Antisymmetric problems in shock diffraction theory

Various aspects of the diffraction of plane shock waves by moving antisymmetric thin bodies are examined. A method is presented for removing the inhomogeneity in the shock condition. This is done without knowledge of the explicit form of the solution, and is applicable to both symmetric and antisymmetric problems. With this reduction, explicit solutions have been previously obtained for symmetric bodies. For the antisymmetric case, the problem has been previously reduced to a complicated set of integrodifferential equations. In the cases where the flow field exhibits conical properties or when the body is slender, solutions may be obtained without recourse to solving the governing integral equations. In this paper it is shown that two-dimensional conical solutions are obtainable for moving antisymmetric wings only in the restricted case of the wing Mach numbers relative to the stream ahead of and behind the shock being the same. An analytical solution is presented for the above problem. In the case of slender bodies, it is shown that the classical steady slender body theory may be extended to shock diffraction problems and again analytical solutions are presented. It is shown that for general slender bodies, the lift and moment coefficients, and therefore the center of lift is influenced by the shock wave only through the Mach number change across the shock. Results are presented for the pressure distribution on the body, the lift and moment coefficients, and the center of lift for various slender body configurations at angle of attack.

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Résumé Les différents aspects de la diffraction des ondes de choc par les corps antisymétriques en mouvement sont examinés. Une méthode pour éliminer l'inhomogénéité dans la condition de choc, sans avoir recours à la forme explicite de la solution est présentée. Cette méthode peut être utilisée pour l'étude des problèmes symétriques aussi bien qu'antisymétriques. A l'aide de cette réduction, des solutions explicites ont été obtenues précédemment pour les corps symétriques. Dans les cas antisymétriques, il est connu que le problème peut être réduit à la résolution d'un système d'équations intégro-différentielles assez compliquées. Dans le cas où le champ d'écoulement possède certaines propriétés coniques, ou quand le corps est mince, on obtient des solutions sans reoudre les équations intégrales associées. Dans cet article il est démontré que des solutions coniques bi-dimensionnelles peuvent être obtenues pour des mouvements des ailes antisymétriques seulement dans le cas restrictif ou le nombre de Mach de l'aile relatif au courant en amont ainsi qu'en aval du choc est le même. Dans le cas des corps minces il est montré que la théorie classique pour les corps minces en équilibre peut être étendue aux problèmes de diffraction des chocs et on obtient des expressions analytiques pour la représentation des solutions. En outre, il est montré que pour des corps minces en général le coefficient de la portance et le coefficient du moment et, par conséquent, le centre de portance sont influencés uniquement par le changement du nombre de Mach causé par le choc. On obtient ainsi des résultats relatifs à la distribution de la pression sur le corps, le coefficient de la portance, le coefficient du moment et le centre de portance pour différentes configurations des corps minces avec un angle d'attaque.

     

On the Macrolactonization of β-Hydroxy Acids. Crystal structures of the pentolide and the hexolide from (R)-3-hydroxybutanoic acid. Molecular modeling studies of the tetrolide

The temperature and concentration dependence of the previously reported formation of oligolides from (R)- or (S)-3-hydroxybutanoic acid under Yamaguchi's macrolactonization conditions (2,4,6-trichlorobenzoyl chloride/base) was studied. While the content of hexolide 2 in the product mixture is almost invariably ca. 35%, the amounts of pentolide 1 and of the larger rings strongly depend upon the temperature employed (Fig.1). Cyclic oligomers ( 5,6 ) are also obtained from 3-hydroxypentanoic acid. Enantiomerically pure β-butyrolactone can be used for the preparation of pento-, hexo-, and heptolide under Shanzer's macrolactonization conditions (tetra-oxadistannacyclodecane ‘template’). The X-ray crystal structures of the pentolide 1 and of two modifications (space groups C 2 and P 2₁) of the hexolide 2 were determined (Figs. 2–6 and Tables 1 and 5). No close contacts between substituent atoms and atoms in the rings or between ring atoms are observed in these structures. The hexolide C 2 modification is ‘just a large ring’, while the crystals of the P 2₁ modification contain folded rings the backbones of which resemble the seam of a tennis ball. A comparison of the torsion angles in the folded hexolide ring of the P 2₁ modification with those in the helical poly-(R)-3-hydroxybutanoate ( PHB ) suggests (Table 2) that the same interactions might be responsible for folding in the first and helix formation in the second case. Molecular modeling with force-field energy minimization of the tetrolide from four homochiral β-hydroxybutanoic acid units was undertaken, in order to find possible reasons for the fact that we failed to detect the tetrolide in the reaction mixtures. The calculated conformational energies (per monomer) for some of the tetrolide models (Figs. 7–9 and Tables 3 and 4) are not significantly higher than for the pentolide and hexolide crystal structures. We conclude that thermodynamic instability is an unlikely reason for the lack of tetrolide isolation. This result and failure to observe equilibration of pentolide 1 to a mixture of oligomers under the reaction conditions suggest that product distribution is governed by kinetic control.     

Analytische Anwendung von Polymethylenammoniumsalzen

Zusammenfassung Unter den Hexamethonium [HM]-Übergangsmetall-Halogeniden, bzw. Halogenoiden, von welchen eine Reihe der komplexen Rhodanide beschrieben werden, sind die Verbindungen [HM][PtCl₆], [HM][PdCl₄] und [HM][IrCl₆] zum Nachweis der betreffenden Platinmetalle mit Empfindlichkeiten zwischen 0,2 und 3g Metall geeignet. Das Hexamethonium-Ion kann als [HM][Cr(NCS)₄(NH₃)₂]₂ in Mengen ab 1,5 mg gravimetrisch bestimmt werden.

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Summary The hexamethonium [HM] compounds of transition metal halogenides and halogenoides have been examined and some complex rhodanides have been described. The compounds [HM][PtCl₆], [HM][PdCl₄], and [HM][IrCl₆] have proved to be suitable for the detection of the metals concerned with sensitivities between 0,2 and 3g of the metal. The gravimetric determination of the hexamethonium ion in quantities above 1.5mg has been achieved by help of the compound [HM][Cr(NCS)₄(NH₃)₂]₂.

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II. Teil:Ziegler, M., u. G.Pape ¹.

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HerrWolfgang Renner hat in dankenswerter Weise Darstellung und Analysen der Rhodanokomplexe ausgeführt.     

The chemistry of coordinate polymerization of dienes

Conclusions This review has brought together the diverse ionic initiators for dienes into a consistent series of four polymerization mechanisms. The ionic freedom characteristic of the electrophilic and free anionic initiators catalyze the rapid formation of 1–4 trans structures. Coordinate initiation produces 1–4 cis structures via a cyclic transition state while anionic initiation produces 1–2 (3–4) structures.The catalytic activity in the coordinate and anionic catalysts depends largely on complex formation. The equilibrium characteristics of complex formation produces the different rate, structure and molecular weight effects observed in coordinate initiation studies.I wish to thank Drs. P. H.Moyer and M. R.Frederick for many helpful discussions of the mechanisms of coordinate polymerizations.     

Untersuchungen über Phenthiazinderivate, 19. Mitt. Neue piperazinsubstituierte Phenthiazine

Zusammenfassung Es wird über die Einführung weiterer Substituenten, z. B. Cyanäthyl und Aminopropyl, in Piperazinylalkylphenthiazine und -Piperazinyl-4,10-trimethylenphenthiazin berichtet.18. Mitt. dieser Reihe:O. Hromatka, M. Knollmüller undF. Sauter, Mh. Chem.93, 723 (1962).     

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