A NEW METHOD FOR SEPARATING LONGITUDINAL WAVES IN A LARGE DIAMETER HOPKINSON BAR

This paper outlines various methods for separating fundamental longitudinal waves propagating along a Hopkinson pressure bar. Advantages and disadvantages of the different methods are presented and discussed in detail. A new method is then proposed for separating the fundamental waves in the frequency domain. This new method is based on the assumption that wave propagation can be adequately described by the first mode of the Pochhammer-Chree theory. The method requires two-point strain gauge measurements on the pressure bar. Fourier components of the positive wave at one gauge location are determined either from the corresponding Fourier components of the measured strain histories or from their derivatives. The method also makes use of the derivative of the wave number with respect to the circular frequency of the pressure bar. Important points of the implementation of the technique are described. Numerical accuracy of the proposed method is verified by considering a simple example with analytical solution and by comparing measured data derived from a large diameter Hopkinson pressure bar. The proposed method will find application in dynamic material tests using the split Hopkinson pressure bar technique.     

Simulation of time-resolved vibronic spectra and the possibility of analyzing molecules with similar spectral properties

The possibility of using time-resolved vibronic spectroscopy for spectral analysis of mixtures of chemical compounds with similar optical properties, when traditional methods (based on stedy-state spectra) are inefficient, is demonstrated by using the method of computer simulation. The analysis is carried out by the example of molecules of a series of polyenes (butadiene, hexadiene, octatetraene, decapentaene, and decatetraene), their various cis-and trans-rotational isomers, and phenyl-substituted polyenes. Ranges of relative concentrations of molecules similar in their spectral properties, where reliable interpretation of time-resolved spectra of mixtures and both qualitative and quantitative analyses are possible, are determined. The use of computer simulation methods for optimizing full-scale experiments in femtosecond spectroscopy is shown to hold much promise.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Diffraction of Elastic Waves from a Cylindrical Infinite Cavity with Circular Cross Section Filled by a Liquid

Based on the equations of elasticity theory and hydroacoustics, we calculated the field structures arising when a plane wave is incident on an infinite cylindrical cavity with circular cross section filled by a liquid. The variable pressure component on the cavity axis for longitudinal and shear incident waves is determined.     

Technical Stability of Nonlinear Spatial Dynamic States of Continuous Systems in the Case of Their Interaction with a Flow of a Liquid

Nonlinear Oscillations -     

Functional approach to the theory of two-dimensional quantum Fermi systems in an external periodic field

The behavior of an adsorbed layer of Fermi particles in a weak external field with symmetry of the centered quadratic lattice is investigated. Instability of the weakly inhomogeneous state of the system with respect to small fluctuations in the vicinity ofa ^*=2k _F is established; herea ^* is the magnitude of the vectors of the neighbors closest to the point in the inverse lattice; k_F is the Fermi momentum.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 29–43, 1988.It remains to thank V. N. Popov for constant interest in the work.     

Liquid chromatographic analysis of prednisolone, prednisone and their 20-reduced metabolites in perfusion media

A reversed-phase liquid chromatographic assay was developed to quantitate prednisolone, prednisone and the 20 alpha-dihydro and 20 beta-dihydro reduced metabolites of both parent compounds in tissue culture media from in vitro perfusions of the human placental lobule. Steroids were extracted from perfusate, using reversed-phase cartridges, with average recoveries of 95.2% or greater. The internal standard for the analyses was 6 alpha-methylprednisolone. In this assay cortisol coelutes with prednisolone, however, no other significant interferences were found. Assay of each steroid was linear in the range 0-1 microgram/ml. Intra-assay coefficients of variation were measured at 10 and 750 ng/ml with ranges of 3.4% (20 alpha-dihydroprednisone) to 8.8% (20 beta-dihydroprednisolone) and 4.1% (20 beta-dihydroprednisone) to 8.8% (prednisone). The corresponding inter-assay coefficients of variation were 3.3% (20 alpha-dihydroprednisone) to 9.1% (20 beta-dihydroprednisolone) and 1.9% (prednisolone) to 3.5% (prednisone). The analyses utilized two C18 columns which were linked together and maintained at 40 degrees C.     

UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.