Acoustic wavefront imaging

We introduce a new class of experiments which provide graphic insights into the propagation of acoustic waves in anisotropic media. Simply stated, we have devised a means of observing the expanding acoustic wavefront from a point disturbance in a solid. The data may be viewed as a movie or a series of snapshots. The observed wavefronts represent the group-velocity surfaces of acoustic waves, which reflect the basic elastic anisotropy of the solid. The technique has been applied to coherent acoustic waves with frequencies in the megahertz range (at ambient temperatures) and to incoherent heat pulses in the hundred-gigahertz range (at liquid-helium temperatures). In this article, we first provide a pedagogical introduction to wave propagation in elastically anisotropic media, reviewing some early methods for visualizing acoustic waves. Next, we describe the “acoustic wavefront imaging” method and give representative results in crystals and composite materials. Finally, we show how this method relates to recent advances in phonon imaging and internal diffraction of ultrasound.     

Polychronous kinetics with nonstationary rate constants. Effect of a medium

Characteristic features of the kinetics of solid-state cage reactions with distributed parameters of the relaxing matrix were considered. Depending on the ratio of the constants of the reaction rate and relaxation of environment, the kinetics of chemical conversions can be either exponential or nonexponential. Plausible reasons for the unsteady-state character of the kinetics of the processes of two types,viz., the reactions of alkyl radicals in amorphous alcohol matrices and conversions in biological systems, were discussed. The main reason for the unsteady-state character of the reactions of the first type is a dispersion of the equilibrium distances between the reagents. Kinetics of the reactions of the second type, such as rebinding of the ligands in the heme-containing proteins (e.g., in myoglobin), is determined by the distances in the pairs of reagents and the relaxation transitions. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 469–476, March, 1997.     

Molecular vibrations in a gradient extremal path

Summary The calculation of vibrational states using a gradient extremal path is discussed. Gradient extremal paths are defined by local criteria, which lead to stable solutions. This has certain advantages in comparison with a steepest-descent path, which is often difficult to determine accurately. For cases where a reaction path formalism is applicable, a path based on the gradient extremal concept gives results in close agreement with those obtained using traditional steepest-descent methods. We present algorithms for carrying out such calculations and also give some numerical results.     

A simple scheme for calculating the energy levels and the spectra of molecular crystals

A simple matrix method for calculating the vibrational and electron energy levels and spectra in molecular crystals is proposed.     

DFT study and vibrational spectra of the phoshorus-containing G0 generation dendrimer

The Raman (10–3500 cm⁻¹) and infrared (150–3500 cm⁻¹) spectra have been recorded for tris(4-oxibenzaldehyde)thiophosphate. This compound includes structural parts of elementoorganic dendrimers: a core and terminal aldehyde groups. The structural optimization and normal mode analysis are performed for elementoorganic dendrimer on the basis of the ab initio density functional theory. It is found that the dendrimer exist in a single stable conformation with planar C₆H₄CHO fragments. Our calculations show that conformer with one trans and two gauche 4-oxibenzaldehyde groups is realized. All these observations suggest that steric congestion does not disturb the construction of dendrimers even for the highest generations, and that terminal groups are readily available for further reactions. Relying on DFT calculations a complete vibrational assignment is proposed for different parts of the studied dendrimers.     

E ⊗ ϵ Jahn–Teller anharmonic coupling for an octahedral system

The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian derived. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Vibrational spectra of 2-biphenylmethanol. Spectrum simulation and molecular structure

The vibrational spectra of a solid crystalline sample of 2-biphenylmethanol have been measured at room temperature. The IR absorption spectra were recorded in the range 400 cm^–1–3600 cm^–1; Raman spectra were measured in the range 10 cm^–1–1640 cm^–1. The direct mechanical and optoelectronic problems were solved using the fragment method realized as Lev-100 software; the intensity distribution in the IR spectrum of 2-biphenylmethanol was obtained by the same method. The experimental Raman and IR absorption spectra were interpreted by analyzing the calculated data on the frequencies and forms of normal vibrations and their intensities in the IR spectra. IR absorption spectra were simulated for several models of 2-biphenylmethanol conformers that differ in the mutual orientation of fragments. Based on the results of simulation and comparison of the calculated and experimental spectra of conformers we suggested a model for the conformer realized in the solid phase under normal conditions.Original Russian Text Copyright © 2004 by L. M. Babkov, J. Baran, N. A. Davydova, J. I. Kukielskii, and S. V. TrukhachevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 624–631, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Theoretical DFT and experimental Raman and NMR studies on thiophene, 3-methylthiophene and selenophene

The results of extended MO calculations using density functional theory (DFT) approximation supported by experimental Raman, ¹H and ¹³C NMR studies on thiophene are reported. Raman spectra of liquid thiophene were re-examined and the performance of a hybrid B3PW91 density functional was compared with the ab initio restricted Hartree–Fock (RHF) method. With the basis sets of the 6-311++G^** quality, the DFT calculated bond lengths, dipole moments and harmonic vibrations were predicted in a very good agreement with available experimental data.

Additionally, the results on thiophene were extended by calculations on 3-methylthiophene and selenophene. In this case, a significant change in geometry and charge distribution in thiophene ring due to a methyl group substituent or replacement of sulphur by selene atom was observed.

A linear correlation between the predicted harmonic vibrational frequencies (scaled using SQM method) and experimental ones for thiophene, selenophene and 3-methylthiophene was shown. The theoretically calculated spectra have satisfactorily reproduced the available experimental spectra for thiophene and selenophene.     

Time domain simulation of vortex-induced vibrations in stationary and oscillating flows

This paper focuses on the further development of a previously published semi-empirical method for time domain simulation of vortex-induced vibrations (VIV). A new hydrodynamic damping formulation is given, and the necessary coefficients are found from experimental data. It is shown that the new model predicts the observed hydrodynamic damping in still water and for cross-flow oscillations in stationary incoming flow with high accuracy. Next, the excitation force model, which is one component of the total hydrodynamic force model, is optimized by simulating the VIV response of an elastic cylinder in a series of experiments with stationary flow. The optimization is performed by repeating the simulations until the best possible agreement with the experiments is found. The optimized model is then applied to simulate the cross-flow VIV of an elastic cylinder in oscillating flow, without introducing any changes to the hydrodynamic force modeling. By comparison with experiment, it is shown that the model predicts the frequency content, mode and amplitude of vibration with a high level of realism, and the amplitude modulations occurring at high Keulegan–Carpenter numbers are well captured. The model is also utilized to investigate the effect of increasing the maximum reduced velocity and the mass ratio of the elastic cylinder in oscillating flow. Simulations show that complex response patterns with multiple modes and frequencies appear when the maximum reduced velocity is increased. If, however, the mass ratio is increased by a factor of 5, a single mode dominates. This illustrates that, in oscillating flows, the mass ratio is important in determining the mode participation at high maximum reduced velocities.     

Dynamical instability of laminated plates with external cutout

A method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutouts essentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.