Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.Comment: 17 pages, RevTeX LATeX file, to appear in Journal of Mathematical Physic

The confinement of phonon propagation in TiAlN/Ag multilayer coatings with anomalously low heat conductivity

TiAlN/Ag multilayer coatings with a different number of bilayers and thicknesses of individual layers were fabricated by DC magnetron co-sputtering. Thermal conductivity was measured in dependence of Ag layer thickness. It was found anomalous low thermal conductivity of silver comparing to TiAlN and Ag bulk standards and TiAlN/TiN multilayers. The physical nature of such thermal barrier properties of the multilayer coatings was explained on the basis of reflection electron energy loss spectroscopy. The analysis shows that nanostructuring of the coating decreases the density of states and velocity of acoustic phonons propagation. At the same time, multiphonon channels of heat propagation degenerate. These results demonstrate that metal-dielectric interfaces in TiAlN/Ag coatings are insurmountable obstacles for acoustic phonons propagation

Sub-milliarcsecond Imaging of Quasars and Active Galactic Nuclei. IV. Fine Scale Structure

We have used VLBA fringe visibility data obtained at 15 GHz to examine the compact structure in 250 extragalactic radio sources. For 171 sources in our sample, more than half of the total flux density seen by the VLBA remains unresolved on the longest baselines. There are 163 sources in our list with a median correlated flux density at 15 GHz in excess of 0.5 Jy on the longest baselines. For about 60% of the sources, we have at least one observation in which the core component appears unresolved (generally smaller than 0.05 mas) in one direction, usually transverse to the direction into which the jet extends. BL Lacs are on average more compact than quasars, while active galaxies are on average less compact. Also, in an active galaxy the sub-milliarcsecond core component tends to be less dominant. IDV sources typically have a more compact, more core-dominated structure on sub-milliarcsecond scales than non-IDV sources, and sources with a greater amplitude of intra-day variations tend to have a greater unresolved VLBA flux density. The objects known to be GeV gamma-ray loud appear to have a more compact VLBA structure than the other sources in our sample. This suggests that the mechanisms for the production of gamma-ray emission and for the generation of compact radio synchrotron emitting features are related. The brightness temperature estimates and lower limits for the cores in our sample typically range between 10^11 and 10^13 K, but they extend up to 5x10^13 K, apparently in excess of the equipartition brightness temperature, or the inverse Compton limit for stationary synchrotron sources. The largest component speeds are observed in radio sources with high observed brightness temperatures, as would be expected from relativistic beaming (abridged).Comment: 31 pages, 13 figures, 4 tables, accepted for publication in the Astronomical Journal; minor changes to the text are mad

Nonlinear acoustic waves in channels with variable cross sections

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted symmetry group is extended and the invariant solutions corresponding to these profiles are obtained. Approximate analytic solutions to the generalized Webster equation are derived for channels with smoothly varying cross sections and arbitrary initial conditions.Comment: Revtex4, 10 pages, 2 figure. This is an enlarged contribution to Acoustical Physics, 2012, v.58, No.3, p.269-276 with modest stylistic corrections introduced mainly in the Introduction and References. Several typos were also correcte

Investigation of the effect of high strength strips steel modification with rare-earth metal (REM)

The present work describes the study on influence of modifying steel with rare-earth metals on metallurgical quality of ingots and finished steel. To achieve the assigned task, the laboratory melting of 08G2NMDFBT (Х100) pipe steel was carried as in open (UIP 100 – 2,4), so in vacuum induction furnace (ISV-0,01 - PI) with use of conditioning agents, which contain rare-earth metals. Next materials were used as conditioning agents: mischmetal (MM), which contain total amount of rare-earth metal (REM) up to 93 %, АlPCIr and RENTN which contain total amount of from 31 to 32,6 %

Stable multiple-charged localized optical vortices in cubic-quintic nonlinear media

The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and two-charged but also multiple-charged stable vortex solitons do exist. A vortex soliton occurs robust with respect to symmetry-breaking modulational instability in the self-defocusing regime provided that its radial profile becomes flattened, so that a self-trapped wave beam gets a pronounced surface. It is demonstrated that the dynamics of a slightly perturbed stable vortex soliton resembles an oscillation of a liquid stream having a surface tension. Using the idea of sustaining effective surface tension for spatial vortex soliton in a media with competing nonlinearities the explanation of a suppression of the modulational instability is proposed.Comment: 4 pages, 3 figures. Submitted to Journal of Optics A. The proceedings of the workshop NATO ARW, Kiev 2003 Singular Optics 200

Features of Structural and Phase Transformations in Mo–Si–B and Сr–Al–Si–B Systems During Self-Propagating High-Temperature Synthesis

