Non-linear wave interactions

Non-linear wave interactions in physical systems are considered and analytical solutions of the governing equations obtained. Stability criteria are developed by obtaining general solutions for the first-order perturbations of the solutions. The problems discussed include various wave resonance interactions including Davydov's alpha-helix and Langmuir waves in a plasma.     

A nonuniform shock wave subjected to an oblique magnetic field

Summary A family of exact solutions for the one dimensional, unsteady, non-isentropic flow of an ideal, inviscid, perfectly conducting, compressible fluid subjected to an oblique magnetic field, is connected by a nonuniform shock wave to gas at rest in which the density distribution is nonuniform. The method of solution is inverse in the sense that the shock path is determined by the usual jump conditions, and then the density distribution in front of the shock is obtained in parametric form in terms of the equation of the shock locus.     

The decay of a magnetohydrodynamic shock wave

Résumé On utilise l'analyse linéaire pour étudier les faibles perturbations non-isentropiques des équations relatives aux écoulements unidimensionnels et non-stationnaires d'un fluide non visqueux idéal, parfaitement conducteur de l'électricité et compressible, soumis à l'action d'un champ magnétique transversal. On utilise la solution générale de la perturbation non-isentropique d'un écoulement par ondes simples centrées pour déterminer la perturbation qui se manifeste lorsqu'une onde de choc magnétohydrodynamique, tout d'abord uniforme et de force arbitraire, rencontre le régime d'onde simple.Dans le cas limité d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz. C'est la une confirmation de la validité de la théorie.

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This research was supported by National Science Foundation grant GP 87190.     

Reactivity and core-ionization energies in conjugated dienes. Carbon 1s photoelectron spectroscopy of 1,3-pentadiene

The high-resolution carbon 1s photoelectron spectrum of trans-1,3-pentadiene has been resolved into contributions from the five inequivalent carbon atoms, and carbon 1s ionization energies have been assigned to each of these atoms. Spectra have also been measured for propene and 1,3-butadiene at better resolution than has previously been available. The ionization energies for the sp2 carbons are found to correlate well with activation energies for electrophilic addition and with proton affinities. Comparing the results for 1,3-pentadiene with those for ethene, propene, and 1,3-butadiene as well as with results of theoretical calculations makes it is possible to assess the effect of the terminal methyl group in 1,3-pentadiene. As in propene, the methyl group contributes electrons to the beta carbon through the pi system. In addition, there is a significant (though smaller) contribution from the methyl group to the terminal (delta) CH2 carbon, also through the pi system. Most of the effect of the methyl group is present in the ground-state molecule. There are only relatively small contributions from the methyl group to the ionization energies from redistribution of charge in the pi system in response to the removal of a core electron. In addition to these specific effects, there is an overall decrease in average ionization energy as the size of the molecule increases as well as effects that are specific to the conjugated systems in 1,3-butadiene and 1,3-pentadiene. The results provide insight into the reactivity and regioselectivity of conjugated dienes.     

One-dimensional magnetohydrodynamic flow and the Monge-Ampère equation

Résumé Nous considérons les écoulements unidimensionnels et non-stationnaires d'un fluide idéal, non-visqueux et compressible, parfaitement conducteur de l'électricité, soumis à l'action d'un champ magnétique transversal, et l'équation de Monge-Ampère. Dans le cas limité d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz.

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This research was supported by a National Aeronautics and Space Administration general research grant to the University of Wisconsin.     

Synthesis and antimycobacterial activity of agelasine E and analogs

Agelasine E, previously isolated from the marine sponge Agelas nakamurai, has been synthesized for the first time, together with analogs with various terpenoid side chains. Treatment of N6-methoxy-9-methyl-9H-purin-6-amine with allylic bromides gave the desired 7,9-dialkylpurinium salts together with minor amounts of the N6-alkylated isomer. The N6-methoxy group was finally removed reductively. 1H-15N HMBC and 1H-15N HSQC NMR spectroscopy gave additional information on tautomerism and charge delocalization in the purine derivatives studied. The heterocyclic products were screened for activity against Mycobacterium tuberculosis and agelasine analogs carrying a relatively long terpenoid substituent in the purine 7-position and a methoxy group at N-6 were potent inhibitors of bacterial growth. Since agelasine analogs with the geranylgeranyl chain at N-7 exhibited antimicrobial activity, several strategies for synthesis of geometrically pure (2E,6E,10E)-geranylgeranyl bromide from geranyllinalool were evaluated.     

