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.

     

Influence of the tank shape on the electrostatic field generated by space charge

Contents The paper provides results of calculations of electric field for parallelepiped and ellipsoidal tanks. The calculations reported in the paper indicate that even at a relatively small volumetric density of charge (q=100 C/m³) the intensity of the electric field in the vapour/air mixture may exceed the critical value (3 MV/m), which may cause a spark discharge. They also show the maximum of the electric field intensity, the maximum potential and energy after the change in shape of the tank, while the volume of the stored liquid remains the same. The calculations of these quantities can be used as a basis for reduction or elimination of the electrostatic ignition hazard.

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Einfluß der Behälterform auf das elektrostatische Feld infolge einer Raumladung

Übersicht Der Beitrag behandelt elektrische Felder in Behältern von der Form eines Parallelepipeds und eines Ellipsoids. Die Berechnungen zeigen, daß selbst bei relativ kleinen Werten der Raumladung (100 C/m³) die elektrische Feldstärke im Dampf-Luftgemisch den kritischen Wert (3 ÖMV/m) überschreiten und einen Durchschlag verursachen kann. Außerdem werden die Maxima der elektrischen Feldstärke, des Potentials und der Energie in Abhängigkeit der Behälterform angegeben unter der Voraussetzung, daß das Volumen der enthaltenen Flüssigkeit konstant bleibt. Die Rechenergebnisse lassen sich als Basis für die Verminderung oder Elimination der Gefahr von Überschlägen verwenden.

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List of symbols A, B, C factors of the ellipsoidal tank - a, b, H length, width and height of the parallelepiped tank, respectively [m] - E electrical field strength [V/m] - h liquid height in the tank [m] - q volumetric charge density [C/m³] - R radius of the sphere [m] - V electric potential [V] - W _E electric field energy [J] - V volume of the tank - _r relative dielectric constant - _O absolute dielectric constant 8.854×10^–12 [As/Vm]     

Diffraction by an elliptic cone and the solution of the wedge diffraction problem

Contents The paper deals with scalar diffraction by an elliptic cone in the limit case of ellipticity parameterk=0. In this case the elliptic cone degenerates into a wedge with exterior opening angle 2₀. We solve the two-parameter eigenvalue problem for two coupled Lamé differential equations fork=0 and obtain the eigenvalues and the eigenfunctions for the wedge problem by a completely analytical calculation. We utilize a precise transformation of the sphero-conal coordinates into spherical coordinates with the edge of the wedge as polar axis and determine, by substitution of the transformed Lamé products into Green's functions for the elliptic cone, the solution of the scalar diffraction problem for the wedge.The results obtained are in full agreement with those reported in [2]. In the special case of half-plane diffraction (₀=) the solution reduces to that in [1].

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Beugung am elliptischen Kegel und die Lösung des Beugungsproblems für den Keil

Übersicht in dieser Arbeit beschäftigen wir uns mit der skalaren Beugung am Kegel elliptischen Querschnitts im Grenzfall des Elliptizitätsparametersk=0. In diesem Fall entartet der elliptische Kegel in einen Keil mit dem Außenöffnungswinkel 2₀. Wir lösen das zweiparametrige Eigenwertproblem für zwei gekoppelte Lamésche Differentialgleichungen fürk=0 und erhalten über eine vollständig analytische Rechnung die Eigenwerte und die Eigenfunktionen für das Keilproblem. Wir ziehen eine exakte Transformation der elliptischen Kegelkoordinaten in Kugelkoordinaten mit der Keilkante als Polarachse heran und gewinnen, durch Substitution der transformierten Laméschen Produkte in den Greenschen Funktionen für den elliptischen Kegel, die Lösung des skalaren Beugungsproblems für den Keil.Die Ergebnisse stimmen vollständig überein mit denjenigen, die in [2] zitiert werden. Im Spezialfall der Beugung an der Halbebene (₀=) wird die Lösung wieder zurückgeführt auf die in [1] abgeleitete Lösung.

     

A new inrush detection method for transformer differential protection

Contents The long-used restraining principle, based on the detection of 2nd harmonics in the currents, can not always satisfactorily meet the demand of blocking the transformer differential protection for all three phases, because the line currents are not the direct image of the core saturation. The differential protection may become inadequate. A transformer can however be switched on for all cases, without the false or fail-safe tripping, when the harmonic restraint is derived from the magnetic field strength of the core.If a delta-connected winding is present, the magnetic field strengths can not be easily recognized in the line currents, because their zero-sequence component is distorted. A new method is presented, which can estimate the fundamental and the 2nd harmonic of this zero-sequence component. The components of the magnetic field strength can therefore be determined in currents only, whose ratio is known to be characteristic for the core saturation.The proposed method was implemented on an industrial protection system based on a microprocessor and was tested on data obtained from computer-simulation and a model transformer in a laboratory. It turned out that the proposed method performed well on all cases.

