Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations

The purpose of this paper is to present new oscillation theorems and nonoscillation theorems for the nonlinear Euler differential equation t²x''′+g(x)=0. Here we assume that xg(x)>0 if x≠0, but we do not necessarily require that g(x) be monotone increasing. The obtained results are best possible in a certain sense. To establish our results, we use Sturm’s comparison theorem for linear Euler differential equations and phase plane analysis for a nonlinear system of Liénard type.Наведено нові осцнляційні та неосцнляційні теореми для нелінійного диференціального рівняння Ейлера t²x''′+g(x)=0, де припускається, що xg(x)>0 при x≠0, але вимога про монотонне зростання g(x) не є обов'язковою. Одержані результати є найкращими у певному сенсі. Для їх встановлення використано порівняльну теорему Штурма для лінійних диференціальних рівнянь Ейлера та фазовий площинний аналіз для нелінійної системи типу Льєнарда

Charge-Focusing Readout of Time Projection Chambers

Time projection chambers (TPCs) have found a wide range of applications in particle physics, nuclear physics, and homeland security. For TPCs with high-resolution readout, the readout electronics often dominate the price of the final detector. We have developed a novel method which could be used to build large-scale detectors while limiting the necessary readout area. By focusing the drift charge with static electric fields, we would allow a small area of electronics to be sensitive to particle detection for a much larger detector volume. The resulting cost reduction could be important in areas of research which demand large-scale detectors, including dark matter searches and detection of special nuclear material. We present simulations made using the software package Garfield of a focusing structure to be used with a prototype TPC with pixel readout. This design should enable significant focusing while retaining directional sensitivity to incoming particles. We also present first experimental results and compare them with simulation.Comment: 5 pages, 17 figures, Presented at IEEE Nuclear Science Symposium 201

Coalescing binary systems of compact objects: Dynamics of angular momenta

The end state of a coalescing binary of compact objects depends strongly on the final total mass M and angular momentum J. Since gravitational radiation emission causes a slow evolution of the binary system through quasi-circular orbits down to the innermost stable one, in this paper we examine the corresponding behavior of the ratio J/M^2 which must be less than 1(G/c) or about 0.7(G/c) for the formation of a black hole or a neutron star respectively. The results show cases for which, at the end of the inspiral phase, the conditions for black hole or neutron star formation are not satisfied. The inclusion of spin effects leads us to a study of precession equations valid also for the calculation of gravitational waveforms.Comment: 22 pages, AASTeX and 13 figures in PostScrip

Survey of long-term variability of stars I. Reliability of magnitudes in old star catalogues

The comparison of visual magnitudes of stars compiled in old catalogues is expected to yield information about their long-term magnitude variations. In seven old catalogues whose historical data have been intensively compared, 2123 sampled stars have been studied, disregarding stars that we could not identify, double stars which could be misidentified, or stars observed under poor conditions, and known variable stars with large amplitude discrepancies. The independence of stellar magnitude catalogues is demonstrated by comparing seven old studies to each other, suggesting that the magnitude estimates in each catalogue reflect the brightness at each observational period. Furthermore, by comparing them with a modern star catalogue, the magnitude differences show a Gaussian distribution. Therefore, if they are sufficiently larger than the deduced standard deviations, the magnitude variations between the catalogues can be considered real. Thus, the stellar magnitudes compiled in old studies can be used as scientific data within the average intrinsic uncertainty. These seven old catalogues can be used as data for the survey of the long-term variability of stars.Comment: 7 pages including 2 figures, accepted for publication in A&

The Evolution of X-ray Bursts in the "Bursting Pulsar" GRO J1744-28

GRO J1744-28, commonly known as the `Bursting Pulsar', is a low mass X-ray binary containing a neutron star and an evolved giant star. This system, together with the Rapid Burster (MXB 1730-33), are the only two systems that display the so-called Type II X-ray bursts. These type of bursts, which last for 10s of seconds, are thought to be caused by viscous instabilities in the disk; however the Type II bursts seen in GRO J1744-28 are qualitatively very different from those seen in the archetypal Type II bursting source the Rapid Burster. To understand these differences and to create a framework for future study, we perform a study of all X-ray observations of all 3 known outbursts of the Bursting Pulsar which contained Type II bursts, including a population study of all Type II X-ray bursts seen by RXTE. We find that the bursts from this source are best described in four distinct phenomena or `classes' and that the characteristics of the bursts evolve in a predictable way. We compare our results with what is known for the Rapid Burster and put out results in the context of models that try to explain this phenomena.Comment: Accepted to MNRAS Aug 17 201