Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors

We consider a chain of oscillators with hyperbolic chaos coupled via diffusion. When the coupling is strong the chain is synchronized and demonstrates hyperbolic chaos so that there is one positive Lyapunov exponent. With the decay of the coupling the second and the third Lyapunov exponents approach zero simultaneously. The second one becomes positive, while the third one remains close to zero. Its finite-time numerical approximation fluctuates changing the sign within a wide range of the coupling parameter. These fluctuations arise due to the unstable dimension variability which is known to be the source for non-hyperbolicity. We provide a detailed study of this transition using the methods of Lyapunov analysis.Comment: 24 pages, 13 figure

Fast numerical test of hyperbolic chaos

The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a distribution of a characteristic value which is bounded within the unit interval and whose zero indicate the presence of tangency between expanding and contracting subspaces. To perform the test one needs to solve several copies of equations for infinitesimal perturbations whose amount is equal to the sum of numbers of positive and zero Lyapunov exponents. Since for high-dimensional system this amount is normally much less then the full phase space dimension, this method provide the fast and memory saving way for numerical hyperbolicity test of such systems.Comment: 4 pages and 4 figure

Contribution of α2\alpha^2-terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter

It is shown that the corrections of $\alpha^2$ order to the total cross sections for interaction of elementary hydrogen-like atoms with target atoms, reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520 (1987)], do not include some terms of the same order of magnitude. That results in a significant contribution of these corrections in particular cases. The full $\alpha^2$-corrections have been derived and it is shown that they are really small and could be omitted for most practical applications.Comment: 5 page

Location of the Energy Levels of the Rare-Earth Ion in BaF2 and CdF2

The location of the energy levels of rare-earth (RE) elements in the energy band diagram of BaF2 and CdF2 crystals is determined. The role of RE3+ and RE2+ ions in the capture of charge carriers, luminescence, and the formation of radiation defects is evaluated. It is shown that the substantial difference in the luminescence properties of BaF2:RE and CdF2:RE is associated with the location of the excited energy levels in the band diagram of the crystals

Изготовление элементов проточной части модели бустерного s-насоса двустороннего действия

The article describes a new design of the primary pump to run in powerful units (more than 1 GW) of power plants. The new construction has some advantages such as compactness, theoretical lack of radial and axial forces, and high efficiency in a wide range of flow. The abovementioned advantages can be possible owing to applying an innovative shape of the pump flow path. An impeller with the guide vanes forms the three-row single stage in the each row axial double entry blade system. The inlet and outlet parts have a shape of the involute that can ensure (according to calculated data) the efficiency and stability in a wide range of flow because of a lack of the spiral parts. The results of numerical calculations of the pump working flow theoretically confirm that demanding parameters of the pump (H=286 m; Q=1,15 m3 /s) can be obtained with competitive efficiency. To verify the proposed advantages of the construction, there was decision made to conduct the real physical experiment. For this purpose the small model of a real pump was designed with parameters H=14 m, Q=13 l/s. Construction of the pump model has a cartridge conception. In addition, there is a possibility for quick replacement of the some parts of the blade system in case of operational development of the pump. In order to obtain hydraulic characteristics of the pump to say nothing of the electromotor the torque gauge coupling is used. Numerical calculations for the pump model were also performed which confirm the operability. For manufacturing of the blade system the new perspective technology is applied. The main hydraulic components (impellers and guide vanes) are made of ABS plastic by using 3D-printer. According to this technology parts are made layer by layer by means of welded plastic filament. Using this method the satisfactory tolerance (approximately ±0,3 mm) of the parts was obtained. At that moment, it is possible to create the parts with the maximum size no higher than 150 mm. Immersing finished parts in acetone vapor enable us to increase the surface strength and reduce roughness. At this stage of the work some plastic parts are ready for assembling operation. Now manufacturing of other plastic parts of the blade system is under way along with pre-production of the rotor and stator components.Излагается процесс изготовления элементов проточной части полирядного лопастного насоса с s-образной меридиональной проекцией и элементами подвода и отвода в форме эвольвенты. Приведена конструкция опытной модели бустерного s-насоса двустороннего действия. В основу конструкции заложена картриджная концепция агрегата. Изложены результаты численного моделирования рабочего процесса проточной части модели. Описана технология изготовления элементов проточной части насоса из высокопрочного ABS пластика с применением 3D-принтера с последующей процедурой поверхностного упрочнения готовых изделий в парах ацетона. Показаны изготовленные детали рабочих органов активной части насоса: колесо рабочее, аппарат направляющий, шнек. DOI: 10.7463/aplts.0415.079327

Check of knowleadge using score-rating system and independent test control

Анализируется проблема дублирования балльно-рейтинговой системы оценивания и независимого тестового контроля в системе подготовки специалистов. Предложены мероприятия по устранению недостатковIn article it is told about duplication of score-rating system and independent test controlin training system of specialists. Actions for elimination of shortcomingsare offere

Violation of hyperbolicity in a diffusive medium with local hyperbolic attractor

Departing from a system of two non-autonomous amplitude equations, demonstrating hyperbolic chaotic dynamics, we construct a 1D medium as ensemble of such local elements introducing spatial coupling via diffusion. When the length of the medium is small, all spatial cells oscillate synchronously, reproducing the local hyperbolic dynamics. This regime is characterized by a single positive Lyapunov exponent. The hyperbolicity survives when the system gets larger in length so that the second Lyapunov exponent passes zero, and the oscillations become inhomogeneous in space. However, at a point where the third Lyapunov exponent becomes positive, some bifurcation occurs that results in violation of the hyperbolicity due to the emergence of one-dimensional intersections of contracting and expanding tangent subspaces along trajectories on the attractor. Further growth of the length results in two-dimensional intersections of expanding and contracting subspaces that we classify as a stronger type of the violation. Beyond of the point of the hyperbolicity loss, the system demonstrates an extensive spatiotemporal chaos typical for extended chaotic systems: when the length of the system increases the Kaplan-Yorke dimension, the number of positive Lyapunov exponents, and the upper estimate for Kolmogorov-Sinai entropy grow linearly, while the Lyapunov spectrum tends to a limiting curve.Comment: 11 pages, 11 figures, results reproduced with higher precision, new figures added, text revise

Accounting of motivators and demotivators under introduction of the brc system

Рассматривается необходимость учета демотиваторов при работе с балльно-рейтинговой системой оцениванияThe article considers the need to take into account demotivators when working with the BRS syste

Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure