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

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

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

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

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

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