Beugung am Kegel elliptischen Querschnitts und die Sommerfeldsche Lösung des Halbebenenproblems

Übersicht In dieser Arbeit wird die Beugung am Kegel elliptischen Querschnitts behandelt. Wir leiten zwei Greensche Funktionen ab, die der Dirichlet- bzw. der Neumann-Bedingung auf dem Kegel genügen und die Ausstrahlungsbedingung erfüllen. Das Randwertproblem wird zurückgeführt auf die Lösung eines zweiparametrigen Eigenwertproblems mit zwei gekoppelten Laméschen Differentialgleichungen. Wir analysieren insbesondere die Beugung einer ebenen Welle an der sektorförmigen Fläche. Im Grenzfall eines Sektoröffnungswinkels von 180° gehen die Reihenentwicklungen unter Zuhilfenahme eines speziellen Gegenbauerschen Additionstheorems und einer erzeugenden Funktion für Besselfunktionen mit ganzzahligem und halbzahligem Index über in die Sommerfeldsche Lösung des Halbebenenproblems.

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Diffraction by an elliptic cone and Sommerfeld's half-plane solution

Contents In this article we examine the diffraction by an elliptic cone. We derive two Green's functions satisfying the Dirichlet-resp. Neumann-condition on the boundary of the cone. The boundary value problem is reduced to a two-parametric eigenvalue problem with two coupled Lamé equations. We analyse the diffraction of a plane wave by a plane angular sector. In the limiting case of a sector angle of 180° the series expansions pass — using a special form of Gegenbauer's addition theorem and the generating function for Bessel functions with integral and half-integral indices — into Sommerfeld's half-plane solution.

     

Towards monitoring electrostatics in gas–solid fluidized beds

The electrostatic charge distribution in a lab‐scale 2‐D fluidized bed of 900 µm glass beads was determined using arrays of induction probes, and the influence of relative humidity and superficial gas velocity was examined. The bubble presence, relative humidity, and superficial gas velocity were found to influence charge separation. Bipolar charging was observed; the net charge build‐up was found to be negligible. Moreover, the system was monitored by applying the attractor comparison method to the electrostatic charge signals from an induction probe. It was concluded that this approach can indeed be used to monitor changes in the electrostatic behaviour.     

Study on microhardness,dynamic mechanical,and tribological properties of PEEK/Al2O3 composites

The wear and friction properties of poly (ether‐ether‐ketone) (PEEK) reinforced with 0–33 vol % (60 wt %) micron size Al₂O₃ composites were evaluated at a sliding speed of 1.0 m/s and nominal pressure from 0.5 to 1.25 MPa under dry sliding conditions using a pin‐on‐disk wear tester. The wear resistance of the pure PEEK is 10‐fold higher than that of mild steel under the similar test condition. It is improved to 18‐fold as compared with mild steel at 3.5 vol % Al₂O₃ content. The improvement in wear properties may be attributed to the thin, tenacious, and coherent transfer film formed between the steel countersurface and composite pin. However, the wear resistance of PEEK containing above 3.5 vol % Al₂O₃ was deteriorated, despite their higher hardness and stiffness as compared with that of composites containing lower Al₂O₃ content. This is attributed to the formation of thick and noncoherent transfer film, which does not prevent the wear of the composites from hard asperities of countersurface. Moreover, hard Al₂O₃ particles present in transfer film act as third body wear mechanism. The coefficient of friction of the composites is higher than that of pure PEEK. SEM and optical microscopy have shown that wear of pure PEEK occurs by the mechanism of adhesion mainly whereas of PEEK composites by microploughing and abrasion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Sila-haloperidol, a silicon analogue of the dopamine (D2) receptor antagonist haloperidol: synthesis, pharmacological properties, and metabolic fate

