Strongly Focused Gravitational Waves

This paper contains a new proof of the formation of trapped spheres, in vacuum spacetimes, by the focusing of gravitational waves, from generic data. The first such result was obtained by Christodoulou (Zurich: Eur Math Soc, 2009). We exploit the same physical mechanism, but give a logically independent construction of these spacetimes.     

Über das komplexchemische Verhalten einiger substituierter 2-Merkapto-p-Kresole. II

Zusammenfassung Ein Verfahren zur Herstellung diverser Merkapto-Liganden wird angegeben. Merkaptide, Chelate und Mischligandkomplexe wurden präparativ hergestellt und beschrieben. Zur Konstitutionsermittlung werden IR-, NMR-, UV-VIS-Spektren und Elementaranalysen der Liganden und Ligand-Metall-Verbindungen angegeben und kommentiert. Unterschiedliche Wechselwirkungen zwischen Ligand und Ion, die infolge verschiedener Substituenten an der 6-Stelle auftreten, werden in einer Reihe von Versuchen aufgezeigt.

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The complexometric behaviour of some 2-mercapto-p-cresols. II

Summary A method for the preparation of ligands is given. Mercaptides, chelates and mixed-ligand-complexes are prepared and described. IR, NMR, UV-VIS spectra and elementary analysis for the investigation of constitution of the ligands and ligand metal compounds are given and commented. Unlike interactions between ligand and ion, appearing because of different substituents at the 6-position, are shown by a series of experiments.

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Herrn Prof. Dr. Gustav Zigeuner zum 60. Geburtstag gewidmet.     

Fluorimetric determination of tyrosine and iodinated thyronines as the fluorescamine derivatives

Summary The formation of fluorescamine derivatives of tyrosine, triiodothyronine (T₃) and tetraiodothyronine (T₄) has been studied. The three compounds react quantitatively within 60 sec and form strongly fluorescent derivatives with an emission maximum at 490 nm. Limits of detection are between 26 ng/ml (T₃) and 50 ng/ml (T₄), if the reaction mixture is measured directly. Excellent TLC-separations on cellulose are possible for the derivatives of T₃ and T₄. In-situ fluorescence measurements result in linear calibration curves up to 1g (T₄) with a limit of detection of 1.5 ng/spot.

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Zusammenfassung Die Herstellung von Fluorescamin-Derivaten des Tyrosins, des Trijodthyronins (T₃) und des Tetrajodthyronins (T₄) wurde untersucht. Diese drei Verbindungen reagieren quantitativ innerhalb 60 sec unter Bildung stark fluoreszierender Derivate mit einem Emissionsmaximum bei 490 nm. Die Nachweisgrenzen liegen zwischen 26 ng/ml (T₃) und 50 ng/ml (T₄), wenn man das Reaktionsgemisch direkt zur Messung verwendet. Die T₃-und T₄-Derivate lassen sich auf Zellulose-Dünnschichten sehr gut trennen. In-situ-Messungen der Fluoreszenz ergaben Eichgerade bis 1gT ₄ mit einer Nachweisgrenze von 1,5 ng/Fleck.

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This paper is dedicated to Prof. Dr. H. Lieb on the occasion of his 90th birthday.     

New Discrete Model Boltzmann Equations for Arbitrary Partitions of the Velocity Space

Modified discrete Boltzmann equations for arbitrary partitions of the velocity space are established. The new equations can be derived from the continuous Boltzmann equation and are a generalization of previous discrete-velocity models. They preserve mass, momentum, and energy, and an H-theorem holds. The new model equations are tested by comparing their solutions with the analytical ones of the continuous Boltzmann equation for the Krook–Wu and the very hard particle models.     

Damping Of Pedestrian‐Induced Bridge Vibrations By Tuned Liquid Column Dampers

The excessive lateral vibrations of Londons Millenium Bridge and the Toda Park Bridge in Japan due to a large number of crossing pedestrians have raised an unexpected problem in footbridge constructions. Secondary tuned structures, like the conventional tuned mass damper (TMD) or the tuned liquid damper (TLD) were installed to the bridge in order to suppress these vibrations. In the present investigation it is proposed to apply the more efficient and more economic tuned liquid column damper (TLCD), which relies on the motion of a liquid mass in a sealed tube to counteract the external motion, while a built‐in orifice plate induces turbulent damping forces that dissipate kinetic energy. For optimal tuning of TLCDs the natural frequency and equivalent linear damping coefficient have to be chosen suitable, likewise to the conventional TMDs, as given in Den Hartog [1]. The advantages of TLCDs are: simple tuning of natural frequency and damping, low cost of design and maintenance and a simple construction. A mathematical model of a three degree‐of‐freedom (DOF) bridge coupled with an optimal tuned TLCD is derived and analyzed numerically. Furthermore, a small scale experimental model set‐up has been constructed in the laboratory of the TU‐Insitute. The experimental results are in good agreement with the theoretical predictions and indicate that TLCDs are effective damping devices for the undesired pedestrian induced footbridge vibrations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)