Bifurcation in Rotational Spectra of Nonlinear AB2_2 Molecules

A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical non-linear molecules AB$_2$ is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model. The formation of fourfold energy clusters has already been experimentally verified for H$_2$Se and it has been demonstrated in fully-dimensional quantum mechanical calculations using the MORBID computer program. We show in the present work that apart from the level clustering, the bifurcation produces physically important effects including molecular symmetry-breaking and a transition from the normal mode to the local mode limit for the stretching vibrations due to rovibrational interaction. The application of the present theory with realistic molecular potentials to the H$_2$Te, H$_2$Se and H$_2$S hydrides results in predictions of the bifurcation points very close to those calculated previously. However for the lighter H$_2$O molecule we find that the bifurcation occurs at higher values of the total angular momentum than obtained in previous estimations. The present work shows it to be very unlikely that the bifurcation in H$_2$O will lead to clustering of energy levels. This result is in agreement with recent variational calculations.Comment: latex, 19 pages including 2 figures provided as *.uu fil

JUMPING FROG METHOD FOR OPTIMAL CLASSIFICATIONS

In the article the problem of finding optimal classifications on a finite set is investigated. It is shown that the problem of finding an optimal classification is generated by a tolerance relation on a finite set. It is also reduced to an optimization problem on a set of permutations. It is proposed a modification of the mixed jumping frogs to find suboptimal solutions of the problem of classification.In the article the problem of finding optimal classifications on a finite set is investigated. It is shown that the problem of finding an optimal classification is generated by a tolerance relation on a finite set. It is also reduced to an optimization problem on a set of permutations. It is proposed a modification of the mixed jumping frogs to find suboptimal solutions of the problem of classification

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene∕vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to ≈23000cm−1 above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC–CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH–CC diatom-diatom coordinates

Integral method for the development of motor abilities and psycho-physiological functions in children from 2 to 4 years old

The aim of the work: to develop and substantiate the method of integral development of the child on the basis of the integrated application of poems about nature and imitation movements. A greater number of significant differences were found between the test scores of the children of the experimental group compared with the control group after the experimen

Excitonic effects in time-dependent density functional theory from zeros of the density response

We show that the analytic structure of the dynamical xc kernels of semiconductors and insulators can be sensed in terms of its poles which mark physically relevant frequencies of the system where the counter-phase motion of discrete collective excitations occurs: if excited, the collective modes counterbalance each other, making the system to exhibit none at all or extremely weak density response. This property can be employed to construct simple and practically relevant approximations of the dynamical xc kernel for time-dependent density functional theory (TDDFT). Such kernels have simple analytic structure, are able to reproduce dominant excitonic features of the absorption spectra of monolayer semiconductors and bulk solids, and promise high potential for future uses in efficient real-time calculations with TDDFT.Comment: 10 pages, 4 figure

A Computer Model of the Evaporator for the Development of an Automatic Control System

For the implementation of a closed nuclear fuel cycle it is necessary to carry out a series of experimental studies to justify the choice of technology. In addition, the operation of the radiochemical plant is impossible without high-quality automatic control systems. In the technologies of spent nuclear fuel reprocessing, the method of continuous evaporation is often used for a solution conditioning. Therefore, the effective continuous technological process will depend on the operation of the evaporation equipment. Its essential difference from similar devices is a small size. In this paper the method of mathematic simulation is applied for the investigation of one-effect evaporator with an external heating chamber. Detailed modelling is quite difficult because the phase equilibrium dynamics of the evaporation process is not described. Moreover, there is a relationship with the other process units. The results proved that the study subject is a MIMO plant, nonlinear over separate control channels and not selfbalancing. Adequacy was tested using the experimental data obtained at the laboratory evaporation unit