1,789 research outputs found
Dilated Floor Functions That Commute
We determine all pairs of real numbers such that the
dilated floor functions and
commute under composition, i.e., such that holds for all
real .Comment: 6 pages, to appear in Amer. Math. Monthl
Dilated floor functions having nonnegative commutator II. Negative dilations
This paper completes the classification of the set of all real parameter
pairs such that the dilated floor functions , have a
nonnegative commutator, i.e. for all real . This paper treats the case where
both dilation parameters are negative. This result is
equivalent to classifying all positive satisfying for all real . The classification analysis is
connected with the theory of Beatty sequences and with the Diophantine
Frobenius problem in two generators.Comment: 18 pages, 8 figure
The ligo gravitational wave observatories: Recent results and future plans
The LIGO interferometers are operating as gravitational wave observatories, with a noise level near an order of magnitude of the goal and the first scientific data recently taken. This data has been analyzed for four different categories of gravitational wave sources; millisecond bursts, inspiralling binary neutron stars, periodic waves from a known pulsar, and stochastic background. Research and development is also underway for the next generation LIGO detector, Advanced LIGO
Upper limits on the strength of periodic gravitational waves from PSR J1939+2134
The first science run of the LIGO and GEO gravitational wave detectors
presented the opportunity to test methods of searching for gravitational waves
from known pulsars. Here we present new direct upper limits on the strength of
waves from the pulsar PSR J1939+2134 using two independent analysis methods,
one in the frequency domain using frequentist statistics and one in the time
domain using Bayesian inference. Both methods show that the strain amplitude at
Earth from this pulsar is less than a few times .Comment: 7 pages, 1 figure, to appear in the Proceedings of the 5th Edoardo
Amaldi Conference on Gravitational Waves, Tirrenia, Pisa, Italy, 6-11 July
200
Improving the sensitivity to gravitational-wave sources by modifying the input-output optics of advanced interferometers
We study frequency dependent (FD) input-output schemes for signal-recycling
interferometers, the baseline design of Advanced LIGO and the current
configuration of GEO 600. Complementary to a recent proposal by Harms et al. to
use FD input squeezing and ordinary homodyne detection, we explore a scheme
which uses ordinary squeezed vacuum, but FD readout. Both schemes, which are
sub-optimal among all possible input-output schemes, provide a global noise
suppression by the power squeeze factor, while being realizable by using
detuned Fabry-Perot cavities as input/output filters. At high frequencies, the
two schemes are shown to be equivalent, while at low frequencies our scheme
gives better performance than that of Harms et al., and is nearly fully
optimal. We then study the sensitivity improvement achievable by these schemes
in Advanced LIGO era (with 30-m filter cavities and current estimates of
filter-mirror losses and thermal noise), for neutron star binary inspirals, and
for narrowband GW sources such as low-mass X-ray binaries and known radio
pulsars. Optical losses are shown to be a major obstacle for the actual
implementation of these techniques in Advanced LIGO. On time scales of
third-generation interferometers, like EURO/LIGO-III (~2012), with
kilometer-scale filter cavities, a signal-recycling interferometer with the FD
readout scheme explored in this paper can have performances comparable to
existing proposals. [abridged]Comment: Figs. 9 and 12 corrected; Appendix added for narrowband data analysi
Searching for gravitational waves from known pulsars
We present upper limits on the amplitude of gravitational waves from 28
isolated pulsars using data from the second science run of LIGO. The results
are also expressed as a constraint on the pulsars' equatorial ellipticities. We
discuss a new way of presenting such ellipticity upper limits that takes
account of the uncertainties of the pulsar moment of inertia. We also extend
our previous method to search for known pulsars in binary systems, of which
there are about 80 in the sensitive frequency range of LIGO and GEO 600.Comment: Accepted by CQG for the proceeding of GWDAW9, 7 pages, 2 figure
Search for Gravitational Waves Associated with 39 Gamma-Ray Bursts Using Data from the Second, Third, and Fourth LIGO Runs
We present the results of a search for short-duration gravitational-wave
bursts associated with 39 gamma-ray bursts (GRBs) detected by gamma-ray
satellite experiments during LIGO's S2, S3, and S4 science runs. The search
involves calculating the crosscorrelation between two interferometer data
streams surrounding the GRB trigger time. We search for associated
gravitational radiation from single GRBs, and also apply statistical tests to
search for a gravitational-wave signature associated with the whole sample. For
the sample examined, we find no evidence for the association of gravitational
radiation with GRBs, either on a single-GRB basis or on a statistical basis.
Simulating gravitational-wave bursts with sine-gaussian waveforms, we set upper
limits on the root-sum-square of the gravitational-wave strain amplitude of
such waveforms at the times of the GRB triggers. We also demonstrate how a
sample of several GRBs can be used collectively to set constraints on
population models. The small number of GRBs and the significant change in
sensitivity of the detectors over the three runs, however, limits the
usefulness of a population study for the S2, S3, and S4 runs. Finally, we
discuss prospects for the search sensitivity for the ongoing S5 run, and beyond
for the next generation of detectors.Comment: 24 pages, 10 figures, 14 tables; minor changes to text and Fig. 2;
accepted by Phys. Rev.
Setting upper limits on the strength of periodic gravitational waves from PSR J1939+2134 using the first science data from the GEO 600 and LIGO detectors
Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar's gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar's equatorial ellipticity
First upper limits from LIGO on gravitational wave bursts
We report on a search for gravitational wave bursts using data from the first
science run of the LIGO detectors. Our search focuses on bursts with durations
ranging from 4 ms to 100 ms, and with significant power in the LIGO sensitivity
band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than
1.6 events per day at 90% confidence level. This result is interpreted in terms
of the detection efficiency for ad hoc waveforms (Gaussians and sine-Gaussians)
as a function of their root-sum-square strain h_{rss}; typical sensitivities
lie in the range h_{rss} ~ 10^{-19} - 10^{-17} strain/rtHz, depending on
waveform. We discuss improvements in the search method that will be applied to
future science data from LIGO and other gravitational wave detectors.Comment: 21 pages, 15 figures, accepted by Phys Rev D. Fixed a few small typos
and updated a few reference
- …