An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Turbulent kinetic energy in the energy balance of a solar flare

The energy released in solar flares derives from a reconfiguration of magnetic fields to a lower energy state, and is manifested in several forms, including bulk kinetic energy of the coronal mass ejection, acceleration of electrons and ions, and enhanced thermal energy that is ultimately radiated away across the electromagnetic spectrum from optical to X-rays. Using an unprecedented set of coordinated observations, from a suite of instruments, we here report on a hitherto largely overlooked energy component -- the kinetic energy associated with small-scale turbulent mass motions. We show that the spatial location of, and timing of the peak in, turbulent kinetic energy together provide persuasive evidence that turbulent energy may play a key role in the transfer of energy in solar flares. Although the kinetic energy of turbulent motions accounts, at any given time, for only \sim (0.5-1)\% of the energy released, its relatively rapid (\sim1-10~s) energization and dissipation causes the associated throughput of energy (i.e., power) to rival that of major components of the released energy in solar flares, and thus presumably in other astrophysical acceleration sites

Structural Properties of the SnxSy Films Obtained by the Thermal Vacuum Co-evaporation

The present work deals with the study of the structural properties of the SnxSy thin films deposited by the closed-spaced vacuum co-evaporation (CSVCE) method. Calculation of temperature dependencies of the sulfur and tin vapor pressures allows to estimate growth conditions of the films with the stoichiometric composition. The effect of growth conditions on surface morphology and structural properties of SnxSy films were studied. Surface morphology of obtained films was determined by the scanning electron microscope (SEM-102Е). Structural investigations of the films were performed with the X-ray diffraction (XRD) method. The analysis of chemical composition of the layers was carried out by the scanning electron microscope by energy dispersive X-ray (ЕDAX) spectroscopy. Influence of the substrate temperature on chemical composition of thin films and their structural characteristics was also investigated

The Study of the Influence of Static Magnetic Field on Brushite Crystallization in the Presence of Magnesium

The paper describes the influence of the imposition of static magnetic field on brushite crystallization. Two different configurations of the magnetic field were used. The flasks with the precipitates were placed near the different poles. It was shown that changing the magnetic field configuration and positioning the samples in proximity to north or south poles can greatly affect their crystallinity and texture with most of them having the preferred orientation along the b-axis according to the X-Ray diffraction data. The imposition of the magnetic field also influences the microstrain ratio decreasing it significantly. It was also verified [1] that the Mg substrate availability decreases the crystallinity of DCPD. The micrographs of the nanoparticles with the different magnifications were obtained by the transmission electron microscopy (TEM). The comparative analysis of the electron microscopy data correlates with the XRD data. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3546

First imaging spectroscopy observations of solar drift pair bursts

Drift pairs are an unusual and puzzling type of fine structure sometimes observed in dynamic spectra of solar radio emission. They appear as two identical short narrowband drifting stripes separated in time; both positive and negative frequency drifts are observed. Currently, due to the lack of imaging observations, there is no satisfactory explanation for this phenomenon. Using the Low Frequency Array (LOFAR), we report unique observations of a cluster of drift pair bursts in the frequency range of 30−70 MHz made on 12 July 2017. Spectral imaging capabilities of the instrument have allowed us for the first time to resolve the temporal and frequency evolution of the source locations and sizes at a fixed frequency and along the drifting pair components. Sources of two components of a drift pair have been imaged and found to propagate in the same direction along nearly the same trajectories. Motion of the second component source is seen to be delayed in time with respect to that of the first one. The source trajectories can be complicated and non-radial; positive and negative frequency drifts correspond to opposite propagation directions. The drift pair bursts with positive and negative frequency drifts, as well as the associated broadband type-III-like bursts, are produced in the same regions. The visible source velocities are variable from zero to a few 104 (up to ∼105) km s−1, which often exceeds the velocities inferred from the drift rate (∼104 km s−1). The visible source sizes are of about 10′−18′; they are more compact than typical type III sources at the same frequencies. The existing models of drift pair bursts cannot adequately explain the observed features. We discuss the key issues that need to be addressed, and in particular the anisotropic scattering of the radio waves. The broadband bursts observed simultaneously with the drift pairs differ in some aspects from common type III bursts and may represent a separate type of emission

