Bemerkungen zum Biot-Savartschen Gesetz

Übersicht Die folgende Arbeit verfolgt u. a. auch didaktische Absichten. Das Biot-Savartsche Gesetz wird oft falsch oder mindestens sehr mißverständlich dargestellt und auch auf unzulässige Weise benutzt. Ausgangspunkt der Mißverständnisse ist die auch in vielen Lehrbüchern anzutreffende unkorrekte Aussage, man könne einem von StromI durchflossenen Linienelement ds ein magnetostatisches Feld dB [entsprechend der Gleichung (32) des folgenden Beitrags] zuordnen. Im folgenden werden derartige Aussagen untersucht und in modifizierter Form korrekt dargestellt.

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Remarks concerning the Law of Biot-Savart

Contents The following paper is at least partly of a didactic nature. The Biot-Savart law of magnetostatics is often interpreted in an illegitimate manner and consequently applied incorrectly. The source of these misunderstandings and errors is the incorrect statement that a magnetic field dB [as given by equation (32) of this paper] is caused by an electric currentI flowing along a line element ds, a statement very popular also in many textbooks. Questions related to this problem are investigated and widespread misleading statements are replaced by correct ones.

     

Categorical ML — Category-theoretic modular programming

We consider an extension of the functional programming language Standard ML with a modular structure based upon concepts in category theory such as categories, functors, natural transformations and adjunctions. In essence, we are following the categorical imperative of considering arrows as well as objects. This is intended to enforce a certain mathematical rigour on the programmer, so that the only programs that can be expressed are those with a categorical significance. The essentially algebraic nature of category theory means that we may generate equational correctness conditions for the modular structure of programs, thus separating the correctness of individual functions from that of modules. We describe this programming language, give examples of its use, and explain how it is implemented in a type system.     

Direkte und indirekte Randelementmethoden zur Bestimmung der Lage des Schubmittelpunktes beliebig geformter Stabquerschnitte

Zusammenfassung Die Koordinaten des Schubmittelpunktes eines beliebig berandeten Stabquerschnittes werden in dieser Arbeit aus der Torsionsverw?lbung des Querschnittes berechnet. Zur Bestimmung der Querschnittsverw?lbung wird die Randelementmethode (Boundary-Element-Method) herangezogen. Dabei entstehen durch verschiedene Vorgehensweisen mehrere Fredholmsche Integralgleichungen erster und zweiter Art, von denen jedoch nur bestimmte zur L?sung des genannten Problems geeignet sind. Einige direkte und indirekte Integralgleichungen werden hier für beliebig berandete Stabquerschnitte bezüglich ihrer Einsetzbarkeit untersucht und miteinander verglichen. Es zeigt sich dabei, da? auch eine Integralgleichung erster Art problemlos eingesetzt werden kann. Die Randelemente werden bei der numerischen L?sung der Integralgleichungen durch Polynome dritten Grades und die unbekannten Funktionen durch Polynome zweiten Grades approximiert, um eine glatte Berandung und stetigen Funktionenverlauf zu sichern.—Die Methode ist auf dünnwandige, dickwandige, offene und auf geschlossene Profile anwendbar. Numerische Ergebnisse für verschiedene Querschnittsformen aus den DIN-Normen zeigen die Effektivit?t sowohl der direkten als auch der indirekten Methode.     

The occurrence of multiple solutions for the TSD-Euler equation

Summary In a recent paper the TSD-Euler equation for transonic flow has been derived. This equation is similar in some respects to the TSD equation but has both entropy and vorticity terms retained. In this paper the existence of multiple solutions for the TSD-Euler equation is examined and it is found that such solutions exist for a small range of Mach numbers and airfoil thickness. It is found also that the addition of a vorticity flux on the airfoil surface can enhance the appearance of multiple solutions.With 4 Figures     

Guaranteed inclusions for the complex generalized eigenproblem

A method is described which produces guaranteed bounds for a solution of the generalized complex eigenproblem. The method extends a similar approach for general systems of nonlinear equations to the special case of complex pencils, where under weaker assumptions stronger assertions can be proved.     

Solar duct for lighting and ventilation Santa Amalia building Barcelona -Spain

The Santa Amalia building in Barcelona is a block of six flats incorporating a duct by which ligth is sent to the kitchens - previously without natural ligthing- and also allows natural ventilation. Moreover, the passive solar gains obtained from the extensive glazed surfaces and the conservation of internal heat gains, along with a high degree of isulation, give energy saving of 68% for heating.     

Reactive energy measurement using frequency controlled analog-to-pulse-rate converter

Contents This paper analyzes a problem of phase shifting and deseribes a novel method for electronic reactive energy measurement. The proposed measurement structure, composed of an integrator as a phase shifting circuit and a frequency controlled analog-to-pulse-rate converter, provides for the measurement completely in accordance with IEC definition of reactive energy, which is performed with simple but high performance metering device.

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Die Blindverbrauchsmessung anhand eines netzsynchronisierten Analog-Frequenz-Wandlers

Übersicht In diesem Artikel wird das Problem der Phasenverschiebung analysiert und eine neue Meßmethode für elektronische Blindverbrauschsmessung aufgezeigt. Die vorgeschlagene Strucktur, bestehend aus einem Integrator als Phasenschieber und netzkontrolliertem Analog-Frequenz-Wandler, ermöglicht die Verwirklichung eines einfachen aber präzisen Elektrizitätszählers zur Messung der Blindenergie, dessen Arbeitsprinzip mit den IEC Empfehlungen vollkommen übereinstimmt.

     

Twisted axially loaded rod with shear and compressibility

Summary Stability of a twisted and axially compressed elastic rod is analysed using the Euler method of adjacent equilibrium configuration. The constitutive equations of the rod are assumed in the form that takes into account both shear of the cross-sections and compressibility of the rod axis. It is shown that bifurcation points of the non-linear system of equations describing equilibrium are determined from the linearized system of equations. The influence of shear and compressibility on the critical values of twisting couple and compressive force is obtained. Moreover, the bifurcation pattern is examined by using the Liapunov-Schmidt method.     

Induced free liquid surface oscillations in a visco-elastic liquid column due to angular temperature fluctuations

The response due to time-fluctuating temperature distribution applied at the free surface of a viscoelastic cylindrical liquid column with no axial dependency has been determined analytically. The amplitude of the radial- and angular velocity as well as the free liquid surface elevation has been presented as a function of the “reduced” forcing frequency of the oscillatory temperature and has numerically been evaluated for an angular temperature field proportional to sin 2φ. It was found, that visco-elasticity as described by the Maxwell model has quite some influence upon the liquid behavior. It shows for larger relaxation times besides the enlarged resonance peak additional peaks below and above resonance. This is particularly evident inside the liquid column, indicating a more pronounced elastic behavior of the liquid.