Flow of an Oldroyd-fluid in a contracting channel with a moving boundary

The industrial process of coating flat surfaces with polymeric substances is numerically simulated by solving the full equations of motion for a flow through a contraction with a moving boundary. The four-constant Oldroyd constitutive equation is used to represent the viscoelastic fluid. Some adjustments to existing finite-difference methods are made in such a way as to avoid singular iterative matrices during the solution process. Results are presented for flow situations with Weissenberg numbers up to about three times larger than any previously published results for this problem.     

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Bestimmung von Blei, Chrom, Kupfer und Nickel in Polyethylen mit der direkten Zeeman-Atomabsorptionsspektralphotometrie

Zusammenfassung Die Möglichkeiten der Bestimmung von Blei, Chrom, Kupfer und Nickel in Polyethylen mit der direkten Zeeman-AAS sind untersucht worden. Dabei wurde festgestellt, daß Blei bis 0,2%, Chrom bis 0,03%, Kupfer bis 0,05% und Nickel bis 0,06% in Polyethylen als Obergrenze bestimmt werden kann, indem Probestückchen von bis zu 1 mg direkt auf einer Mikrogrammwaage in ein Graphitschiffchen eingewogen werden. Die Analyse kann ohne chemische Vorbereitung durchgeführt werden. Die Feststoffanalyse ermöglicht gleichzeitig Studien zur Homogenität des Polyethylens.

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Determination of heavy metals (Pb, Cr, Cu, Ni) in polyethylene using direct Zeeman-AAS

Summary The determination of lead, copper, chromium and nickel in polyethylene by means of direct Zeeman-AAS was investigated. It has been found that lead up to 0.2% and Cr up to 0.03%, copper up to 0.05% and nickel up to 0.06% in polyethylene can be determined by weighing polyethylene up to 1 mg into a graphite boat by means of a microbalance. Putting the boat directly into the graphite furnace the analysis was done without chemical pretreatment. The solid sampling analysis technic by direct Zeeman-AAS allows homogeneity studies in polyethylene.

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Wir danken der Firma Bischof + Klein Verpackungswerke, Lengerich, für die Beschaffung von Rohstoffen zur Probenherstellung und Klaus Will vom Laborbereich Kunststofftechnologie des Fachbereichs Chemieingenieurwesen der Fachhochschule Münster für die Unterstützung bei der Probenherstellung.     

Study of the neutron quantum states in the gravity field

We have studied neutron quantum states in the potential well formed by the earths gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of m was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment.Received: 31 July 2004, Published online: 7 March 2005PACS: 03.65, 28.20 Correspondence to: V. Nesvizhevsky     

\alpha-decay spectroscopy of light odd-odd Bi isotopes - II: 186Bi and the new nuclide 184Bi

Alpha-decay of the new nuclide ¹⁸⁴Bi has been studied in the complete-fusion reaction ⁹³Nb(⁹⁴Mo, 3n)¹⁸⁴Bi at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of recoil- , recoil- - analysis and excitation functions measurements. Two -decaying isomeric states in ¹⁸⁴Bi with half-life values of 13(2) ms and 6.6(1.5) ms were identified. The -branching ratio of ¹⁸⁰Tl was deduced for the first time as . Improved data on the fine-structure -decay of ¹⁸⁶Bi were obtained in the ⁹³Nb(⁹⁵Mo, 2n)¹⁸⁶Bi reaction. A similarity of the decay energies and half-life values of ^184,186Bi is pointed out and a possible explanation for this effect is suggested.Received: 14 March 2003, Revised: 29 April 2003, Published online: 2 September 2003PACS: 23.60.+e decay - 27.70.+q - 27.80.+w K. Heyde: Present address: EP-ISOLDE, CERN, CH-1211, Geneva 23, Switzerland.     

On the addition of convex sets in the hyperbolic plane

Analogue to the definition $K + L := \bigcup_{x\in K}(x + L)$ of the Minkowski addition in the euclidean geometry it is proposed to define the (noncommutative) addition $K \vdash L := \bigcup_{0\, \leqsl\, \rho\,\leqsl\, a(\varphi),0\,\leqsl\,\varphi\,<\, 2\pi}T_{\rho}^{(\varphi)}(L)$ for compact, convex and smoothly bounded sets K and L in the hyperbolic plane $\Omega$ (Kleins model). Here $\rho = a(\varphi)$ is the representation of the boundary $\partial$ K in geodesic polar coordinates and $T_{\rho}^{(\varphi)}$ is the hyperbolic translation of $\Omega$ of length $\rho$ along the line through the origin o of direction $\varphi$. In general this addition does not preserve convexity but nevertheless we may prove as main results: (1) $o \in$ int $K, o \in$ int L and K,L horocyclic convex imply the strict convexity of $K \vdash L$, and (2) in this case there exists a hyperbolic mixed volume $V_h(K,L)$ of K and L which has a representation by a suitable integral over the unit circle.     

Completion of Semiuniform Convergence Spaces

Semiuniform convergence spaces form a common generalization of filter spaces (including symmetric convergence spaces [and thus symmetric topological spaces] as well as Cauchy spaces) and uniform limit spaces (including uniform spaces) with many convenient properties such as cartesian closedness, hereditariness and the fact that products of quotients are quotients. Here, for each semiuniform convergence space a completion is constructed, called the simple completion. This one generalizes Császár's -completion of filter spaces. Thus, filter spaces are characterized as subspaces of convergence spaces. Furthermore, Wyler's completion of separated uniform limit spaces can be easily derived from the simple completion.