THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Radiative characteristics of pulsed power driven Z-pinch aluminumplasmas

In this paper, we study the dynamics of a massive aluminum Z-pinch plasma load and evaluate its performance as a soft X-ray radiator. A radiation hydrodynamic model self-consistently driven by a circuit describes the dynamics. Comparisons are made for the K- and L-shell soft X-ray emission as a function of the ionization dynamic model. The ionization dynamic models are represented by: 1) a time-dependent nonequilibrium (NEQ) model, 2) a collisional radiative equilibrium (CRE) model, and 3) a local thermodynamic equilibrium (LTE) model. For all three scenarios the radiation is treated 1) in the free streaming optically thin approximation where the plasma is treated as a volume emitter and 2) in the optically thick regime where the opacity for the lines and continuum is self-consistently calculated online and the radiation is transported through the plasma. Each simulation is carried out independently to determine the sensitivity of the implosion dynamics to the ionization and radiation model, i.e., how the ionization dynamic model affects the radiative yield and emission spectra. Results are presented for the L- and K-shell radiation yields and emission spectra as a function of photon energy from 10 eV to 10 keV. Also, departure coefficients from LTE are presented for selected levels and ionization stages     

The Michael addition of indoles to alpha,beta-unsaturated ketones catalyzed by CeCl3.7H2O-NaI combination supported on silica gel

Alkylation of indoles by means of the Michael addition has been the subject of a number of investigation. It is well established that regioselectivity in the additions of indoles to electron-deficient alkenes is strongly controlled by the reaction medium. In a continuation of the work on developing greener and cleaner technologies, the cerium(III) chloride heptahydrate and sodium iodide combination supported on silica gel catalyzes the alkylation of various indoles with alpha,beta-unsaturated ketones giving 3-(3-oxoalkyl)indole derivatives in good yields. The substitution on the indole nucleus occurred exclusively at the 3-position, and N-alkylation products have not been observed.     

New polyazaheterocycles. 9-Methyl-di-s-triazolo[4,3-a:4,3-c]pyrimidine and 9-methyl-s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidine

9-Methyl-di-s-triazolo[4,3-a:4,3-c]pyrimidine and 9-methyl-s-triazolo[4,3-c]tetrazolo[1,5-a]pyrimidine have been synthetized from 4-hydrazino-7-methyl-s-triazolo[4,3-c]pyrimidine. Structural assignments based on nmr, ir and chemical manipulations are discussed.