On the integrability of hyperbolic systems of riccati-type equations

We consider equations of the form U_xy = U * U_x, where U(x, y) is a function taking values in an arbitrary finite-dimensional algebra T over the field ℂ. We show that every such equation can be naturally associated with two characteristic Lie algebras, L_x and L_y. We define the notion of a ℤ-graded Lie algebraB corresponding to a given equation. We prove that for every equation under consideration, the corresponding algebraB can be taken as a direct sum of the vector spaces L_x and L_y if we define the commutators of the elements from L_x and L_y by means of the zero-curvature relations. Assuming that the algebra T has no left ideals, we classify the equations of the specified type associated with the finite-dimensional characteristic Lie algebras L_x and L_y. All of these equations are Darboux-integrable. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 2, pp. 261–275, November, 1997.     

Effect of amorphization on the electronic and lattice specific heat of an Ni2B alloy

The specific heats of the Ni₂B amorphous system and of its crystal analog were studied in the temperature range 3–270 K. The data obtained permitted us to isolate the contribution due to atomic vibrations from the experimentally measured specific heat, determine the electronic density of states at the Fermi level and the temperature dependence of the characteristic Debye parameter Θ, and to calculate some average frequencies (moments) of the vibrational spectrum. The electronic density of states at the Fermi level increases under amorphization. An analysis of the temperature dependence of the lattice specific heat showed that amorphization brings about a substantial growth in the density of vibrational states at low frequencies, whereas the spectrum-averaged and rms frequencies change very little, which is in good agreement with neutron diffraction measurements.     

The effect of complexing processes on energy transfer Tl+→Gd3+ and Tl+→Tb3+ in glass

T. Shevchenko Kiev University, 252022 Kiev, Pr. Akad. Glushakova, 6, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 3, pp. 192–196, May–June, 1995.     

Influence of octupole interactions on the behavior of negative-parity states at low spins

The energies of negative-parity levels based on two-particle states exhibit a nonlinear behavior at low spins versus the core-rotation energy because the alignment process has not yet been completed for them. This behavior of negative-parity levels in the low-spin region is satisfactorily described upon the inclusion of octupole-octupole interactions. This is demonstrated within the rotational model involving the Coriolis mixing of states for the even-even isotopes ^162–168Hf.     

Propagation of a focused light beam in a circuital system of tunnel-coupled waveguides

The propagation of a pencil beam in a circuital system of tunnel-coupled waveguides is considered. It is shown that the beam periodically focuses into a point when moving along the trajectory. A maximal number of waveguides supporting the propagation of the beam can be estimated in simple terms. The cross-sectional area of the waveguides can be subdivided into three zone with the beam pulsing only in the central one.     

Optical properties of Fe-doped silica films on Si

Optical properties of Fe-doped silica films on Si were investigated by ellipsometric technique in the region 1-5 eV. Samples were produced by sol-gel method. Precursors were prepared by mixing tetraethoxysilane (TEOS) solution in ethanol and water with aqueous solution of Fe-chloride or Fe-acetate. The coating solution was deposited on Si substrates by spin on technique. The size of Fe-containing nanometric-sized particles depended on technology and varied from 20 to 100 nm. Optical response of complex hybrid samples SiO₂:Fe/Si was interpreted in a multi-layer model. In the inverse problem, the Maxwell equations were solved by transfer matrix technique. Dielectric function of Fe-doped silica layers was calculated in the model of effective media. Analysis of optical data has shown that various Fe-oxides formed. Experimental data for films obtained from precursors with Fe-acetate and annealed in hydrogen were well described by the model calculations taking into account a small contribution 1-5% of metal Fe imbedded in silica. The Fe/Fe-O contribution to optical response increased for samples grown from FeCl₃-precursor. Ellipsometric data for Fe-doped silica films on Si were interpreted taking into account the structural AFM studies as well as the results of magnetic measurements.     

Preparation of MgB<Subscript>2</Subscript>/Fe superconductor wire by electrical self-heating

MgB₂/Fe wires were prepared by electrical self-heating of in situ powder-in-tube wires for the first time at ambient conditions. Characterization of the wires processed at 750 °C, 800 °C and 850 °C for 15 min by XRD, SEM, ϱ–T, susceptibility and J_C measurements shows that the MgB₂ formed is of high quality particularly with respect to phase purity and transport J_C. The method considerably reduces the overall energy consumption vis-à-vis the production cost, simplifies the complexity of the fabrication procedure and is promising for manufacture of high-quality MgB₂ superconducting wires. PACS 74.70.Ad; 74.62.Bf; 74.25.Fy; 74.25.Ha; 81.20.Hy