Haloperidol (1 a), a dopamine (D(2)) receptor antagonist, is in clinical use as an antipsychotic agent. Carbon/silicon exchange (sila-substitution) at the 4-position of the piperidine ring of 1 a (R(3)COH --> R(3)SiOH) leads to sila-haloperidol (1 b). Sila-haloperidol was synthesized in a new multistep synthesis, starting from tetramethoxysilane and taking advantage of the properties of the 2,4,6-trimethoxyphenyl unit as a unique protecting group for silicon. The pharmacological profiles of the C/Si analogues 1 a and 1 b were studied in competitive receptor binding assays at D(1)-D(5), sigma(1), and sigma(2) receptors. Sila-haloperidol (1 b) exhibits significantly different receptor subtype selectivities from haloperidol (1 a) at both receptor families. The C/Si analogues 1 a and 1 b were also studied for 1) their physicochemical properties (log D, pK(a), solubility in HBSS buffer (pH 7.4)), 2) their permeability in a human Caco-2 model, 3) their pharmacokinetic profiles in human and rat liver microsomes, and 4) their inhibition of the five major cytochrome P450 isoforms. In addition, the major in vitro metabolites of sila-haloperidol (1 b) in human liver microsomes were identified using mass-spectrometric techniques. Due to the special chemical properties of silicon, the metabolic fates of the C/Si analogues 1 a and 1 b are totally different.     

Low temperature production of glass ceramics in the anorthite–diopside system via sintering and crystallization of glass powder compacts

The production of glass ceramics (GCs) with theoretical anorthite–diopside (An–Di) weight ratios of 60/40, 50/50 and 45/55 via sintering and crystallization of glass powder compacts was investigated at different temperatures between 800 and 950 °C. The investigated compositions are located in the cross-section of the ternary fluorapatite–An–Di system close to An–Di binary joint, with constant fluorapatite content of 4.8 wt.%. Two different groups of glass powders, with mean particle size of 2 and 10 μm, were used. The experimental results showed that sintering is almost complete at 800 °C, preceding crystallization, which takes place via surface crystallization mechanism. The properties values of the produced GCs, which are the best for the composition close to An–Di eutectic line, are discussed with respect to the evolution of crystalline phases and the microstructure over increasing firing temperature. Under the technology perspective, the investigated processing route is significantly superior in comparison to the attempts reported in earlier studies.     

Sintering of clay-chamotte ceramic composites for refractory bricks

Clay-chamotte composites were realized for manufacturing refractory bricks. We used two kaolinitic refractory clays mined in Cameroon and two calcined clays (chamottes) with a large grain size (0.1–4 mm). Clay-chamotte composites containing various quantities of chamotte (0–50 wt%) were shaped and sintered at 1200–1350 °C. The structural characteristics of composites indicated the presence of quartz from the initial clay, cristobalite and mullite. SEM observations revealed very heterogeneous microstructures where porosity is weakly distributed and large pores are entrapped at the vicinity of large chamotte and quartz grains. In general, the global porosity increases with the chamotte content. A specific interpretation of the matrix role on the global sintering behaviour reveals that only a part of the matrix acts effectively. Since the most part of the global porosity is within the matrix, it is distributed in matrix zones, which participate effectively to sintering and in inert matrix zones where larger pores occur. The global mechanical strength is controlled by the matrix behaviour, but the high porosity of this phase is unfavourable to high strength values. Besides, the occurrence of larges pores and local cracks at large grain interfaces from thermal stresses are critical flaws, which reduce the mechanical strength.     

Crystallization kinetics of some new olefinic block copolymers

Blocky ethylene-octene copolymers synthesized by chain-shuttling polymerization differ from statistical copolymers in their rapid rate of crystallization and in the formation of space-filling spherulites even when the crystallinity is as low as 7%. The bulk crystallization rate, measured with DSC, was rapid even in copolymers with a relatively large fraction of non-crystallizable soft block and only slowed somewhat as the amount of crystallizable hard block decreased from 100 to 18 wt%. As measured with the polarized optical microscope, the linear spherulite growth rate exhibited the same dependence on soft block content as the bulk crystallization rate. The fold surface energy was extracted from an analysis of the growth rate according to the Lauritzen-Hoffman theory. A gradual increase in the fold surface energy with soft block content reflected some increasing disorder of the fold surface. In contrast, even a small amount of statistically distributed comonomer was very effective in disrupting the fold surface regularity as demonstrated by the high fold surface energy.     

