How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Deposition of copper coatings in a magnetron with liquid target

Copper coatings were deposited on monocrystalline Si substrates using a magnetron discharge with a liquid cathode in the metal vapour plasma. During the deposition, the bias voltage in the range from 0 V to–400 V was applied to the substrate. The prepared films were investigated by a scanning electron microscope, and their adhesive properties were studied using a scratch tester. It was demonstrated that the adhesion of the deposited films strongly depends on the bias voltage and varies in a wide range.

     

Temperature-controlled 'breathing' of carbon dioxide bubbles

We report a microfluidic (MF) approach to studies of temperature mediated carbon dioxide (CO(2)) transfer between the gas and the liquid phases. Micrometre-diameter CO(2) bubbles with a narrow size distribution were generated in an aqueous or organic liquid and subsequently were subjected to temperature changes in the downstream channel. In response to the cooling-heating-cooling cycle the bubbles underwent corresponding contraction-expansion-contraction transitions, which we term 'bubble breathing'. We examined temperature-controlled dissolution of CO(2) in four exemplary liquid systems: deionized water, a 0.7 M aqueous solution of NaCl, ocean water extracted from Bermuda coastal waters, and dimethyl ether of poly(ethylene glycol), a solvent used in industry for absorption of CO(2). The MF approach can be extended to studies of other gases with a distinct, temperature-dependent solubility in liquids.     

Development of protective metal coatings on aluminum by magnetron sputtering

Depositions of copper and titanium coatings on aluminum foils and polished aluminum plates for thier protection against corrosion in alkaline media were performed. The coatings were deposited in three different types of magnetron sputtering systems: a direct current (DC) magnetron discharge, a high current impulse magnetron discharge, and a DC magnetron discharge with melted cathode. Only aluminum foils coated with copper films obtained by combined ion-plasma technology, which included preliminarily sputtering of the aluminum surface with an ion beam, deposition of a dense interlayer in the DC magnetron discharge with ion assistance of initial stage of deposition, and deposition of additional layer in the magnetron discharge with melted cathode, were resistant against 30 wt % NaOH solution.     

The effect of synthesis conditions on the structure of compounds formed in the Dy<Subscript>2</Subscript>O<Subscript>3</Subscript>–TiO<Subscript>2</Subscript> system

Crystallization and phase transition processes taking place in the Dy₂O₃–TiO₂ system during the isothermal annealing of the precursors synthesized by co-precipitation were studied. The phase composition of the obtained powders is determined by not only the chemical composition of the precursor (Dy₂O₃: TiO₂ ratio) and annealing temperature but also by the procedure of precursor synthesis determining the uniformity of Dy and Ti distribution in the precursor precipitate. Higher homogeneity of precursor particles provides the formation of almost single-phase nanocrystaline dysprosium titanate (Dy₂TiO₅, Dy₂Ti₂O₇) powders at annealing temperatures of 800–1000°C.     

Coxeter polytopes with a unique pair of non-intersecting facets

We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88-91] and the second author [P. Tumarkin, Compact hyperbolic Coxeter n-polytopes with n+3 facets, Electron. J. Combin. 14 (2007), R69, 36 pp.], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and in dimension 8.     

Domain epitaxial growth of ferroelectric films of barium strontium titanate on sapphire

A model of the epitaxial growth of crystalline multicomponent films on single-crystal substrates with a domain correspondence is presented using a solid solution of barium strontium titanate on sapphire substrates (r cut). The domain epitaxial growth suggests the matching of the lattice planes of the film and the substrate having similar structures by comparison of domain multiple of an integral number of the interplanar spacings. Variation of the component composition of the solid solution enables changes in the domain size in the range sufficient for epitaxial growth. This method can be used to project the epitaxial growth of films of various solid solutions on single-crystal substrates.     

Microwave properties of film Ba x Sr1 ? x TiO3 ferroelectric variconds with a magnesium-containing additive

The electrophysical properties of bulk ceramics based on Ba _x Sr_{1 ? x} TiO₃ solid solutions with a Mg-containing additive and planar variconds based on ferroelectric films obtained by the ion-plasma sputtering of targets with different elemental compositions are studied. Controllability n(U) = C(0)/C(U) and the dielectric loss tangent (tan??) of ferroelectric variconds are measured as functions of the elemental composition of the ferroelectric. The figure of merit of the variconds is estimated, and the film composition providing the best electrophysical parameters is determined.     

Hyperbolic subalgebras of hyperbolic Kac–Moody algebras

We investigate regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras via their Weyl groups. We classify all subgroup relations between Weyl groups of hyperbolic Kac–Moody algebras, and show that for every pair of a group and subgroup there exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for a given hyperbolic Kac–Moody algebra, and present a finite algorithm classifying all embeddings.