Influence of air Gap Between the Transformer of Resistance and Object of Monitoring on Temperature Measurement Error

In operation the description of the developed heattransfer model in thermotransformers of resistance (RTD) in the conditions of air gap between surfaces of the sensor and object of measurement is provided. Research of influence of thickness of air gap on the relative error of temperature measurement by platinum, copper and nickel thermotransformers of resistance in the ranges of temperatures corresponding to each type is executed. Dependences of minimum necessary duration of heating up of sensors on the taken temperatures are received

An Extreme Solar Event of 20 January 2005: Properties of the Flare and the Origin of Energetic Particles

The extreme solar and SEP event of 20 January 2005 is analyzed from two perspectives. Firstly, we study features of the main phase of the flare, when the strongest emissions from microwaves up to 200 MeV gamma-rays were observed. Secondly, we relate our results to a long-standing controversy on the origin of SEPs arriving at Earth, i.e., acceleration in flares, or shocks ahead of CMEs. All emissions from microwaves up to 2.22 MeV line gamma-rays during the main flare phase originated within a compact structure located just above sunspot umbrae. A huge radio burst with a frequency maximum at 30 GHz was observed, indicating the presence of a large number of energetic electrons in strong magnetic fields. Thus, protons and electrons responsible for flare emissions during its main phase were accelerated within the magnetic field of the active region. The leading, impulsive parts of the GLE, and highest-energy gamma-rays identified with pi^0-decay emission, are similar and correspond in time. The origin of the pi^0-decay gamma-rays is argued to be the same as that of lower energy emissions. We estimate the sky-plane speed of the CME to be 2000-2600 km/s, i.e., high, but of the same order as preceding non-GLE-related CMEs from the same active region. Hence, the flare itself rather than the CME appears to determine the extreme nature of this event. We conclude that the acceleration, at least, to sub-relativistic energies, of electrons and protons, responsible for both the flare emissions and the leading spike of SEP/GLE by 07 UT, are likely to have occurred simultaneously within the flare region. We do not rule out a probable contribution from particles accelerated in the CME-driven shock for the leading GLE spike, which seemed to dominate later on.Comment: 34 pages, 14 Postscript figures. Solar Physics, accepted. A typo corrected. The original publication is available at http://www.springerlink.co

Parity Violation in Proton-Proton Scattering

Measurements of parity-violating longitudinal analyzing powers (normalized asymmetries) in polarized proton-proton scattering provide a unique window on the interplay between the weak and strong interactions between and within hadrons. Several new proton-proton parity violation experiments are presently either being performed or are being prepared for execution in the near future: at TRIUMF at 221 MeV and 450 MeV and at COSY (Kernforschungsanlage Juelich) at 230 MeV and near 1.3 GeV. These experiments are intended to provide stringent constraints on the set of six effective weak meson-nucleon coupling constants, which characterize the weak interaction between hadrons in the energy domain where meson exchange models provide an appropriate description. The 221 MeV is unique in that it selects a single transition amplitude (3P2-1D2) and consequently constrains the weak meson-nucleon coupling constant h_rho{pp}. The TRIUMF 221 MeV proton-proton parity violation experiment is described in some detail. A preliminary result for the longitudinal analyzing power is Az = (1.1 +/-0.4 +/-0.4) x 10^-7. Further proton-proton parity violation experiments are commented on. The anomaly at 6 GeV/c requires that a new multi-GeV proton-proton parity violation experiment be performed.Comment: 13 Pages LaTeX, 5 PostScript figures, uses espcrc1.sty. Invited talk at QULEN97, International Conference on Quark Lepton Nuclear Physics -- Nonperturbative QCD Hadron Physics & Electroweak Nuclear Processes --, Osaka, Japan May 20--23, 199