Recrystallization studies on isotropic cold-crystallized PET: Influence of heating rate

The nanostructural changes associated to the multiple melting behaviour of isotropic cold-crystallized poly(ethylene terephthalate) (PET) have been investigated by means of simultaneous wide- and small-angle X-ray scattering, using a synchrotron radiation source. Variations in the degree of crystallinity, coherent lateral crystal size and long period values, as a function of temperature, for two different heating rates are reported for cold-crystallized samples in the 100-190 °C range. The Interface Distribution Function analysis is also employed to provide the crystalline and amorphous layer thickness values at various temperatures of interest. Results suggest that samples crystallized at both low (T_a = 100-120 °C) and high (T_a = 160-190 °C) temperatures are subjected to a nearly continuous nanostructural reorganization process upon heating, starting immediately above T_g (≈80 °C) and giving rise to complete melting at ≈260 °C. For all the T_a investigated, a melting-recrystallization mechanism seems to take place once T_a is exceeded, concurrently to the low-temperature endotherm observed in the DSC scans. For low-T_a and slow heating rates (2 °C/min), a conspicuous recrystallization process is predominant within T_a + 30 °C ≤ T ≤ 200 °C. In contrast, for high-T_a, an increasingly strong melting process is observed. For both, high- and low-T_a, an extensive structural reorganization takes place above 200 °C, involving the appearance of new lamellar stacks simultaneously to the final melting process. The two mechanisms should contribute to the high-temperature endotherm in the DSC scan. Finally, the use of a high heating rate is found to hinder the material's overall recrystallization process during the heating run and suggests that the high-temperature endotherm is ascribed to the melting of lamellae generated or thickened during the heating run.     

A novel approach of measuring the dielectric properties of PET preforms for stretch blow moulding

Polyethylene terephthalate (PET) is the most common plastic material used in injection stretch blow molding (ISBM) process for the manufacturing of bottles. The injection‐molded PET preform has to be preheated uniformly to a pliable state before the blowing stage of the process. Microwave technology offers a potentially more economical means for preheating the preform in place of the conventional infrared oven heating. For such applications, determination of dielectric properties of PET preform of a given geometry is essential. This article describes a novel approach of measuring the dielectric properties of PET preforms at microwave frequencies instead of the common experimental procedures used for such measurements. The dielectric properties are determined by using both CST Microwave Studio electromagnetic simulation software and the automatic network analyzer together. No complex mathematical solutions are required. Validation of this new approach has been made by comparing the measured dielectric properties of some polymers with those available in the published literature. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Synthesis of α‐Carbolines Starting from 2,3‐Dichloropyridines and Substituted Anilines

9H‐α‐Carbolines have been prepared via consecutive intermolecular Buchwald–Hartwig reaction and Pd‐catalyzed intramolecular direct arylation from commercially available 2,3‐dichloropyridines and substituted anilines. The combination of a high reaction temperature (180 °C) and the use of DBU were found to be crucial for the intramolecular direct arylation reactions of the 3‐chloro‐N‐phenylpyridin‐2‐amines as no reaction was observed at 120 °C and 180 °C using different inorganic and other organic bases. On the other hand, nitrogen‐methylated pyridine analogues of these substrates {N‐[3‐chloro‐1‐methylpyridin‐2(1H)‐ylidene]anilines} do undergo ring closure at 120 °C, with K₃PO₄ as base, affording the respective 1‐methyl‐1H‐α‐carbolines in good yields.