An analog to Kamenkov’s critical stability case for nonstationary systems of impulsive differential equations

A new approach to the investigation of the stability of nonlinear nonautonomous differential equations with impulse effects in critical cases is proposed. The approach is based on the direct method of Lyapunov with the use of piecewise differentiable functions. The sufficient conditions of the asymptotic stability of the critical position of equilibrium in one case are obtained. The case is analogous to Kamenkov’s critical case.     

Single-shot extreme ultraviolet laser imaging of nanostructures with wavelength resolution

We have demonstrated near-wavelength resolution microscopy in the extreme ultraviolet. Images of 50 nm diameter nanotubes were obtained with a single ~1 ns duration pulse from a desktop-size 46.9 nm laser. We measured the modulation transfer function of the microscope for three different numerical aperture zone plate objectives, demonstrating that 54 nm half-period structures can be resolved. The combination of near-wavelength spatial resolution and high temporal resolution opens myriad opportunities in imaging, such as the ability to directly investigate dynamics of nanoscale structures.     

Stochastic simulation of physicochemical processes performance over supported metal nanoparticles

The statistical lattice model has been proposed which permits one to take into account the change in the shape and surface morphology of the nanoparticle under the influence of the reaction media. The influence of monomolecular and dissociative adsorption on the particles equilibrium shape and surface morphology has been studied. It has been shown that by taking into account of attraction "adsorbate-metal" the reshaping of the initial hemispheric particle into cone-shaped one occurs induced by adsorption, similar to the experimentally observed reversible reshaping of active nanoparticles. The model reaction A+B(2) has been studied taking into account the roughening of the active particle surface and the spillover phenomena of the adsorbed A(ads) species over the support surface.     

Morphological transformations of native petroleum emulsions. I. Viscosity studies

Emulsions of water in as-recovered native crude oils of diverse geographical origin evidently possess some common morphological features. At low volume fractions varphi of water, the viscosity behavior of emulsions is governed by the presence of flocculated clusters of water droplets, whereas characteristic tight gels, composed of visually monodisperse small droplets, are responsible for the viscosity anomaly at varphi approximately 0.4-0.5. Once formed, small-droplet gel domains apparently retain their structural integrity at higher varphi, incorporating/stabilizing new portions of water as larger-sized droplets. The maximum hold-up of disperse water evidently is the close-packing limit of varphi approximately 0.74. At higher water contents (up to varphi approximately 0.83), no inversion to O/W morphology takes place, but additional water emerges as a separate phase. The onset of stratified flow (W/O emulsion gel + free water) is the cause of the observed viscosity decrease, contrary to the conventional interpretation of the viscosity maximum as a reliable indicator of the emulsion inversion point.     

C‐phosphorylation of 5,10‐dimethyl‐5,10‐dihydrophenazine and its carbo‐ and heteroanalogs

This study covers phosphorylation of heterocyclic analogues of N‐methyldiphenylamine with phosphorus tribromide in pyridine solution. The reaction is found to proceed regioselectively in accordance with the orienting effect of the amino group. Mono and bis‐phosphorylated derivatives of the heterocycles have been isolated and characterized. It is pointed out that the heterocyclic systems under study exhibit reduced reactivity in electrophilic phosphorylation as compared to N‐methyldiphenylamine. The results of calculations by the PM3 method are reported for the starting molecules and their σ‐complexes. © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:652–657, 2001     

Structural and Spectroscopic Effects of Li+ Substitution for Na+ in LixNa1-xCaGd0.5Ho0.05Yb0.45(MoO4)3 Scheelite-Type Upconversion Phosphors

A set of new triple molybdates, Li_xNa_1-xCaGd_0.5(MoO₄)₃:Ho³⁺_0.05/Yb³⁺_0.45, was successfully manufactured by the microwave-accompanied sol–gel-based process (MAS). Yellow molybdate phosphors Li_xNa_1-xCaGd_0.5(MoO₄)₃:Ho³⁺_0.05/Yb³⁺_0.45 with variation of the Li_xNa_1-x (x = 0, 0.05, 0.1, 0.2, 0.3) ratio under constant doping amounts of Ho³⁺ = 0.05 and Yb³⁺ = 0.45 were obtained, and the effect of Li⁺ on their spectroscopic features was investigated. The crystal structures of Li_xNa_1-xCaGd_0.5(MoO₄)₃:Ho³⁺_0.05/Yb³⁺_0.45 (x = 0, 0.05, 0.1, 0.2, 0.3) at room temperature were determined in space group I4₁/a by Rietveld analysis. Pure NaCaGd_0.5Ho_0.05Yb_0.45(MoO₄)₃ has a scheelite-type structure with cell parameters a = 5.2077 (2) and c = 11.3657 (5) Å, V = 308.24 (3) ų, Z = 4. In Li-doped samples, big cation sites are occupied by a mixture of (Li,Na,Gd,Ho,Yb) ions, and this provides a linear cell volume decrease with increasing Li doping level. The evaluated upconversion (UC) behavior and Raman spectroscopic results of the phosphors are discussed in detail. Under excitation at 980 nm, the phosphors provide yellow color emission based on the ⁵S₂/⁵F₄ → ⁵I₈ green emission and the ⁵F₅ → ⁵I₈ red emission. The incorporated Li⁺ ions gave rise to local symmetry distortion (LSD) around the cations in the substituted crystalline structure by the Ho³⁺ and Yb³⁺ ions, and they further affected the UC transition probabilities in triple molybdates Li_xNa_1-xCaGd_0.5(MoO₄)₃:Ho³⁺_0.05/Yb³⁺_0.45. The complex UC intensity dependence on the Li content is explained by the specificity of unit cell distortion in a disordered large ion system within the scheelite crystal structure. The Raman spectra of Li_xNa_1-xCaGd_0.5(MoO₄)₃ doped with Ho³⁺ and Yb³⁺ ions were totally superimposed with the luminescence signal of Ho³⁺ ions in the range of Mo–O stretching vibrations, and increasing the Li⁺ content resulted in a change in the Ho³⁺ multiplet intensity. The individual chromaticity points (ICP) for the LiNaCaGd(MoO₄)₃:Ho³⁺,Yb³⁺ phosphors correspond to the equal-energy point in the standard CIE (Commission Internationale de L’Eclairage) coordinates.     

Performance of a silicon monochromator under high heat load

The performance of a cryogenically cooled double‐crystal silicon monochromator was studied under high‐heat‐load conditions with total absorbed powers and power densities ranging from 8 to 780 W and from 8 to 240 W mm^?2, respectively. When the temperature of the first crystal is maintained close to the temperature of zero thermal expansion of silicon, the monochromator shows nearly ideal performance with a thermal slope error of 0.6 µrad. By tuning the size of the first slit, the regime of the ideal performance can be maintained over a wide range of heat loads, i.e. from power densities of 110 W mm^?2 (at total absorbed power of 510 W) to 240 W mm^?2 (at total absorbed power of 240 W).