Criteria for controllability and observability in complex domain models of stationary systems

We propose criteria for controllability and observability of stationary systems specified by complex domain models. Conclusions concerning controllability and observability are made on the basis of coefficients in the corresponding transfer functions. Translated fromDinamicheskie Sistemy, Vol. 12, pp. 120–126, 1993.     

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)     

Duality in two-dimensional Z(N)-symmetric spin models on a finite lattice

We propose a method for deriving duality relations for two-dimensional inhomogeneous Z(N)-symmetric models on a finite square lattice wound around a torus. The method is used to obtain duality relations for the vector Potts model, the Berezinskii-Villain Z(N)-model, the Ashkin-Teller model, and the 8-vertex model on a lattice obliquely wound around a torus, as well as an exact relation linking the partition functions of the latter two models. Zh. éksp. Teor. Fiz. 113, 240–260 (January 1998)     

Thermal expansion of crystal lattices of germanium with different isotopic compositions

The linear thermal expansion coefficient of crystal lattices of germanium with different isotopic compositions is analyzed. Fiz. Tverd. Tela (St. Petersburg) 40, 1829–1831 (October 1998)     

Entropy of crystallization of materials from a “molten” sublattice of superionic conductors

It is shown that the entropy of crystallization of materials (such as Cu, Ag, Au, and Li) in a “molten” sublattice of superionic conductors→crystal system may substantially exceed the entropy of crystallization of the same materials from a melt. The observed behavior explains the known tendency of various superionic conductors to form filamentary crystals (whiskers) in the solid phase, together with the completely different structure of these whiskers. Fiz. Tverd. Tela (St. Petersburg) 40, 227–228 (February 1998)     

Distinctive features of time-resolved photoluminescence of porous silicon coated with a layer of diamondlike carbon

Time-resolved photoluminescence from porous silicon coated with a diamondlike carbon film is investigated. The intensity of the photoluminescence from the carbon film is obserd to increase after deposition, and there is an accompanying change in the intensity and a shortwavelength shift of the photoluminescence band of porous silicon that depends on the porosity of its original layers. These changes are explained by the formation of carbon nanoclusters on the surface of the silicon filaments. Zh. Tekh. Fiz. 68, 83–87 (April 1998)     

A spectropolarimetric study of theH α radiation from ellerman bombs

Polarization data are given for three whiskers recorded with the large solar vacuum telescope at the Baikal Observatory, Institute of Solar-Terrestrial Physics, Russian Academy of Sciences. The observed degree of polarization varies from 2 to 13%. The direction of the polarization plane for the mediumintensity whisker was tangential, while that for the weakest one was radial. The brightest whisker had the polarization plane direction close to radial at the center of the line but tangential at the flanks. It is assumed that the polarization is due to impact excitation of a hydrogen-atom ensemble in the solar chromosphere by an electron beam, and estimates are made of the beam energy. St. Petersburg Fine Mechanics and Optics Institute, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 41, No. 12, pp. 85–89, December 1998.     

The temperature jump and slow evaporation in molecular gases

We set up model transport equations that describe the behavior of molecular (diatomic and polyatomic) gases with a molecule collision rate proportional to the molecular velocity. In deriving these equations we allow for the internal (rotational) degrees of freedom, while the vibrational degrees of freedom are assumed “frozen.” We also set up an exact equation for the problem of the temperature jump with allowance for slow evaporation from the liquid surface into the saturated vapor atmosphere. Finally, we derive explicit formulas for calculating the coefficients of the temperature jump and gas-density jump above a flat surface and do the necessary numerical calculations. Zh. éksp. Teor. Fiz. 114, 956–971 (September 1998)     

Specific properties and spatial symmetry group of nonassociative spinor field

On the basis of nonassociative spinor field theory, the specific properties of a nonassociative spinor field are investigated. A new quantum number is introduced: the associator, which is a measure of the nonassociativeness of the field. To calculate the associator and spin in nonassociative algebra, open and closed products are introduced. It is shown that the spin consists of two components: the first half (calculated by the open-product rule) is similar to ordinary spin, while the second half (calculated by the closed-product rule) is attributed to the associator, i.e., is related to shear in the auxiliary isotopic space. The associator basis is expanded to a complete octonion basis, and the Poincaré group of four-dimensional space is expanded to a Poincaré group of eight-dimensional space. It is shown that, from these generators, in the particle rest system, the nonzero independent eigenvalues are: one, the sign of the particle energy, one of the spin components, one of the associator spatial components, and c₇. Tbilisi Medical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 101–109, October, 1998.