6,943 research outputs found
Multispace and Multilevel BDDC
BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl
Studies of waveform requirements for intermediate mass-ratio coalescence searches with advanced detectors
The coalescence of a stellar-mass compact object into an intermediate-mass
black hole (intermediate mass-ratio coalescence; IMRAC) is an important
astrophysical source for ground-based gravitational-wave interferometers in the
so-called advanced configuration. However, the ability to carry out effective
matched-filter based searches for these systems is limited by the lack of
reliable waveforms. Here we consider binaries in which the intermediate-mass
black hole has mass in the range 24 - 200 solar masses with a stellar-mass
companion having masses in the range 1.4 - 18.5 solar masses. In addition, we
constrain the mass ratios, q, of the binaries to be in the range 1/140 < q <
1/10 and we restrict our study to the case of circular binaries with
non-spinning components. We investigate the relative contribution to the
signal-to-noise ratio (SNR) of the three different phases of the coalescence:
inspiral, merger and ringdown. We show that merger and ringdown contribute to a
substantial fraction of the total SNR over a large portion of the mass
parameter space, although in a limited portion the SNR is dominated by the
inspiral phase. We further identify three regions in the IMRAC mass-space in
which: (i) inspiral-only searches could be performed with losses in detection
rates L in the range 10% < L < 27%, (ii) searches based on inspiral-only
templates lead to a loss in detection rates in the range 27% < L < 50%$, and
(iii) templates that include merger and ringdown are essential to prevent
losses in detection rates greater than 50%. We investigate the effectiveness
with which the inspiral-only portion of the IMRAC waveform space is covered by
comparing several existing waveform families in this regime. Our results
reinforce the importance of extensive numerical relativity simulations of
IMRACs and the need for further studies of suitable approximation schemes in
this mass range.Comment: 10 pages, 3 figure
Characteristics and processing of fps-16/ jimsphere raw radar data
Error analysis of fps-16/jimsphere raw radar dat
Selecting digital filters for application to detailed wind profiles
Selecting digital filters for application to detailed wind profiles - table
Capability of the FPS-16 radar/jimsphere system for direct measurement of vertical air motions
Capability and procedure for direct measurement of vertical air currents using FPS-16 radar/ jimsphere syste
Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case
The objective of this paper is to show how the recently proposed method by
Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to
a case of real polynomial equation solving. Our main result concerns the
problem of finding one representative point for each connected component of a
real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a
method for symbolically solving a zero-dimensional polynomial equation system
in the affine (and toric) case. Its main feature is the use of adapted data
structure: Arithmetical networks and straight-line programs. The algorithm
solves any affine zero-dimensional equation system in non-uniform sequential
time that is polynomial in the length of the input description and an
adequately defined {\em affine degree} of the equation system. Replacing the
affine degree of the equation system by a suitably defined {\em real degree} of
certain polar varieties associated to the input equation, which describes the
hypersurface under consideration, and using straight-line program codification
of the input and intermediate results, we obtain a method for the problem
introduced above that is polynomial in the input length and the real degree.Comment: Late
Towards Rapid Parameter Estimation on Gravitational Waves from Compact Binaries using Interpolated Waveforms
Accurate parameter estimation of gravitational waves from coalescing compact
binary sources is a key requirement for gravitational-wave astronomy.
Evaluating the posterior probability density function of the binary's
parameters (component masses, sky location, distance, etc.) requires computing
millions of waveforms. The computational expense of parameter estimation is
dominated by waveform generation and scales linearly with the waveform
computational cost. Previous work showed that gravitational waveforms from
non-spinning compact binary sources are amenable to a truncated singular value
decomposition, which allows them to be reconstructed via interpolation at fixed
computational cost. However, the accuracy requirement for parameter estimation
is typically higher than for searches, so it is crucial to ascertain that
interpolation does not lead to significant errors. Here we provide a proof of
principle to show that interpolated waveforms can be used to recover posterior
probability density functions with negligible loss in accuracy with respect to
non-interpolated waveforms. This technique has the potential to significantly
increase the efficiency of parameter estimation.Comment: 7 pages, 2 figure
Time-frequency analysis of extreme-mass-ratio inspiral signals in mock LISA data
Extreme-mass-ratio inspirals (EMRIs) of ~ 1-10 solar-mass compact objects
into ~ million solar-mass massive black holes can serve as excellent probes of
strong-field general relativity. The Laser Interferometer Space Antenna (LISA)
is expected to detect gravitational wave signals from apprxomiately one hundred
EMRIs per year, but the data analysis of EMRI signals poses a unique set of
challenges due to their long duration and the extensive parameter space of
possible signals. One possible approach is to carry out a search for EMRI
tracks in the time-frequency domain. We have applied a time-frequency search to
the data from the Mock LISA Data Challenge (MLDC) with promising results. Our
analysis used the Hierarchical Algorithm for Clusters and Ridges to identify
tracks in the time-frequency spectrogram corresponding to EMRI sources. We then
estimated the EMRI source parameters from these tracks. In these proceedings,
we discuss the results of this analysis of the MLDC round 1.3 data.Comment: Amaldi-7 conference proceedings; requires jpconf style file
Resonant control of spin dynamics in ultracold quantum gases by microwave dressing
We study experimentally interaction-driven spin oscillations in optical
lattices in the presence of an off-resonant microwave field. We show that the
energy shift induced by this microwave field can be used to control the spin
oscillations by tuning the system either into resonance to achieve near-unity
contrast or far away from resonance to suppress the oscillations. Finally, we
propose a scheme based on this technique to create a flat sample with either
singly- or doubly-occupied sites, starting from an inhomogeneous Mott
insulator, where singly- and doubly-occupied sites coexist.Comment: 4 pages, 5 figure
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