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Eine neue Methode der Einschalterkennung für den Transformator-Differentialschutz

Übersicht Die üblicherweise benützte Blockierung beim Einschalten eines Transformators beruht auf der Bewertung der zweiten Harmonischen in den Strömen. Dieses Prinzip kann nicht immer den Transformatorvergleichsschutz in allen drei Phasen blockieren. Dagegen kann ein Transformator in allen Fällen ohne Fehlauslösung eingeschaltet werden, wenn die Blockierung aus der Harmonischen der magnetischen Feldstärke des Kerns abgeleitet wird.Eine neue Methode wird vorgestellt, wie die Homopolarkomponente der Grundschwingung und der zweiten Harmonischen näherungsweise berechnet werden kann. Die benötigten Anteile der Feldstärken können damit aus den Differenzströmen ermittelt werden.Das vorgeschlagene Verfahren wurde auf einer industriell gefertigten Schutzkarte implementiert. Die Überprüfung des Verfahrens erfolgte mit Berechnungsverfahren und durch Messungen im Labor.

     

Mapping the Limits of Substrate Specificity of the Adenylation Domain of TycA

The limits and potential of substrate promiscuity of the adenylation domain of tyrocidine synthetase 1 were systematically explored. Substrate acceptance is governed by hydrophobic effects (as shown by the correlation of k_cat/K_M and side‐chain log P), shape complementarity and steric exclusion. The quantification of these factors provides ground rules for understanding and possibly evolving substrate specificity in this class of enzymes.

     

New Pacidamycin Antibiotics Through Precursor‐Directed Biosynthesis

Pacidamycins, mureidomycins and napsamycins are structurally related uridyl peptide antibiotics that inhibit translocase I, an as yet clinically unexploited target. This potentially important bioactivity coupled to the biosynthetically intriguing structure of pacidamycin make this natural product a fascinating subject for study. A precursor‐directed biosynthesis approach was employed in order to access new pacidamycin derivatives. Strikingly, the biosynthetic machinery exhibited highly relaxed substrate specificity with the majority of the tryptophan analogues that were administered; this resulted in the production of new pacidamycin derivatives. Remarkably, 2‐methyl‐, 7‐methyl‐, 7‐chloro‐ and 7‐bromotryptophans produced their corresponding pacidamycin analogues in larger amounts than the natural pacidamycin. Low levels or no incorporation was observed for tryptophans substituted at positions 4, 5 and 6. The ability to generate bromo‐ and chloropacidamycins opens up the possibility of further functionalising these compounds through chemical cross‐coupling in order to access a much larger family of derivatives.     

Crystalline Nanorods as Possible Templates for the Synthesis of Amorphous Biosilica during Spicule Formation in Demospongiae

In tandem : High‐resolution TEM shows that during the initial stages of demosponge spicule formation, a primordial crystalline structure is formed within the axial filament. The recently developed electron diffraction tomography technique (ADT) reveals that the nanorods have a layered structure that matches smectitic phyllosilicates. These intracellular nanorods have been considered as precursors of mature spicules.

     

Observing Proteins as Single Molecules Encapsulated in Surface‐Tethered Polymeric Nanocontainers

Protein unfolding inside immobilized polymerosomes : One of the most interesting properties of polymeric vesicles is their remarkable stability against extreme temperatures and osmotic stress, and their longevity even under harsh environmental conditions. We have demonstrated, in an application on protein folding, that surface‐tethered polymerosomes are suitable for performing time‐resolved single molecule studies with encapsulated proteins, as illustrated here.

     

Screening for Cytochrome P450 Reactivity by Harnessing Catalase as Reporter Enzyme

The big screen : We have devised a high‐throughput screening method for organic peroxide‐dependent P450 reactivity by taking advantage of a previously undescribed activity of catalase, which was used as reporter enzyme. This two‐step assay, followed by liquid chromatography/mass spectrometry analyses, allowed the facile identification of several new substrates for bacterial P450 enzymes.

     

Rational Biosynthetic Engineering for Optimization of Geldanamycin Analogues

Tailor made : We report the rational biosynthesis of C15 hydroxylated non‐quinone geldanamycin analogues by site‐directed mutagenesis of the geldanamycin polyketide synthase (PKS), together with a combination of post‐PKS tailoring genes. Rational biosynthetic engineering allowed the generation of geldanamycin derivatives, such as DHQ3 illustrated in the figure, which had superior pharmacological properties in comparison to the parent compound.