Potential systems for PDEs having several conservation laws

A generalization of the usual procedure for constructing potential systems for systems of partial differential equations with multidimensional spaces of conservation laws is considered. More precisely, for the construction of potential systems with a multi-dimensional space of local conservation laws, instead of using only basis conservation laws, their arbitrary linear combinations are used that are inequivalent with respect to the equivalence group of the class of systems or symmetry group of the fixed system. It appears that the basis conservation laws can be equivalent with respect to groups of symmetry or equivalence transformations, or vice versa; in this sense the number of independent linear combinations of conservation laws can be grater than the dimension of the space of conservation laws. The first possibility leads to an unnecessary, often cumbersome, investigation of equivalent systems, the second one makes possible that a great number of inequivalent potential systems are missed. Examples of all these possibilities are given.     

Anomalous light transmission by nematic liquid crystal cells

Light transmission through nematic liquid crystal (NLC) cells with a planar alignment and various boundary conditions has been studied as a function of the bias voltage in the regimes of maximum transmittance and complete extinction. The phenomenon of anomalous light leakage in the regime of complete extinction has been observed in the NLC sells with alignment layers of amorphous hydrogenated carbon (a-C:H) and poly(vinyl alcohol) (PVA), in which an anisotropy was induced by rubbing the electrode surface (for a-C:H) and the alignment layer (for PVA). The anomalous transmission is caused by the deformation of nematic molecules, which are situated near the surface, in the direction perpendicular to the direction of rubbing. The magnitude of anomalous transmission increases with the bias voltage. This behavior is explained by the anisotropy of the surface anchoring energy of nematic molecules at the interface.     

Catalytic hydrodesulfurization of petroleum distillates

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 12, pp. 6–7, December, 1990.     

Deactivation of titanium during temperature-induced hydrogen absorption–desorption cycling: I. Effects of water, oxygen and nitrogen traces

The cyclic stability of metallic titanium during absorption–desorption runs in continuous flow system has been studied in the presence of variable level of impurities such as H₂O, O₂ and N₂ in argon and helium flows. Hydrogen absorption–desorption cycles performed in vacuo were reproducible with respect to the absorption rates and uptakes, while absorption–desorption cycles carried out in the flows of carrier gases in the thermoprogrammed mode resulted in the gradual decrease of hydrogen uptakes followed by a shift of absorption maxima from 800 K to 1000 K.

Mass-spectral analysis of the main impurities in a flow of gases revealed that during hydrogen absorption–desorption traces of water, oxygen and nitrogen are consumed by titanium. For the samples subjected to several absorption–desorption cycles in the flow of inert gas XRD revealed the formation of nitrogen-containing titanium compounds, while XPS showed surface enrichment in nitrogen, while oxygen concentration was constant. Nitrogen consumed at higher temperatures during the TPD runs provides better inhibition of hydrogen absorption compared to water and oxygen. Final deactivation state of titanium correlates in general with the overall amount of impurities in the stream.

Although deactivation is controlled mostly by the level of toxic impurities in the feed, certain parameters, i.e., hydrogen absorption/desorption rates are dependent on the nature of neutral media—in contrast to helium, noticeable hydrogen desorption occurs even at room temperature in a flow of pure argon.     

Glass formation in oxide-halide systems

Recently the halide and oxidechalide glasses have been the object of great interest because they are promising materials for optics. Up to now many unsolved problems exist in relation to their glass formation, chemical resistance and the thermal stability of these glasses. An object of our investigation is the study of the glass formation in halide systems with the participation of PbCl₂, NaCl, KCl, BaCl₂ and oxide-halide systems with the participation of the TeO₂. The ranges of glass formation in the systems: TeO₂-PbCl₂-NaCl-KCl and TeO₂-BaCl₂-CdCl₂-NaCl are determined at different cooling rates. Stable glasses possessing low melting temperature, good chemical resistance were prepared.