Resonant oscillations in open tubes

Summary The problem of a gas-filled tube excited by sinusoidal piston motion at one end and open at the other end is reinvestigated.It is shown that the key idea for the solution of the problem is a suitable combination of the usual amplitude nonlinearity and distortion effects. The main consequence of this is that the solution cannot be expressed in terms of a hierarchy associated with an expansion in the Mach number. Nevertheless an equation can be constructed which describes the behaviour of the flow in the limit of small Mach numbers. At the open end shock waves appear in the solution within a well-defined frequency band at each resonant frequency. Two different models which have been proposed by Wijngaarden and Jimenez respectively are used to define the boundary condition. It is seen that some basic properties of the resonant oscillations are independent of the boundary condition. Wijngaarden's model leads to very good agreement with results from several different experimenters. In this case, the width of the frequency interval where shocks occur is of the orderO(M); the width of the resonance band is of the orderO(M ^1/2), just as for the closed end tube.

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Zusammenfassung Betrachtet wird ein mit Gas gefülltes Rohr, welches an einem Ende offen ist und am andern Ende von einem harmonisch schwingenden Kolben angetrieben wird. Der Schlüssel zur Lösung dieses Problems ist eine geeignete Kombination der üblichen Amplitudennichtlinearität mit den Dispersionseffekten. Dies führt auf die grundlegende Konsequenz, dass es nicht möglich ist, die Lösung im Rahmen einer Hierarchie auszudrücken, welche aus einer Entwicklung in der Machzahl hervorgeht. Es ist gleichwohl möglich, eine Gleichung zu konstruieren, welche die Gasschwingungen für kleine Machzahlen beschreibt. Am offenen Ende treten innerhalb eines wohldefinierten Frequenzbandes (bei jeder Resonanzfrequenz) Stosswellen auf. Zur Definition der Randbedingung am offenen Ende werden zwei Modelle benützt, die (beziehungsweise) von Wijngaarden und Jimenez vorgeschlagen wurden. Einige der grundlegenden Eigenschaften der Lösungen sind unabhängig von der Randbedingung. Wijngaardens Modell führt auf sehr gute Übereinstimmung mit typischen Experimenten. In diesem Fall ist die Breite des Intervalls, in welchen Stösse auftreten, von der Ordnung O(M); die Breite des Resonanzbandes ist (in Übereinstimmung mit den Ergebnissen vom geschlossenen Rohr) von der OrdnungO(M ^1/2).

     

Struktur von S-9,10-Dimethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantan und 9,10-Diethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantan

Structure of S-9,10-Dimethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantane and 9,10-Diethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantane S-9,10-Dimethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantane ( 1 ) and 9,10-diethyl-1,3,5,7-tetraarsa-2,4,6,8-tetraoxaadamantane ( 2 ) have been prepared by the reaction of propionic acid, propionic anhydride and butyric acid, butyric anhydride, respectively, with arsenic(III)-oxide. The crystals of 1 are rhombic, a = 6.902(4), b = 11.121(5), c = 13.988(8), space group P2₁2₁2₁. The crystals of 2 are monoclinic, a = 11.757(10), b = 11.255(10), c = 18.631 (18), β = 91.78(7), space group P2₁/n. The mean bond lengths and angles in 1 are AsO = 1.790 Å, AsC = 1.959 Å, OAsO = 100.60°, CAsO = 99.65°, AsOAs = 128.77°, AsCAs = 118.73°, and in 2 they are AsO = 1.780 Å, AsC = 1.978 Å, OAsO = 101.45°, CAsO = 99.55°, AsOAs = 129.64°, AsCAs = 117.72°.     

Strukturchemische Untersuchungen von Monammin-Kupfer(I)-Komplexen: [CuNH3]2[Pt(CN)6], [CuNH3]2[Pt(CN)4] und Cu3[Co(CN)6]-2 NH3

Structurally Chemical Investigation of Monoammin Copper (I) Complexes : [CuNH₃]₂[Pt(CN)₆], [CuNH₃]₂[Pt(CN)₄] and Cu₃[Co(CN)₆] · 2NH₃ The preparation and the properties of [CuNH₃]₂[Pt(CN)₆], [CuNH₃]₂[Pt(CN)₄] and Cu₃[Co(CN)₆] · 2NH₃ are described. I.R. and Raman spectra have been recorded and assigned. According to X-ray powder diagrams, [CuNH₃]₂[Pt(CN)₆] crystallizes in the trigonal space group D–P3 ml, a = 7.771, c = 5.988 Å, Z = 1. According to the spectroscopic and crystallographic data, it is concluded that the Cu_I ion is coordinated with one NH₃ group and with the N atoms of the cyanometallate anions. The coordination number of the Cu⁺ is 4 in [CuNH₃]₂[Pt(CN)₆] and 3 in [CuNH₃]₂[Pt(CN)₄]. In the Cu₃[Co(CN)₆] · 2 NH₃ complex two Cu atoms have the coordination number 2, the third Cu atom 4.     

