4,793 research outputs found
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 () 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
Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole
We calculate the gravitational perturbations produced by a small mass in
eccentric orbit about a much more massive Schwarzschild black hole and use the
numerically computed perturbations to solve for the metric. The calculations
are initially made in the frequency domain and provide Fourier-harmonic modes
for the gauge-invariant master functions that satisfy inhomogeneous versions of
the Regge-Wheeler and Zerilli equations. These gravitational master equations
have specific singular sources containing both delta function and
derivative-of-delta function terms. We demonstrate in this paper successful
application of the method of extended homogeneous solutions, developed recently
by Barack, Ori, and Sago, to handle source terms of this type. The method
allows transformation back to the time domain, with exponential convergence of
the partial mode sums that represent the field. This rapid convergence holds
even in the region of traversed by the point mass and includes the
time-dependent location of the point mass itself. We present numerical results
of mode calculations for certain orbital parameters, including highly accurate
energy and angular momentum fluxes at infinity and at the black hole event
horizon. We then address the issue of reconstructing the metric perturbation
amplitudes from the master functions, the latter being weak solutions of a
particular form to the wave equations. The spherical harmonic amplitudes that
represent the metric in Regge-Wheeler gauge can themselves be viewed as weak
solutions. They are in general a combination of (1) two differentiable
solutions that adjoin at the instantaneous location of the point mass (a result
that has order of continuity typically) and (2) (in some cases) a
delta function distribution term with a computable time-dependent amplitude.Comment: 25 pages, 5 figures, Updated with minor change
Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
We present an extension of work in an earlier paper showing high precision
comparisons between black hole perturbation theory and post-Newtonian (PN)
theory in their region of overlapping validity for bound, eccentric-orbit,
Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical
fitting scheme to extract eccentricity coefficients in the PN expansion of the
gravitational wave fluxes, which are then converted to exact analytic form
using an integer-relation algorithm. In this work, however, we fit to
individual modes to exploit simplifying factorizations that lie therein.
Since the previous paper focused solely on the energy flux, here we concentrate
initially on analyzing the angular momentum flux to infinity. A first step
involves finding convenient forms for hereditary contributions to the flux at
low-PN order, analogous to similar terms worked out previously for the energy
flux. We then apply the upgraded techniques to find new PN terms through 9PN
order and (at many PN orders) to in the power series in eccentricity.
With the new approach applied to angular momentum fluxes, we return to the
energy fluxes at infinity to extend those previous results. Like before, the
underlying method uses a \textsc{Mathematica} code based on use of the
Mano-Suzuki-Takasugi (MST) function expansion formalism to represent
gravitational perturbations and spectral source integration (SSI) to find
numerical results at arbitrarily high precision.Comment: 36 pages, 1 figur
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 . 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
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
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
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
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