Localized bifurcations and defect instabilities in the convection of a nematic liquid crystal

The stationary and the time-dependent homogeneous ordered states in convection may both become unstable against localized perturbations. Defects are then created and they may contribute to the disorganization of the homogeneous state. We present an experimental study of defects in some homogeneous stationary structures as well as in the traveling-wave states of convection of a nematic liquid crystal. We show that the core of the defects is a germ of the unstable state and it can become unstable under the external stress. Then, either fully homogeneous states with the symmetry of the core, or complex disordered states can develop from the local instability of defects in processes quite similar to displacive transitions in solids. Some of the main features are qualitatively similar to numerical simulations of an appropriate Landau-Ginzburg equation.     

Difference between canonical and grand canonical ensembles in discrete lattice gas models

We calculate the site occupation probabilities of one-dimensional lattice gas models within the canonical and grand canonical ensembles. The appearing differences do not vanish if we increase the system size keeping the site energies discrete. In this way one can explain the surprising numerical results of Barszczak and Kutner. This effect in the single-site occupation number disappears in higher dimensions.     

Synthesis, structure and optical properties of Eu/TiO2 nanocrystals at room temperature

The nanocrystal samples of titanium dioxide doped with europium ion (Eu³⁺/TiO₂ nanocrystal) are synthesized by the sol-gel method with hydrothermal treatment. The Eu³⁺ contents (molar ratio) in the samples are 0, 0.5%, 1%, 2%, 3% and 4%. The X-ray diffraction, UV-Vis spectroscopy data and scanning electron microscope image show that crystallite size is reduced by the doping of Eu³⁺ into TiO₂. Comparing the Raman spectra of TiO₂ with Eu³⁺/TiO₂ (molar ratio Eu³⁺/TiO₂=1%, 2% and 4%) nanocrystals at different annealing temperatures indicates that the anatase-to-rutile phase transformation temperatures of Eu³⁺/TiO₂ nanocrystals are higher than that of TiO₂. This is due to the formation of Eu-O-Ti bonds on the surface of the TiO₂ crystallite, as characterized by the X-ray photoelectron spectroscopy. The photoluminescence spectra of TiO₂ in Eu³⁺/TiO₂ nanocrystals are interpreted by the surface self-trapped and defect-trapped exciton relaxation. The photoluminescence of Eu³⁺ in Eu³⁺/TiO₂ nanocrystals has the strongest emission intensity at 2% of Eu³⁺ concentration.     

Characterization of surface deformation around Vickers indentations in InGaAsP epilayers on InP substrate

The deformation surrounding Vickers indentations on InGaAsP/InP epilayers have been studied in detail. The surface topography was characterized by using atomic force microscopy (AFM). The material pile-up and sink-in regions around the indentation impression was observed for the quaternary InGaAsP/InP epilayers. The sectional analysis mode of the AFM shows the depth profile at the indented region. Microindentation studies were carried out for different atomic fraction of the quaternary InGaAsP/InP compound semiconductor alloys. The microhardness values of InGaAsP/InP epilayers were found to be in the range of 5.08 and 5.73 GPa. These results show that the hardness value of the quaternary alloy drastically increases as the composition of As was increased by 0.01 atomic fraction and when the phosphorous concentration decreases from 0.4 to 0.38. The reason may be that the increase in As concentration hardens the lattice when phosphorous concentration was less and hardness decreases when phosphorous was increased.     

Effect of the paste molding pressure on the mechanical strength of an iron oxide catalyst in the dehydrogenation of methylbutenes

The effect of the paste molding pressure on the physicomechanical and texture characteristics of catalysts was studied. An indirect criterion is suggested to evaluate the molding pressure in industrial extruders, whose optimal value ensures good physicomechanical properties of the catalysts and kinetic control over the catalyzed reaction. The results obtained were verified in paste molding on various industrial extruders, and this enabled the optimal choice of the molding equipment.     

Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

Integrability of a system of two nonlinear Schrödinger equations

P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 2, pp. 180–184, May, 1989.