This study is dedicated to investigation of the combustion mechanisms during the SHS of ceramic materials in multicomponent Mo–Si–B and Cr–Al–Si–B systems. It is concluded that the following processes are defined the SHS for Si-rich Mo–Si–B compositions: Si melting, its spreading over the surfaces of the solid Mo and B particles, followed by B dissolution in the melt, and formation of intermediate Mo3Si phase film. The subsequent diffusion of Si into Mo results in the formation of MoSi2 grains and MoB phase forms due to the diffusion of Mo into B-rich melt. The formation of MoB phase for B-rich compositions may occur via gas-phase mass transfer of MoO3 gaseous species to B particles and B2O2 to Mo particles. In Cr–Al–Si–B system firstly, the Al–Si eutectic mixture undergoes contact melting followed by formation of the reactionary surface as the eutectic melt spreads over the Cr and B particles surface. An increase in Al content increases the proportion of the Al–Si eutectic melt. The dissolution of Cr particles in this melt becomes the rate-limiting stage of the combustion process. The melt is saturated with these elements followed by crystallization of CrB and Cr(Si,Al)2 grains. In the Cr- and B-rich areas and low melt concentration, the formation of CrB may occur via gas-phase mass transfer of B2O2 gaseous species to Cr particles. Consecutive formation of chromium and molybdenum borides and silicides is established by means of dynamic X-ray diffraction analysis. Compact ceramic samples were produced using forced SHS pressing technique. Their structural investigations were conducted by XRD and SEM

The July 2010 outburst of the NLS1 PMN J0948+0022

We report about the multiwavelength campaign on the Narrow-Line Seyfert 1 (NLS1) Galaxy PMN J0948+0022 (z = 0.5846) performed in 2010 July-September and triggered by high activity as measured by Fermi/LAT. The peak luminosity in the 0.1-100 GeV energy band exceeded, for the first time in this type of source, the value of 10^48 erg/s, a level comparable to the most powerful blazars. The comparison of the spectral energy distribution of the NLS1 PMN J0948+0022 with that of a typical blazar - like 3C 273 - shows that the power emitted at gamma rays is extreme.Comment: 2011 Fermi Symposium proceedings - eConf C11050

Оценка боковой силы при взаимодействии колеса автомобиля с дорожной колеёй

The operation of roads under modern conditions associated with high speeds and traffic density results in wear of pavement and formation of a rut. When crossing the ruts, instability can occur when relatively small steering inputs lead to large changes in the trajectory. The lateral force acting on a wheel of a car is of particular importance in the study of stability and controllability. The magnitude of this force is determined by various factors: tire stiffness, speed, change in the angle of rotation of the wheel, the geometry of the transverse profile of the rut.The objective of the study refers to the problem of determining the angles of inclination of side walls of the rut that are safe for movement at different speeds. The paper considers the interaction of a car wheel with the road surface, proposes a mathematical model for interaction of a tire with ruts, considers the angle of the wheel running on the rut wall. To describe the elastic response of a tire in contact with a rut, an elastic foundation model and a plane section method are used. The lateral force was estimated based on equations of motion of the wheel when crossing the rut. The dependences of the ratio of the lateral force to the normal load for various rut depths and angles of inclination of its walls on the angle of rotation of the wheel and the speed of the vehicle were obtained. It is shown that at a rut inclination angle exceeding five degrees, the lateral force begins to increase significantly with an increase in the angle of rotation of the wheel, as well as the speed of the vehicle, and may exceed the applied normal load. According to the condition of vehicle stability against skidding on a wet surface, limiting average angles of inclination of the side walls of the rut are estimated for various values of the vehicle speed and wheel rotation angles.Эксплуатация дорог в современных условиях, связанных с высокими скоростями и плотностью потоков, приводит к изнашиванию покрытия и образованию дорожной колеи. При пересечении колеи может возникать неустойчивость движения, когда относительно небольшие воздействия при управлении приводят к большим изменениям траектории. Особое значение при изучении устойчивости и управляемости приобретает боковая сила, действующая на колесо автомобиля. Величина этой силы определяется различными факторами: жёсткостью шины, скоростью, изменением угла поворота колеса, геометрией поперечного профиля колеи.Цель настоящего исследования связана с проблемой определения безопасных для движения углов наклона боковых стенок дорожной колеи при разных скоростных режимах. В работе рассмотрено взаимодействие колеса автомобиля с дорожным покрытием, предложена математическая модель взаимодействия шины с колеёй, принимая во внимание угол набегания колеса на стенку колеи. Для описания упругого отклика шины в контакте с колеёй используется модель упругого основания и метод плоских сечений. На основе уравнений движения колеса при пересечении колеи проведена оценка боковой силы. Получены зависимости отношения боковой силы к нормальной нагрузке для различной глубины колеи и углов наклона её стенок от угла поворота колеса и скорости движения автомобиля. Показано, что при угле наклона колеи, превышающем пять градусов, боковая сила начинает существенно возрастать с ростом угла поворота колеса, а также скорости движения автомобиля и может превысить приложенную нормальную нагрузку. По условию устойчивости автомобиля против заноса на мокром покрытии дана оценка предельных средних углов наклона боковых стенок колеи при различных значениях скорости движения автомобиля и углов поворота колеса