Hyperbolic Chaos of Turing Patterns

We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as 1:3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.Comment: 4 pages, 4 figure

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

Manipulation of Microparticles By Bessel Light Beam

We consider perspectives of optical manipulation of microscopic objects in the area of biology, biophysics and medicine. The first part of the work is devoted to a brief review of the microparticles’ manipulation. The second part contains calculations of the focusing of laser radiation parameters and some results on the formation of Bessel light beams. The experimental setup based on the optical manipulation technique of micron-sized particles was developed

Flow distributed oscillation, flow velocity modulation and resonance

We examine the effects of a periodically varying flow velocity on the standing and travelling wave patterns formed by the flow-distributed oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a simple, spatiotemporally periodic longitudinal displacement. On the other hand, when the diffusion is significant, periodic modulation of the velocity can disrupt the wave pattern, giving rise in the downstream region to travelling waves whose frequency is a rational multiple of the velocity perturbation frequency. We observe frequency locking at ratios of 1:1, 2:1 and 3:1, depending on the amplitude and frequency of the velocity modulation. This phenomenon can be viewed as a novel, rather subtle type of resonant forcing.Comment: submitted to Phys. Rev.

Bullouslung disease in children

Article presents the data about results ofa medical examination and treatment of children with bullous lung disease operatedin Nizhniy Novrogod Regional Children’s Clinical Hospital. Part of CT scan registered in diagnostic of this pathology. Effectivenessof thoracoscopyproved in treatment of the bullous lung disease in children.В сообщении представлены данные о результатах обследования и лечения детей с буллезной болезнью легких, прооперированных в Нижегородской областной детской клинической больнице. Отмечена роль компьютерной томографии в диагностике данной патологии. Доказана эффективность торакоскопии в лечении буллезной болезни легких у детей

Novel A-B type oscillations in a 2-D electron gas in inhomogenous magnetic fields

We present results from a quantum and semiclassical theoretical study of the $\rho_{xy}$ and $\rho_{xx}$ resistivities of a high mobility 2-D electron gas in the presence of a dilute random distribution of tubes with magnetic flux $\Phi$ and radius $R$, for arbitrary values of $k_f R$ and $F=e\Phi/h$. We report on novel Aharonov-Bohm type oscillations in $\rho_{xy}$ and $\rho_{xx}$, related to degenerate quantum flux tube resonances, that satisfy the selection rule ${(k_fR)}^2=4F(n+{1\over 2})$, with $n$ an integer. We discuss possible experimental conditions where these oscillations may be observed.Comment: 11 pages REVTE

Power supply of remote objects

У роботі розглянуто порядок вибору системи електропостачання промислового об’єкта, що віддалений від енергосистеми, розглянуто можливість встановлення дизель-генераторів, а також побудови лінії від центру живлення. Виконане моделювання за допомогою середовища Mathlab.In the article it has been discussed how to select the power supply system of the site which is remoted from the grid. Installation of a diesel generator and the construction of a line from the center of power have been considered. Method for determining the optimal method of remote object supplying was created in this article. It has been simulated by Mathlab.В работе рассмотрен порядок выбора системы электроснабжения промышленного объекта, который отдален от энергосистемы, рассмотрена возможность установки дизель-генератора, а также построения линии от центра питания. Выполнено моделирование с помощью среды Mathlab

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

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

Penetration of the magnetic field into the twinning plane in the type I and II superconductors

It is demonstrated that in the type I and II superconductors with low-transparent twinning planes (TP) the penetration of external parallel magnetic field into the region of the twinning plane can be energetically favorable. In the type I superconductors the twinning planes become similar to Josephson junctions and the magnetic field penetrates into the center of the TP in the form of soft Josephson-like vortices. This leads to increase in the critical magnetic field values. The corresponding phase diagram in the parameter plane "temperature - magnetic field" essentially differs from the one obtained without taking the finite value of the magnetic field near the TP into account. Comparison between obtained phase diagrams and experimental data for different type I superconductors can allow to estimate the value of the TP transparency, which is the only fitting parameter in our theory.Comment: 5 pages, 2 figure