Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable motion. We also investigate situations when the particle dynamics exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincar\'e surfaces of section and of recurrence plots.Comment: 11 pages, 6 figures, published in the proceedings of the conference "Relativity and Gravitation: 100 Years after Einstein in Prague" (25. - 29. 6. 2012, Prague

Plasma Speaker

The article describes the design and construction of one-channel plasma speaker. Absence of mechanical membrane gives the plasma speaker no frequency limitation. The design consists of power source to supply control electronic for signal modulation, converter and output transformer. Modulation of audio signal is realized by integrated circuit TL 594 that provides the PWM modulation. Duty cycle and frequency is adjusted by potentiometers. Dual forward converter is used to voltage amplification. High voltage discharge between the electrodes on the secondary winding is modulated by the PWM signal and produces sound

Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects

Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the Recurrence Plots (RP) and we compare them with Poincar\'e surfaces of section. We describe the Recurrence Plots in terms of the Recurrence Quantification Analysis (RQA), which allows us to identify the transition between different dynamical regimes. We demonstrate that this new technique is able to detect the chaos onset very efficiently, and to provide its quantitative measure. The chaos typically occurs when the conserved energy is raised to a sufficiently high level that allows the particles to traverse the equatorial plane. We find that the role of the black-hole spin in setting the chaos is more complicated than initially thought.Comment: 21 pages, 20 figures, accepted to Ap

Comparison of tillage systems in terms of water infiltration into the soil during the autumn season

ArticleThe soil belongs to the most valuable parts of the planet Earth. It is, endangered by water erosion, which causes huge destruction every year, or damage to farmland. More than half of the agricultural land in the Czech Republic is threatened by water erosion. The measurement was performed in the location Nesperská Lhota. The trial has been established on loamy sand Cambisol. In the field experiment, there were created 6 different variants which wad differed by soil tillage and crop. In the individual variants maize and oats were located. The field trial has been existing for a long time, as it was founded in 2009. Two measuring methods of water infiltration were used for the measurements: a mini disk infiltrometer and a single ring. The measurement was performed in the period of September 2016 before the harvest of maize. The soil aggregates were already stabilized at that time after all tillage operations. The measurement result showed the difference between the methods of soil tillage. The greatest ability of infiltration had a variant of maize with inter-row oats. Surprisingly, it was followed by maize, which was processed by ploughing technology. The lowest infiltration capacity was showed by oats reduced by soil tillage. A variant without vegetation had the second lowest infiltration. Our results obtained at rate of water infiltration into the soil affirm the need to control measures in the late vegetative stages. It is important for most of the rainfall to be quickly infiltrated so that it prevents the formation of massive surface runoff

On prediction of non-uniform temperature fields in heat analysis of aero engines using machine learning approach

Authors acknowledge support from the ESIF, EU Operational Programme Research, Develop ment and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/ 0.0/0.0/16 019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague. This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS22/151/OHK2/3T/12

Equilibrium conditions of spinning test particles in Kerr-de Sitter spacetimes

Equilibrium conditions and spin dynamics of spinning test particles are discussed in the stationary and axially symmetric Kerr-de Sitter black-hole or naked-singularity spacetimes. The general equilibrium conditions are established, but due to their great complexity, the detailed discussion of the equilibrium conditions and spin dynamics is presented only in the simple and most relevant cases of equilibrium positions in the equatorial plane and on the symmetry axis of the spacetimes. It is shown that due to the combined effect of the rotation of the source and the cosmic repulsion the equilibrium is spin dependent in contrast to the spherically symmetric spacetimes. In the equatorial plane, it is possible at the so-called static radius, where the gravitational attraction is balanced by the cosmic repulsion, for the spinless particles as well as for spinning particles with arbitrarily large azimuthal-oriented spin or at any radius outside the ergosphere with a specifically given spin orthogonal to the equatorial plane. On the symmetry axis, the equilibrium is possible at any radius in the stationary region and is given by an appropriately tuned spin directed along the axis. At the static radii on the axis the spin of particles in equilibrium must vanish

Compressor cascade total pressure loss correlation modelling at design points using artificial neural networks

grant No. SGS22/148/OHK2/3T/12, project TK03030121 Conceptual Design of an Innovative Safety System for Gas-cooled Nuclear Reactor

Compressor cascade correlations modelling at design points using artificial neural networks

In recent years, the flow analysis by means of computational fluid dynamics (CFD) has become a useful design and optimization tool. Unfortunately, despite advances in the computational power, numerical simulations are still very time consuming. Thus, empirical correlation models keep their importance as a tool for early stages of axial compressor design and for prediction of basic performance parameters. These correlations were developed based on experimental data obtained from 2D measurements performed on cases of classical airfoils such as the NACA 65-series or C.4 profiles. There is insufficient amount of experimental data for other families of airfoils, but CFD simulations can be used instead and their results correlated using artificial neural networks (ANN), as described in this work. Unlike the classical deep learning approach using perceptrons, this work presents neural networks employing higher order neural units