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

Simulation of the Directional Dark Matter Detector (D3) and Directional Neutron Observer (DiNO)

Preliminary simulation and optimization studies of the Directional Dark Matter Detector and the Directional Neutron Observer are presented. These studies show that the neutron interaction with the gas-target in these detectors is treated correctly by GEANT4 and that by lowering the pressure, the sensitivity to low-mass WIMP candidates is increased. The use of negative ion drift might allow us to search the WIMP mass region suggested by the results of the non-directional experiments DAMA/LIBRA, CoGeNT and CRESST-II.Comment: Proceedings of the 3rd International conference on Directional Detection of Dark Matter (CYGNUS 2011), Aussois, France, 8-10 June 201

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

Studies of the Relativistic Binary Pulsar PSR B1534+12. II. Origin and Evolution

We have recently measured the angle between the spin and orbital angular momenta of PSR B1534+12 to be either 25+/-4 deg or 155+/-4 deg. This misalignment was almost certainly caused by an asymmetry in the supernova explosion that formed its companion neutron star. Here we combine the misalignment measurement with measurements of the pulsar and companion masses, the orbital elements, proper motion, and interstellar scintillation. We show that the orbit of the binary in the Galaxy is inconsistent with a velocity kick large enough to produce a nearly antialigned spin axis, so the true misalignment must be ~25 deg. Similar arguments lead to bounds on the mass of the companion star immediately before its supernova: 3+/-1 Msun. The result is a coherent scenario for the formation of the observed binary. After the first supernova explosion, the neutron star that would eventually become the observed pulsar was in a Be/X-ray type binary system with a companion of at least 10--12 Msun. During hydrogen (or possibly helium) shell burning, mass transfer occurred in a common envelope phase, leaving the neutron star in a roughly half-day orbit with a helium star with mass above ~3.3 Msun. A second phase of mass transfer was then initiated by Roche lobe overflow during shell helium burning, further reducing both the helium star mass and orbital period before the second supernova. Scenarios that avoid Roche lobe overflow by the helium star require larger helium star masses and predict space velocities inconsistent with our measurements. The companion neutron star experienced a velocity kick of 230+/-60 km/s at birth, leading to a systemic kick to the binary of 180+/-60 km/s.Comment: 9 pages, submitted to ApJ. Abstract shortened. Version with high-resolution figures available at http://www.astro.ubc.ca/people/stairs/papers/tds04_orig.ps.g

Earliest detection of the optical afterglow of GRB 030329 and its variability

We report the earliest detection of an extremely bright optical afterglow of the gamma-ray burst (GRB) 030329 using a 30cm-telescope at Tokyo Institute of Technology (Tokyo, JAPAN). Our observation started 67 minutes after the burst, and continued for succeeding two nights until the afterglow faded below the sensitivity limit of the telescope (approximately 18 mag). Combining our data with those reported in GCN Circulars, we find that the early afterglow light curve of the first half day is described by a broken power-law (t^{- alpha}) function with indices alpha_{1} = 0.88 +/- 0.01 (0.047 < t < t_{b1} days), alpha_{2} = 1.18 +/- 0.01 (t_{b1} < t < t_{b2} days), and alpha_{3} = 1.81 +/- 0.04 (t_{b2} < t < 1.2 days), where t_{b1} ~ 0.26 days and t_{b2} ~ 0.54 days, respectively. The change of the power-law index at the first break at t ~ 0.26 days is consistent with that expected from a ``cooling-break'' when the cooling frequency crossed the optical band. If the interpretation is correct, the decay index before the cooling-break implies a uniform ISM environment.Comment: 13 pages, 1 table and 2 figures. Accepted to the Astrophysical Journal Letter

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