13 C 183W-Kopplungen als sonde für metall—carbin-, —carbenund—alkyl-bindungen

Carbon-13 NMR data are reported for trimethyltin derivatives containing ER_n groups where E  C, Si, Ge, Sn, N, O and S including a series of cyclic amines with ring sizes from three to seven. Coupling constant values for the homologous series of fourth group derivatives give goood correlations with the electronegativity of E. The observation of the two-bond, ¦ ²J(¹¹⁹SnE¹³C) ¦ couplings only in the derivatives containing bulky R groups is rationalized by a bimolecular exchange of ER_n groups in the concentrated solutions studied.     

Zur Ermittlung der Äthylen-Sequenzlängenverteilung und der chemischen Uneinheitlichkeit in Copolymeren mit Propylen durch Pyrolyse-Gas-Chromatographie

Pyrolysis coupled with gas chromatography has been applied to investigate the sequence distribution in copolymers of ethylene and propylene. The copolymers analyzed have been prepared with soluble Ziegler-Natta-catalysts and show different degrees of crystallinity. In one series of samples the methyl group of the propylene units has been labeled with tritium. It was then possible to detect carbons by flame ionization detector and simultaneously the methyl groups by the radio-detector in parallel. Within the errors of these methods the results from both detectors are consistent with the calculations from kinetics. The accuracy of the data is best in copolymers with long ethylene sequences. By GPC fractionation a heterogeneity in the chemical composition can be observed. One component of the copolymers is of high molecular weight, while the other has a molecular weight of less than 1000 and is very rich in ethylene. The influence of chemical heterogeneity on sequence distribution derived from kinetics and pyrolysis has been discussed. A mechanism in which chains with different chemical composition are growing from different species of the catalyst has been proposed. The experimental results show that the heterogeneity is not critical for the sequence analysis by kinetics and pyrolysis.     

Alkene loss from metastable methyleneimmonium ions: Unusual inverse secondary isotope effect in ion-neutral complex intermediate fragmentations

The mechanism of propene elimination from metastable methyleneimmonium ions is discussed. The first field-free region fragmentations of complete sets of isotopically labelled methyleneimmonium ions (H₂C = $ \mathop {\rm N}\limits^{\rm +} $⁺R¹R²: R¹ = R² = n-C₃H₇; R¹ = R² = i-C₃H₇; R¹ = n -C₃H₇; R² = C₂H₅; R¹ = n-C₃H₇; R² = CH₃; R¹ = n-C₃H₇; R² = H) were used to support the mechanism presented. The relative amounts of H/D transferred are quantitatively correlated to two distinct mathematical concepts which allow information to be deduced about influences on reaction pathways that cannot be measured directly. Propene loss from the ions examined proceeds via ion-neutral complex intermediates. For the di-n-propyl species rate-determining and H/D distribution-determining steps are clearly distinct Whereas the former corresponds to a 1,2-hydride shift in a 1-propyl cation coordinated to an imine moiety, the latter is equivalent to a proton transfer to the imine occurring from the 2-propyl cation generated by the previous step. For the diisopropyl-substituted ions which directly form the 2-propyl cation-containing complex, the rate-determining hydride shift vanishes. The 2-propyl cation-containing complex can decompose directly or via an intermediate proton-bridged complex. Competition of these routes is not excluded by the experimental results. Assuming a 2:1:3 distribution, a preference for the α- and β-methylene of the initial n-propyl chain as the source of the hydrogen transferred is detected for n-propylimmonium ions containing a second alkyl chain R². This preference shows a clear dependence on the steric influence of R². During the transfer step isotopic substitution is found to affect the H/D distribution strongly. For the alternative route of McLafferty rearrangement leading to C₂H₄ loss, specific γ-H transfer is observed.     

