On the numerical construction of an attractor for the Navier-Stokes system

In this paper the problem of the numerical approximation of the minimal global B-attractor for a semiflow generated by the Navier-Stokes equations in a two-dimensional bounded domain Ω is considered. The method suggested here is based on the formula , where G^N is a sequence of compact subsets of L₂(Ω), . The procedure of constructing G^N is finite and includes the numerical solution of the Navier-Stokes equations by means of the Galerkin method, together with an explicit finite-difference discretization in time. Bibliography: 5 titles. To dear teacher Olga A. Ladyzhenskaya on the occasion of the jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 200, 1992, pp. 91–97. Translated by V. I. Ochkur.     

A projection approach to optimal control of elastic beam dynamics

Controlled lateral motions of an elastic beam – extended body with a cuboid shape – are studied. A generalized statement of the initial-boundary value problem is given in the frame of 3D linear elasticity based on the integral formulation of constitutive relations. A numerical approach relying on the Fourier method and semi-discretization technique is proposed to design the optimal boundary control that moves the beam to a given final state and minimizes a quadratic cost function. Some results of numerical simulation and quality analysis are presented and discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dimephosphone analogs: II. Dialkyl(diaryl)-(2-methyl-4-oxopent-2-yl)phosphine oxide oximes: Synthesis,structure, and generation of iminoxyl radicals

Dialkyl(diaryl)-(2-methyl-4-oxopent-2-yl)phosphine oxide oximes have been synthesized for the first time. According to the X-ray diffraction data, these compounds in crystal exist as a single E isomer. Their structure in solution and the E/Z isomer ratio were determined by ¹H and ¹³C NMR spectroscopy.     

Heterogeneous-catalytic decomposition of ethylenediaminetetraacetic acid and its complexes with iron,nickel, and cobalt on carbon materials in nitrate media

Catalytic thermal destruction of ethylenediaminetetraacetic acid and its complexes with nickel, iron, and cobalt in nitrate solutions on carbon materials (activated unwoven material, sibunite, and BAU–A activated carbon) was studied. The activation energies of thermal destruction were calculated.     

Focusing of a high-energy particle beam at an extremely short distance

It has recently been realized that the focusing of high-energy particle beams at a distance of about 1 cm is promising. A new idea is proposed in this work to focus the beam at a short distance by using a bent plane–parallel silicon plate whose side edges are rotated at a small angle with respect to crystallographic planes. At the U-70 accelerator (IHEP, Protvino), a 50-GeV proton beam has been focused to a narrow line with a width of no more than 30 μm at a distance of 17 cm.     

Characteristics of a cylindrical magnetron and reactive sputtering of binary compound films

The characteristics of a cylindrical magnetron, such as the dependences of the discharge voltage, chamber pressure, and plasma radiation intensity on the reactive gas flow rate and discharge current, are studied. In this magnetron, titanium nitride (TiN) and titanium dioxide (TiO₂) films are obtained by reactive magnetron sputtering. The transmission and reflection spectra of the films in the visual range are taken. From the transmission data for the TiO₂ films, their refractive index and absorption factor in the wavelength range 350–800 nm, as well as the porosity, are found by the Valeev method. The variation of the fundamental absorption edge with film thickness is determined with the Urbach formula.