Nonstationary curves in Hilbert spaces and their correlation functions II

Partially supportted by Grant MM-22/1991 of MESC     

Rotational tunneling dynamics of methyl groups inn-alkane host lattices: An optical investigation of the internal and external isotope effect

We exploited the slow relaxation of methyl group rotational tunneling states to perform optical hole burning inn-alkane crystals. The dye probe used was dimethyl-s-tetrazine and its perdeuterated derivative. We investigatedn-octane, perdeuteratedn-octane andn-hexane as host crystals. By comparing the experimentally observed hole-antihole splitting of the protonated and perdeuterated dye probe, all parameters, i.e. the tunneling splitting in the ground-and in the electronically excited state as well as the respective heights of the potential can be determined, assuming a threefold rotational symmetry axis. We found that matrix deuteration has a severe influence on the potential heights, which increase by a factor of two. With these parameters determined, many features of the complex relaxation behavior of the tunneling states can be qualitatively understood: We found Raman-type conversion processes inn-octane-h ₁₈, Orbach-type processes inn-octane-d ₁₈ and inn-hexane we found, in addition, a relaxation regime governed by a Direct process. The experimental activation energies as well as the cross-over temperatures are in satisfying agreement with current theories.     

Numerical solution of moisture,salinity, and heat transport problem in the aeration zone

A numerical example of the salinity regime of soils in a two-dimensional region is considered with allowance for the effect of temperature fields. The mathematical model is based on solving a system of nonlinear partial differential equations.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 60, pp. 59–65, 1986.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

The application of the Mössbauer spectroscopy for the study of the contaminants in the double circuit water heat-carrier nuclear power plant

The iron containing corrosion products from water heat-carrier and deposits of the second circuit of the nuclear power plant were investigated by means of absorption Mössbauer spectroscopy. The nonstoichiometric magnetite and paramagnetic (superparamagnetic) iron oxide particles were found to be the main corrosion products. The fraction of the magnetically ordered phase varied in the range 0–100% depending on the location in the second circuit.     

Spatial correlation study of internal magnetic fields in magnets by μSR2-technique

It is shown that using position-sensitive detectors in μSR experiments to determine the muon stopping site in a target permits one to study correlation effects in μSR time histograms produced by the decay of muons stopping in the same domain, i.e. to obtain time correlators of μSR histograms of decays from a small region. These correlators contain information on the spatial correlation of magnetic fields in the sample under study. The proposed method (μSR²-technique) allows measuring correlation radii (r _c ) down to 10⁻⁵ cm in a bulk sample. Among interesting physical phenomena occuring overr _c≥3×10⁻⁶ cm are, for instance, long wavelength fluctuations of the order parameter near the phase transition point in ferromagnets and antiferromagnets and magnetic field correlations in magnet domains and spin glasses. One may use this method also on heavy-current accelerators producing pulsed muon beams to investigate the variation in time of spatial correlations in magnets, spin glasses and superconductors.     

Identification of low-energy light nuclei recorded by means of an ionizational mass spectrometer

A method of identifying low-energy nuclei from the readings of an ionizational mass spectrometer is considered. The identification principles for particles recorded by a multilayer detector are discussed, together with the fundamentals of a probabilistic approach to the solution of this problem. The method permits correct analysis of the experimental data obtained. The determination of the charge and isotopic composition of radiation consisting of a mixture of different nuclei is considered. The results of calculations by the given method which permit the determination of the optimal detector parameters for the solution of the specific physical problem are outlined. This approach is also applicable for the analysis of data from other types of measuring apparatus.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 84–88, July, 1991.     

An automated laboratory EXAFS spectrometer of Johansson type: indigenous development and testing

An automated linear laboratory EXAFS spectrometer of the Johansson type has been indigenously developed. Only two translational motions are required to achieve the necessary Rowland circle configuration for the (fixed) X-ray source, the dispersing and focusing bent crystal and the receiving slit. With the available crystals the spectral region from 5 to 25 keV can be scanned. The linear motions of the crystal and receiving slit including the detector assembly are achieved by employing software-controlled DC motors and utilizing optical encoders for position sensing. The appropriate rotation of the crystal is achieved by the geometry of the instrument. There is a facility to place the sample alternately in the path of the X-ray beam and out of the path to record both the incident X-ray intensityI ₀ and the transmitted intensityI employing the scintillation detector. An arrangement with a two-window proportional detector before the sample to measureI ₀ and the scintillation detector to recordI is also developed; in this case it is not necessary to oscillate the sample. Fast electronic circuits are employed to minimize counting errors. The instrument is user-friendly and it is operated through a menu-driven IBM compatible PC. EXAFS spectra of high resolution have been recorded using the spectrometer and employing the Si(111) reflecting planes; the X-ray source being a Rigaku 12 kW rotating anode with Cu target. We describe the spectrometer and discuss its performance with a few representative spectra.     

Variational principles of magnetostatics of superconductors. I

Fundamental and dual variational principles of magnetostatics of superconductors are formulated. It is shown how test fields can be expressed in terms of vector and scalar potentials. General consequences of the variational magnetostatic formulation are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 97–102, September, 1991.