Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Ab<Emphasis Type="Italic"> initio</Emphasis> investigation of boron diffusion paths in germanium

Boron is observed to diffuse very slowly in germanium, as opposed to its behaviour in silicon where it exhibits Transient Enhanced Diffusion effects in implanted samples. As a result of this slow diffusion, boron is a very stable dopant, allowing devices to be created with very well-defined doping regions. To understand this superior performance, calculations were performed on a variety of boron diffusion paths, within vacancy and interstitial mediated methods. It was found that the vacancy mediated diffusion which is associated with the fast diffusion of many other species in germanium exhibits a total barrier of 5.8 eV. Interstitial-mediated diffusion had a total barrier for migration of 3.4 eV in the neutral and singly negative charge states, 3.2 eV for the positive charge state, but a formation barrier of 4.1 eV. Thus the barrier for interstitial-mediated diffusion is dominated by the formation energy of the self-interstitial.     

Characterization and optimization of linearly tapered slot antenna pattern

A parametric study of linearly tapered slot antenna (LTSA) in air and a method for optimization of its pattern are presented. A method of moments code is utilized to investigate the behavior of LTSA’s as the length, height and the taper angle varies. It is shown that the antenna pattern can be improved using a top layer of dielectric material with varying permittivity.     

Quasi-optical measurement of complex dielectric constant at 300 GHz

A two beam interferometer in the Martin-Puplett configuration is used to determine the complex dielectric constant at 300 GHz of teflon, TPX-plastics, SPECTRALON and paraffin waxes with melting temperatures of 48° C and 72° C, respectively. The design of the quasi-optical system leads to a constant beam diameter at the power detector independent of path delay and frequency. The power detector signal is recorded not only along one period but over about 50 periods. A spectrum estimation routine allows to determine more exactly amplitude and phase angle of the signal. A basic problem is noticed: imperfect detector and source match cause harmonic distortion of the power detector signal. The effects on processing the loss tangent and the invalidation are shown. Finally loss tangent and dielectric constant are determined indirectly by optimizing an equivalent microwave circuit using a commercial available microwave design system to take multiple reflections and losses in consideration.     

Betriebsmittelbezogene Lastmodellierung in Verteilungsnetzen

Übersicht Der Betriebszustand eines Verteilungsnetzes wird durch die Strombelastung aller Betriebsmittel beschrieben. Mit Hilfe einer statischen Estimationsmethode werden aus einzelnen Messungen und der Kenntnis der Verbrauchsdaten typische Verbraucherkurven (TVK) berechnet, die das elektrische Verhalten verschiedener Verbrauchergruppen widerspiegeln. Auf dieser Basis ist eine betriebsmittelbezogene Lastmodellierung an beliebigen Betriebsmitteln in Abhängigkeit der Verbraucherzusammensetzung unter Berücksichtigung externer Einflüsse wie der Temperatur möglich. Die so gewonnenen Belastungsverläufe erlauben eine Beschreibung des Netzzustands in den Verteilungsnetzen.

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Bus load modelling in distribution systems

Contents The operating state of a distribution system is determined by the bus load current. Based on individual substation measurements and the load composition typical load curves are calculated using statistical estimation theory. These typical load curves describe the electrical behaviour of the different load types (e.g. household, storage heating, commerce etc.). As soon as the typical load curves are determined it is possible to calculate the bus load current in any substation taking external influences such as temperature into consideration. The bus load current serve as load models which completely describe the operating state of the distribution system.

     

Finite element modelling of calendering — some aspects of the effects of temperature gradients and structure inhomogeneities

The compression of a paper web in a calender nip has been simulated using the finite element method. The mechanical properties of the paper were allowed to vary in the thickness and machine directions of the web. This was done in order to model the influence of temperature gradients as well as density variations (due to the presence of fibre floes) on the deformation behaviour in the nip. Paper was assumed to be an elastic-plastic material exhibiting strain hardening. The yielding behaviour was governed by the Drucker-Prager yield condition. Simulations of the deformation behaviour when paper was subjected to a temperature gradient, clearly revealed that the deformation gradually became more concentrated towards the surface layers as the temperature of the surface increased. This is in accordance with experimental results which indicate that temperature-gradient calendering promotes the surface properties, whereas the bulk of the structure is preserved. Modelling the deformation behaviour of a structure containing density variations reveals that the paper may contain an inhomogeneous strain distribution after unloading, i.e. after passage through the nip.     

Tensile,creep, and low-cycle fatigue behavior of a cast γ-TiAl-based alloy for gas turbine applications

The influence of chemical composition on the microstructure of the γ-titanium aluminide alloy Ti-48Al-2W-0.5Si (at. pct) and the accompanying tensile, low-cycle fatigue, and creep properties has been evaluated. The study showed that small variations in chemical composition and casting procedures resulted in considerable variations in the microstructure, yielding vastly different mechanical properties. Low contents of aluminum and tungsten led to a coarse-grained lamellar (γ/α ₂) microstructure with high creep resistance. A composition close to the nominal one produced a duplex (γ+γ/α ₂) structure with favorable strength, ductility, and low-cycle fatigue properties. By controlling the solidification and cooling rates at casting, a pseudoduplex (PS-DP) microstructure with a unique combination of high strength and high fatigue and creep resistance can be obtained. These unique properties can be explained by the diffuse boundaries between the relatively small γ grains and the neighboring lamellar colonies, combined with semicoherent interfaces between the γ and α ₂ phases. At tensile and low-cycle fatigue loading, these boundaries act like high-angle boundaries, producing a virtually fine-grained material promoting strength, whereas at creep loading, grain-boundary sliding is hindered in the semicoherent interfaces leading to high creep resistance.