On an evasion problem on a semi-infinite interval for a class of controlled distributed systems

In this paper, we study an evasion problem in systems described by equations of parabolic type. We consider four versions of constraints on the control parameters.     

A Study of premixed propagating flame vortex interaction

Experimental data is presented for the interaction between a propagating flame and a simple vortex flow field structure generated in the wake of solid obstacles. The interaction between gas movement and obstacles creates vortex shedding forming a simple flow field recirculation. The presence of the simple turbulent structure within the gas mixture curls the flame front increasing curvature and enhancing burning rate. A novel twin camera Particle Image Velocimetry, PIV, was employed to characterise the flow field recirculation and the interaction with the flame front. The technique allowed the quantification of the flame/vortex interaction. The twin camera technique provides data to define the spatial variation of both the velocity of the flow field and flame front. Experimentally obtained values of local flame displacement speed and flame stretch rate are presented for simple flame/vortex interactions.     

Tunable properties of light propagation in photonic liquid crystal fibers

Tunable properties of light propagation in photonic crystal fibers filled with liquid crystals, called photonic liquid crystal fibers (PLCFs) are presented. The propagation properties of PLCFs strongly depend on contrast between refractive indices of the solid core (pure silica glass) and liquid crystals (LCs) filing the holes of the fiber. Due to relatively strong thermo-optical effect, we can change the refractive index of the LC by changing its temperature. Numerical analysis of light propagation in PLCF, based on two simulation methods, such as finite difference (FD) and multipole method (MM) is presented. The numerical results obtained are in good agreement with our earlier experimental results presented elsewhere [1].     

Experimental study of convection in a model Czochralski crucible using liquid crystal thermography

Steady state temperature distribution in a model Czochralski crucible has been mapped by liquid crystal thermography (LCT). The crucible is a water-filled glass beaker. Water is used as the test fluid because of ease of experimentation, as well as the availability of correct thermo-physical properties. In addition, the Prandtl number of water matches those of molten oxides. A copper cylinder whose diameter is smaller than that of the beaker is placed centrally at the water surface. Convection patterns are set up by applying constant temperature difference between the crucible wall and the cylinder surface, in the temperature range of the liquid crystals. The cylinder is given a fixed rotation, thus creating mixed convection conditions in the test fluid. The LCT images recorded in the present study clearly reveal convective rolls, and the interaction of buoyancy-driven convection in the crucible with cylinder rotation. The resulting temperature distributions match numerical simulation quite well. The pure buoyancy and pure rotation experiments result in axisymmetric temperature fields, while in mixed convection, the field is unsteady and three dimensional.     

Laser-induced breakdown threshold and fracture versus the nanostructure of two-phase glass

The radiation hardness and mechanical strength of single-and two-phase glasses are studied for the case when nanosecond laser pulses (λ= 1.06 μm, τ_0.5 ≈ 12.5 ns) are focused inside the material. Laser interferometry is applied to measure the displacement of the free surface, find optical breakage thresholds, and carry out the fractographic analysis of damaged regions. It is shown that breakdown channels and damage regions develop in a nonlinear manner according to optical breakdown mechanisms, changing each other with an increase in the laser energy. The strength of the two-phase glass is found to be more than four times that of the single-phase glass, although their elastic properties differ insignificantly. Such a considerable difference in the hardness of these materials with chemically similar constitutents is attributed to the presence of the double-lattice nanometer-scale structure of the two-phase glass.     

Near field imaging in microwave regime using double layer split-ring resonator based metamaterial

A planar metamaterial structure consisting of two layers of split-ring resonator (SRR) arrays is demonstrated to form the image of a point source with subwavelength resolution. The source frequency is swept through the resonance gap of the metamaterial layers and the lateral field intensity distribution is recorded on the transmission side of the metamaterial. When the source is tuned to the resonance frequency of SRRs, the metamaterial acts as a high permeability medium and a distinct image with subwavelength resolution in the lateral direction is obtained. Increasing the distance between the individual SRR layers reduces the interlayer coupling, and the intensity and spatial resolution of the image decrease rapidly.     

A Smplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction-band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron bandwidth. This calculation is supplemented by the computation of the loss of ground-state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used to estimate the energy gap in the two materials. The numerical data reported here show that the methods works, in principle, but that some extension of the scheme is also necessary to obtain fully satisfactory results.Dedicated to J.-P. Malrieu on the occasion of his 60th birthday     

Variation of supramolecular structure of heat-resistant polyimide films during thermal treatment

Variation of the supramolecular structure of heat-resistant polymide films in the course of high-temperature treatment was studied by X-ray diffraction analysis and NMR spectroscopy in solids.     

Synthesis and properties of carbon-chain polymers with pendant 1,3,4-oxadiazole rings

Carbon-chain polymers with 1,3,4-oxadiazole rings were prepared by radical polymerization and polymer-analogous transformations. The kinetic relationships of the polymerization of vinyl-1,3,4-oxadiazole monomers and some properties of the resulting polymers were studied. The thermodynamics of interaction of poly-2-vinyl-5-methyl-1,3,4-oxadiazole, a nonionic water-soluble polymer, with water was examined.     

Properties of the extraction system constituted by phosphoric acid produced from Khibiny apatite and tri-n-butyl phosphate

Data on the equilibrium distribution of phosphoric acid among the aqueous and organic phases in extraction of phosphoric acid with tri-n-butyl phosphate are presented for the system constituted by phosphoric acid produced from the Khibiny concentrate and by the extracting agent from the industrial system for purification of extraction phosphoric acid at 25–50°C.