Simulation of nonequilibrium gas flow with vibrational relaxation

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 222–228, 1989.     

Symmetric normal wave spectrum in an orthotropic layer

A solution is constructed for an orthotropic layer with free plane faces, that corresponds to the plane elastic waves symmetric over the thickness. The dynamical reconstruction of the normal wave spectrum during rotation of the wave vector from one to another elastically equivalent direction is investigated on the basis of a numerical analysis of the dispersion equation.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 116–121, 1988.     

Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.     

Simulation of the thermal fragmentation of fullerene C60

Defect formation and annealing processes in fullerene C₆₀ at T = (4000–6000) K are studied using molecular dynamics with a tight-binding potential. The cluster lifetime until fragmentation, which proceeds, as a rule, through the loss of a C₂ dimer, has been found as a function of temperature. The activation energy and the frequency factor in the Arrhenius equation for the fragmentation rate have been found to be E _a = (9.2 ± 0.4) eV and A = (8 ± 1) × 10¹⁹s^?1. It is shown that fragmentation can occur already after the C₆₀ cluster loses its spherical shape. This fact must be taken into account in theoretical calculations of E _a.     

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrödinger perturbation theory in the zero-order approximation of the Möller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.     

The effect of linguistic entropy on speech perception in noise in young and elderly listeners.

The rationale for a method to quantify the information content of linguistic stimuli, i.e., the linguistic entropy, is developed. The method is an adapted version of the letter-guessing procedure originally devised by Shannon [Bell Syst. Tech. J. 30, 50-64 (1951)]. It is applied to sentences included in a widely used test to measure speech-reception thresholds and originally selected to be approximately equally redundant. Results of a first experiment reveal that this method enables one to detect subtle differences between sentences and sentence lists with respect to linguistic entropy. Results of a second experiment show that (1) in young listeners and with the sentences employed, manipulating linguistic entropy can result in an effect on SRT of approximately 4 dB in terms of signal-to-noise ratio; (2) the range of this effect is approximately the same in elderly listeners.     

Spectral-luminescent properties of water-alcohol solutions of coumarin derivatives with additions of lithium chloride

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 965–969, June, 1991.     

Stochastic Visual Interactive Simulation Models

Many writers and practitioners have mentioned the difficulties that result from randomness in visual interactive simulation or animated simulation modelling. This paper discusses the use of VIS to model transient system behaviour, and proposes some approaches to stochastic VIS modelling which may be helpful in overcoming the difficulties.     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.