinetic energy functional that is assumed positive definite; and this property and the reciprocal and energy principles are exploited further to establish some theorems in the theory of small free vibrations.