On the uniform convergence of parabolic spline interpolation on the class of functions with large gradients in the boundary layer

The problem of parabolic spline interpolation, according to Subbotin, of functions with large gradients in the boundary layer is considered. In the case of a uniform grid it is proved and in the case of the Shishkin mesh it is experimentally shown that with a parabolic spline interpolation of functions with large gradients in the exponential boundary layer, the error can unrestrictedly increase when the small parameter tends to zero and the number of grid nodes is fixed. An approximation process using parabolic splines with defect 1 is proposed; the error estimates are found to be uniform in the small parameter.     

Study of thermal transformations of aluminum phosphate binder and composites on its basis with various fillers

Results are reported obtained in a study of the physicochemical processes occurring under heating in the temperature range 150–1100°C of an aluminum phosphate binder and composites on its basis with various fillers (SiO₂, Al₂O₃, BN, and TiO₂ nanoparticles) with the use of an X-ray diffraction analysis.     

Evaluating the spectral sensitivity of the nonlinear-optical terahertz wave radiation detecors via spontaneous parametric down-conversion spectra

Principal parameters of the nonlinear-optical crystals are analyzed, which govern the spectral sensitivity of the terahertz wave detectors based on the frequency conversion from terahertz to optical range. A method is developed and experimentally demonstrated for characterizing these parameters. The method is founded on the spontaneous parametric down-conversion spectra observation without external terahertz wave radiation.     

On the threshold stress in superplasticity

The problem of threshold stress, as applied to superplasticity, is considered in terms of rheological and dynamic approaches. The necessity of introducing threshold stress in rheological relationships is shown. In a dynamic case, the threshold stress is a consequence of model constructions and is an evolution parameter.     

Spontaneous parametric down-conversion

Spontaneous parametric down-conversion (SPDC) in media with no inversion center and the use of this phenomenon in the spectroscopy of natural oscillation states of a crystal lattice (i.e., optical phonons) are retrospectively described. We think that the SPDC spectroscopy method is estimated inappropriately and hope to again attract the attention of readers to one of the most interesting quantum phenomena of nonlinear optics that has no classical analog. The capabilities of SPDC spectroscopy will certainly be used in both fundamental science and technology of new materials.     

Characterization of periodically poled LiTaO3 crystals by means of spontaneous parametric down-conversion

We describe the observation of quasi-phase-matched spontaneous parametric down-conversion in eee-geometry in periodically poled LiTaO₃ crystals. For scattered light, the two-dimensional angular-frequency intensity distribution was studied. Several detuning curves were recorded, corresponding to high orders m=-2, -3, -4, -5 of quasi-phase matching. The measured periods of domain gratings agree with the data obtained by atomic-force microscopy for the etched crystal surfaces. The presence of both odd and even orders indicates that the lengths of positive and negative domains are unequal. To determine the mean duty cycle for regular domain gratings we propose comparing of the intensities of spontaneous parametric down-conversion in different orders of quasi-phase-matching. PACS 42.65.Lm; 42.70.Mp; 81.70.Fy; 78.67.Pt; 42.65.Yj     

Shape memory effect in the vanadium-hydrogen system

The shape memory effect (SME) has been investigated in alloys of the V-H system at concentrations in the range 0.2–0.5 H/V. It is shown that SME occurs over the entire H/V range indicated, but the magnitude of the stresses, the reversibility of the deformation during heating, as well as the magnitude of the thermal hysteresis depend essentially on the hydrogen concentration. The conclusion is drawn that the transformation in this system is of a martensitic character.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 38–43, August, 1982.     

Visible and infrared dispersion of the refractive indices in periodically poled and single domain Nd:Mg:LiNbO3 crystals

3 crystals are measured in the transparency region (with the accuracy ±0.0002) and for the upper phonon polariton branch (with the accuracy ±0.003–±0.05), from 0.44 μm up to 10.5 μm. The method of spontaneous parametric light scattering is used for measurement of the ordinary refractive index dispersion in the mid-infrared region and for determination of the domain grating period d=5.6±0.2 μm in the periodically-poled crystal. Received: 29 January 1997/Revised version: 10 July 1997     

Features of interaction of a narrow light beam with a smectic OCBP. Memory effect

1. A memory effect was observed in a smectic liquid crystal without artificially increasing its absorption in a wide temperature interval — from the nematic-phase temperature (t ≤ 35°C) to room temperature (t ⋍ 21–22°C). 2. We have shown that a narrow light beam produces in the crystal an optical inhomogeneity indicative of transverse anisotropy.