Dative sigma- and pi-bonding in boron-nitrogen compounds: molecular structures of (CH3)2NB(CH3)N(CH3)B(CH3)2 and [(CH3)2B]2NN(CH3)2 determined by gas electron diffraction and quantum chemical calculations

The molecular structures of dimethylamino[(dimethylboryl)methylamino]methylborane, Me2NBMeNMeBMe2 (1) and 1,1-bis(dimethylboryl)-2,2-dimethylhydrazine, (Me2B)2NNMe2 (2) have been determined by gas electron diffraction (GED), density functional theory calculations at the B3PW91/6-311++G** level and ab initio calculations at the MP2/6-311++G** level. 1 adopts an open structure similar to that of the isoelectronic hydrocarbon molecule permethylbutadiene; the central B-N bond distance at 148.0/149.3(7) pm (MP2/GED) corresponds to a single covalent N--B bond distance, the two terminal distances, 140.9/140.5(4) pm and 141.8/141.3(4) pm, correspond to the distance between N and B atoms joined by a covalent sigma-bond and a dative pi-bond. A closed form where the establishment of a dative bond between the terminal N and B atoms has led to the formation of a four-membered ring also corresponds to a minimum on the potential energy surface, but the energy is calculated to be 14.3 kJ mol(-1) higher at the MP2 level. This structure is also incompatible with the GED data. 2 adopts a structure in which a dative sigma-bond between the dimethylamino N atom and one of the boron atoms has led to the formation of a three-membered N(2)B ring. The dative sigma-bond distance is 165.5/164.0(13) pm, the two other bond distances in the ring are N-B=150.6/148.9(9) pm corresponding to a covalent sigma-bond and N-N=145.1/145.4(3) pm. The terminal B--N distance 139.6/138.9(9) pm is consistent with a covalent sigma-bond augmented by a dative pi-bond. An open Y-shaped structure also corresponds to a minimum on the potential energy surface, but the energy is 18.7 kJ mol(-1) higher (MP2) and it is incompatible with the GED data.     

pH-sensitive Photoluminescence of CdSe/ZnSe/ZnS Quantum Dots in Human Ovarian Cancer Cells

The photoluminescence of mercaptoacetic acid (MAA)-capped CdSe/ZnSe/ZnS semiconductor nanocrystal quantum dots (QDs) in SKOV-3 human ovarian cancer cells is pH-dependent, suggesting applications in which QDs serve as intracellular pH sensors. In both fixed and living cells the fluorescence intensity of intracellular MAA-capped QDs (MAA QDs) increases monotonically with increasing pH. The electrophoretic mobility of MAA QDs also increases with pH, indicating an association between surface charging and fluorescence emission. MAA dissociates from the ZnS outer shell at low pH, resulting in aggregation and loss of solubility, and this may also contribute to the MAA QD fluorescence changes observed in the intracellular environment.     

Synthesis of (+)-trixagol and its enantiomer, the terpenoid side chain of (−)-agelasine E

The naturally occurring γ-cyclogeranylgeraniol called (+)-trixagol has been synthesised for the first time. Trixagol was readily available in five steps from (S)-2,2-dimethyl-6-methylene-1-cyclohexanemethanol. The enantiomer of trixagol, which equates to the terpenoid side chain of the naturally occurring 7,9-dialkylpurinium salt (−)-agelasine E, was prepared from the (R) enantiomer of the cyclohexanemethanol. Both trixagol enantiomers were moderately active against Mycobacterium tuberculosis.