Bestimmung des Chiralitätssinns der enantiomeren 2,6-Adamantandiole

Determination of the Chirality Sense of the Enantiomeric 2,6-Adamantanediols The enantiomers of 2,6-adamantanediol ( 1 ) are resolved via the diastereoisomeric camphanoates. The (2R,6R)-chirality sense for (?)- 1 and (2S,6S) for (+)- 1 was determined by chemical correlation with (?)-(1R,5R)-bicyclo[3.3.1]nonan-2,6-dion ((1R,5R)- 3 ) of known absolute configuration in the following way: alkylation of the bis(pyrrolidine enamine) of (?)-(1R,5R)- 3 with CD₂I₂ and hydrolysis of the product gives the enantiomer 4 of (4,4-D₂)-2,6-adamantanedione. Reduction of 4 with LiAlH₄ leads to one enantiomer (Scheme 2) of each of the three diols 5 – 7 of known absolute configuration. The three diols are themselves configurational isomers due to the presence of the CD₂ group, but correspond otherwise entirely to the enantiomeric diols 1 . Accordingly, they can also be separated by means of their diastereoisomeric camphanoates to give the diols 5 / 6 and 7 . These samples are easily distinguished and identified by their characteristic ¹H-NMR spectra (cf. Fig. 2). This allows to identify the (2R,6R)- and (2S,6S)-enantiomer of 1 on the basis of their behavior in the resolution experiment analogous to that of the diols 5 / 6 and 7 , respectively. The diol (?)- 1 must have the (2R,6R)-configuration because it forms, like the diols 5 / 6 , with (?)-camphanic acid the diastereoisomeric ester less soluble in benzene. The diol (+)- 1 has (2S,6S)-configuration, because it forms, like 7 , with (+)-camphanic acid the diastereoisomeric ester less soluble in benzene. The bis(4-methoxybenzoate) of (?)-(2R,6R)- 1 shows chiroptical properties which are in accordance with Nakanishi's rule for two chromophores having coupled electric dipol transition moments arranged with a left-handed torsion angle.     

Synthese von 3-(2-Carboxy-4-Pyridyl)- und 3-(6-Carboxy-3-pyridyl)-DL-alanin

Synthesis of 3-(2-Carboxy-4-pyridyl)-and 3-(6-Carboxy-3-pyridyl)-DL-alanine As starting materials for potential photochemical approaches to betalaines C(R = COOH) and to muscaflavine F(R = COOH), β-(2-carboxy-4-pyridyl)- and β-(6(carboxy-3-pyridyl))-DL-alanine ( A and D with R = COOH or 4 and 11 ), respectively, were prepared (Scheme 1). The synthesis of 4 (= A, R = COOH) started with the 2-[(4-pyridyl)methyl]malonate 1 and proceeded via the N-oxide 2 , cyanation and hydrolysis (Scheme 2). Amino acid 11 was obtained from (3-pyridyl)methyl-bromide ( 6 ) via the malonate 7 by an analogous sequence of reactions (Scheme 3).     

Bestimmung von Sauerstoff auf Al-Oberfl?chen durch R?ntgenspektralanalyse mit Prim?ranregung in Kombination mit einem Hei?extraktions-Verfahren

Zusammenfassung Die Röntgenspektralanalyse mit Elektronenstrahlanregung stellt eine leistungsfähige Methode zur Bestimmung von Sauerstoff auf metallischen Oberflächen dar, wenn man das Heißextraktions-Verfahren zur Eichung heranzieht. Dies wird am Beispiel von 99,5%igem Aluminium mit einem Oberflächen-Sauerstoffgehalt von ca. 0,5 g/cm² demonstriert. Die Ergebnisse stehen in guter Übereinstimmung mit denen der Deuteronenaktivierung.Wir danken Frau A. Kahles für ihre exakten Heißextraktionsanalysen und manche sachverständige Anregung sowie Frau Dr. D. Heesen für ihre Hilfe bei der Probenpräparation und den Messungen an der Makrosonde recht vielmals.     

Einige bestrahlungsexperimente mit 2, 1-Benzisothiazolen

Some Irradiation Experiments with 2, 1-Benzisothiazoles 2, 1-Benzisothiazole ( 1 ) on irradiation with a mercury high-pressure lamp in benzene/diethylamine yields, after acetylation, 2-acetylamino-benzaldehyde ( 3 ; Scheme 1). Similarly, irradiation of 3-chloro-2, 1-benzisothiazole ( 2 ) in benzene/diethylamine leads to a mixture of 3-dimethylamino-2, 1-benzisothiazole ( 6a ) and N, N-diethyl-thioanthranilamide ( 7a ; Scheme 2). Benzisothiazole 6a , on irradiation, is not transformed into 7a . On the other hand, when 2 is irradiated in methanol a mixture of 3-methoxy-2, 1-benzisothiazole ( 4a ) and methyl anthranilate ( 5a ; Scheme 2) is obtained. In this case, 4a on irradiation in methanol or ethanol also yields 5a . No exchange of the methoxy group in 4a is observed when the irradiation is performed in ethanolic solution. Thus, 2, 1-benzisothiazoles 1 , 2 and 4a react photochemically by N,S-bond cleavage and hydrogen-atom abstraction from the solvent (Scheme 3). 3-Chloro-2, 1-benzisothiazole ( 2 ) shows a second photoreaction, i.e. nucleophilic exchange of the chloro substituent by methanol or diethyl amine. The latter reaction can also be observed thermally, e.g. in boiling methanol in the presence of methoxide ions.