Metric perturbations from eccentric orbits on a Schwarzschild black hole: I. Odd-parity Regge-Wheeler to Lorenz gauge transformation and two new methods to circumvent the Gibbs phenomenon

We calculate the odd-parity, radiative ($\ell \ge 2$) parts of the metric perturbation in Lorenz gauge caused by a small compact object in eccentric orbit about a Schwarzschild black hole. The Lorenz gauge solution is found via gauge transformation from a corresponding one in Regge-Wheeler gauge. Like the Regge-Wheeler gauge solution itself, the gauge generator is computed in the frequency domain and transferred to the time domain. The wave equation for the gauge generator has a source with a compact, moving delta-function term and a discontinuous non-compact term. The former term allows the method of extended homogeneous solutions to be applied (which circumvents the Gibbs phenomenon). The latter has required the development of new means to use frequency domain methods and yet be able to transfer to the time domain while avoiding Gibbs problems. Two new methods are developed to achieve this: a partial annihilator method and a method of extended particular solutions. We detail these methods and show their application in calculating the odd-parity gauge generator and Lorenz gauge metric perturbations. A subsequent paper will apply these methods to the harder task of computing the even-parity parts of the gauge generator.Comment: 17 pages, 9 figures, Updated with one modified figure and minor changes to the text. Added DOI and Journal referenc

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'\^{e}tre}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.Comment: 15 pages, 7 figure

Prevalence and Odds of Serious Mental Illness among Homeless LGBT Youth and Young Adults in Atlanta

INTRODUCTION: National estimates of young people who experience homelessness vary, but the numbers are large. Among those numbers, a significantly high percentage of homeless youths identify as LGBT. Additionally, LGBT youth are at higher risk of increased mental health risks than heterosexual youth. Further understanding of this occurrence among the homeless youth population is important in policy and program planning and implementation. AIM: To examine the relationship between serious mental illness (SMI) and sex at birth, race/ethnicity, and sexual minority status in homeless youth. METHODS: Homeless youths, both heterosexual and self-identified lesbian, gay, bisexual, transgender and queer (LGBT), aged 14-25, were recruited via convenience sampling to be part of the Atlanta Youth Count and Needs Assessment in summer of 2015. RESULTS: Multiple logistic regression analyses revealed that SMI occurs in females 1.445 times its occurrence in males, adjusted for race/ethnicity and being lesbian/gay, bisexual or transgender (P=0.0478, 95% CI=1.004, 2.081). Serious mental illness is also 2.196 times more likely in transgender groups than in lesbian/gay and bisexual groups, adjusted for sex at birth and race/ethnicity (P=0.0284, 95% CI=1.085, 4.334). DISCUSSION: With regards to research questions, there were no differences between homeless LGBT and homeless non-LGBT youth in regards to SMI, unlike previous literature. Consistent with previous literature, there was a difference between the transgender group and the LGB groups in regards to SMI. Also hypothesized, being born female and being transgender was associated with higher likelihood of SMI, as with previous literature. However, being bisexual was not associated with higher likelihood of SMI, unlike previous literature

Creep fatigue of low-cobalt superalloys: Waspalloy, PM U 700 and wrought U 700

The influence of cobalt content on the high temperature creep fatigue crack initiation resistance of three primary alloys was evaluated. These were Waspalloy, Powder U 700, and Cast U 700, with cobalt contents ranging from 0 up to 17 percent. Waspalloy was studied at 538 C whereas the U 700 was studied at 760 C. Constraints of the program required investigation at a single strain range using diametral strain control. The approach was phenomenological, using standard low cycle fatigue tests involving continuous cycling tension hold cycling, compression hold cycling, and symmetric hold cycling. Cycling in the absence of or between holds was done at 0.5 Hz, whereas holds when introduced lasted 1 minute. The plan was to allocate two specimens to the continuous cycling, and one specimen to each of the hold time conditions. Data was taken to document the nature of the cracking process, the deformation response, and the resistance to cyclic loading to the formation of small cracks and to specimen separation. The influence of cobalt content on creep fatigue resistance was not judged to be very significant based on the results generated. Specific conclusions were that the hold time history dependence of the resistance is as significant as the influence of cobalt content and increased cobalt content does not produce increased creep fatigue resistance on a one to one basis

Seizing Fourth Amendment Rights

Protections for criminal defendants and suspects have undergone a steady erosion with the increasing conservatism of the United States Supreme Court. A recent decision illustrates how this trend carries over to undermine the rights of all citizens. This Note focuses on the decision in Florida v. Bostick, and its impact on Fourth Amendment rights. Part III of this Note contains a review of the current status of Fourth Amendment interpretation from the standpoint of both search and seizure. In Part IV, the majority opinion and the dissent are analyzed in turn. Finally, in Part V, the argument is put forward that decisions of the current Court may be highlighting the dangers inherent in the discretion allowed by the totality of the circumstances test