1,562 research outputs found

### Statistical analysis of network data and evolution on GPUs: High-performance statistical computing

Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs

### General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes

We assemble the equations of general relativistic magnetohydrodynamics (MHD)
in 3+1 form. These consist of the complete coupled set of Maxwell equations for
the electromagnetic field, Einstein's equations for the gravitational field,
and the equations of relativistic MHD for a perfectly conducting ideal gas. The
adopted form of the equations is suitable for evolving numerically a
relativistic MHD fluid in a dynamical spacetime characterized by a strong
gravitational field.Comment: 8 pages; scheduled for March 10 issue of Ap

### Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes

Following the method of Hoenselaers and Perj\'{e}s we present a new corrected
and dimensionally consistent set of multipole gravitational and electromagnetic
moments for stationary axisymmetric spacetimes. Furthermore, we use our results
to compute the multipole moments, both gravitational and electromagnetic, of a
Kerr-Newman black hole.Comment: This is a revised and corrected versio

### Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation

A quasi-equilibrium (QE) computational scheme was recently developed in
general relativity to calculate the complete gravitational wavetrain emitted
during the inspiral phase of compact binaries. The QE method exploits the fact
that the the gravitational radiation inspiral timescale is much longer than the
orbital period everywhere outside the ISCO. Here we demonstrate the validity
and advantages of the QE scheme by solving a model problem in relativistic
scalar gravitation theory. By adopting scalar gravitation, we are able to
numerically track without approximation the damping of a simple, quasi-periodic
radiating system (an oscillating spherical matter shell) to final equilibrium,
and then use the exact numerical results to calibrate the QE approximation
method. In particular, we calculate the emitted gravitational wavetrain three
different ways: by integrating the exact coupled dynamical field and matter
equations, by using the scalar-wave monopole approximation formula
(corresponding to the quadrupole formula in general relativity), and by
adopting the QE scheme. We find that the monopole formula works well for weak
field cases, but fails when the fields become even moderately strong. By
contrast, the QE scheme remains quite reliable for moderately strong fields,
and begins to breakdown only for ultra-strong fields. The QE scheme thus
provides a promising technique to construct the complete wavetrain from binary
inspiral outside the ISCO, where the gravitational fields are strong, but where
the computational resources required to follow the system for more than a few
orbits by direct numerical integration of the exact equations are prohibitive.Comment: 15 pages, 14 figure

### Implementing an apparent-horizon finder in three dimensions

Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures

### Radiative Falloff in Neutron Star Spacetimes

We systematically study late-time tails of scalar waves propagating in
neutron star spacetimes. We consider uniform density neutron stars, for which
the background spacetime is analytic and the compaction of the star can be
varied continously between the Newtonian limit 2M/R << 1 and the relativistic
Buchdahl limit 2M/R = 8/9. We study the reflection of a finite wave packet off
neutron stars of different compactions 2M/R and find that a Newtonian, an
intermediate, and a highly relativistic regime can be clearly distinguished. In
the highly relativistic regime, the reflected signal is dominated by
quasi-periodic peaks, which originate from the wave packet bouncing back and
forth between the center of the star and the maximum of the background
curvature potential at R ~ 3 M. Between these peaks, the field decays according
to a power-law. In the Buchdahl limit 2M/R -> 8/9 the light travel time between
the center and the maximum or the curvature potential grows without bound, so
that the first peak arrives only at infinitely late time. The modes of neutron
stars can therefore no longer be excited in the ultra-relativistic limit, and
it is in this sense that the late-time radiative decay from neutron stars
looses all its features and gives rise to power-law tails reminiscent of
Schwarzschild black holes.Comment: 10 pages, 7 figures, to appear in PR

### Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral

We present a new method for generating the nonlinear gravitational wavetrain
from the late inspiral (pre-coalescence) phase of a binary neutron star system
by means of a numerical evolution calculation in full general relativity. In a
prototype calculation, we produce 214 wave cycles from corotating polytropes,
representing the final part of the inspiral phase prior to reaching the ISCO.
Our method is based on the inequality that the orbital decay timescale due to
gravitational radiation is much longer than an orbital period and the
approximation that gravitational radiation has little effect on the structure
of the stars. We employ quasi-equilibrium sequences of binaries in circular
orbit for the matter source in our field evolution code. We compute the
gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set
of binary separations. From these data, we construct the gravitational waveform
as a continuous wavetrain. Finally, we discuss the limitations of our current
calculation, planned improvements, and potential applications of our method to
other inspiral scenarios.Comment: 4 pages, 4 figure

### Evolving Einstein's Field Equations with Matter: The ``Hydro without Hydro'' Test

We include matter sources in Einstein's field equations and show that our
recently proposed 3+1 evolution scheme can stably evolve strong-field
solutions. We insert in our code known matter solutions, namely the
Oppenheimer-Volkoff solution for a static star and the Oppenheimer-Snyder
solution for homogeneous dust sphere collapse to a black hole, and evolve the
gravitational field equations. We find that we can evolve stably static,
strong-field stars for arbitrarily long times and can follow dust sphere
collapse accurately well past black hole formation. These tests are useful
diagnostics for fully self-consistent, stable hydrodynamical simulations in 3+1
general relativity. Moreover, they suggest a successive approximation scheme
for determining gravitational waveforms from strong-field sources dominated by
longitudinal fields, like binary neutron stars: approximate quasi-equilibrium
models can serve as sources for the transverse field equations, which can be
evolved without having to re-solve the hydrodynamical equations (``hydro
without hydro'').Comment: 4 postscript figures. Submitted to Phys. Rev. D15 as a Brief Repor

### Insights from 20 years of temperature parallel measurements in Mauritius around the turn of the 20th century

There is considerable import in creating more complete, better understood holdings of early meteorological data. Such data permit an improved understanding of climate variability and long-term changes. Early records are particularly incomplete in the tropics, with implications for estimates of global and regional temperature. There is also a relatively low level of scientific understanding of how these early measurements were made and, as a result, of their homogeneity and comparability to more modern techniques and measurements. Herein we describe and analyse a newly rescued set of long-term, up to six-way parallel measurements undertaken over 1884–1903 in Mauritius, an island situated in the southern Indian Ocean. Data include (i) measurements from a well-ventilated room, (ii) a shaded thermograph, (iii) instruments housed in a manner broadly equivalent to a modern Stevenson screen, (iv) a set of measurements by a hygrometer mounted in a Stevenson screen, and for a much shorter period (v) two additional Stevenson screen configurations. All measurements were undertaken within an ∼ 80 m radius of each other. To our knowledge this is the first such multidecadal multi-instrument assessment of meteorological instrument transition impacts ever undertaken, providing potentially unique insights. The intercomparison also considers the impact of different ways of deriving daily and monthly averages. The long-term comparison is sufficient to robustly characterize systematic offsets between all the instruments and seasonally varying impacts. Differences between all techniques range from tenths of a degree Celsius to more than 1 ∘C and are considerably larger for maximum and minimum temperatures than for means or averages. Systematic differences of several tenths of a degree Celsius also exist for the different ways of deriving average and mean temperatures. All differences, except two average temperature series pairs, are significant at the 0.01 level using a paired t test. Given that all thermometers were regularly calibrated against a primary Kew standard thermometer maintained by the observatory, this analysis highlights significant impacts of instrument exposure, housing, siting, and measurement practices in early meteorological records. These results reaffirm the importance of thoroughly assessing the homogeneity of early meteorological records

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