288 research outputs found
Multi-taper Spectral Analysis in Gravitational Wave Data Analysis
Spectral estimation plays a significant role in gravitational wave data analysis. We provide a brief introduction to multi-taper methods which use multiple orthogonal tapers (or windows) to provide spectral estimators with excellent bias and variance properties. Multi-taper methods are also extremely powerful for the estimation and removal of sharp spectral peaks in the presence of noise such as arise due to power line harmonics or suspension resonances. We present examples of these methods using the GRASP (Gravitational Radiation Analysis and Simulation Package) software package
Automatic cross-talk removal from multi-channel data
A technique is described for removing interference from a signal of interest ("channel 1") which is one of a set of N time-domain instrumental signals ("channels 1 to N"). We assume that channel 1 is a linear combination of "true" signal plus noise, and that the "true" signal is not correlated with the noise. We also assume that part of this noise is produced, in a poorly-understood way, by the environment, and that the environment is monitored by channels 2 to N. Finally, we assume that the contribution of channel n to channel 1 is described by an (unknown!) linear transfer function R_n(t-t'). Our technique estimates the R_i and provides a way to subtract the environmental contamination from channel 1, giving an estimate of the "true" signal which minimizes its variance. It also provides some insights into how the environment is contaminating the signal of interest. The method is illustrated with data from a prototype interferometric gravitational-wave detector, in which the channel of interest (differential displacement) is heavily contaminated by environmental noise (magnetic and seismic noise) and laser frequency noise but where the coupling between these signals is not known in advance
Adsorption of Ammonium Perfluorooctanoate at the Air–Water Interface
The adsorption of ammonium perfluorooctanoate has been investigated at the air-water interface as a function of surfactant concentration at various concentrations of ammonium chloride. The area occupied by the surfactant ion was then calculated from the Gibbs equation with allowance for the presence of salt ions. Independently, the area per surfactant ion at the interface was determined by the technique of neutron reflectiviy. Within experimental error the two sets of measurements were in good agreement
Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String
We calculate the renormalized vacuum polarization and stress tensor for a
massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state
on the horizon of a Schwarzschild black hole threaded by an infinte straight
cosmic string. This calculation relies on a generalized Heine identity for
non-integer Legendre functions which we derive without using specific
properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added
the calculation of the stress tensor. 28 pages, 7 figure
Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops
Cosmic string loops are defined by a pair of periodic functions and
, which trace out unit-length closed curves in three-dimensional
space. We consider a particular class of loops, for which lies along
a line and lies in the plane orthogonal to that line. For this class
of cosmic string loops one may give a simple analytic expression for the power
radiated in gravitational waves. We evaluate exactly in
closed form for several special cases: (1) a circle traversed
times; (2) a regular polygon with sides and interior vertex angle
; (3) an isosceles triangle with semi-angle .
We prove that case (1) with is the absolute minimum of within
our special class of loops, and identify all the stationary points of
in this class.Comment: 15 pages, RevTex 3.0, 7 figures available via anonymous ftp from
directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-1
High Frequency Asymptotics for the Spin-Weighted Spheroidal Equation
We fully determine a uniformly valid asymptotic behaviour for large and fixed of the angular solutions and eigenvalues of the
spin-weighted spheroidal differential equation. We fully complement the
analytic work with a numerical study.Comment: The .tar.gz file should contain 1 tex file, 24 figures in .ps format
and 1 bibliography file in .bbl format. All these files are located in the
same director
Waveforms for Gravitational Radiation from Cosmic String Loops
We obtain general formulae for the plus- and cross- polarized waveforms of
gravitational radiation emitted by a cosmic string loop in transverse,
traceless (synchronous, harmonic) gauge. These equations are then specialized
to the case of piecewise linear loops, and it is shown that the general
waveform for such a loop is a piecewise linear function. We give several simple
examples of the waveforms from such loops. We also discuss the relation between
the gravitational radiation by a smooth loop and by a piecewise linear
approximation to it.Comment: 16 pages, 6 figures, Revte
Detection of Anisotropies in the Gravitational-Wave Stochastic Background
By correlating the signals from a pair of gravitational-wave detectors, one
can undertake sensitive searches for a stochastic background of gravitational
radiation. If the stochastic background is anisotropic, then this correlated
signal varies harmonically with the earth's rotation. We calculate how the
harmonics of this varying signal are related to the multipole moments which
characterize the anisotropy, and give a formula for the signal-to-noise ratio
of a given harmonic. The specific case of the two LIGO (Laser Interferometric
Gravitational Observatory) detectors, which will begin operation around the
year 2000, is analyzed in detail. We consider two possible examples of
anisotropy. If the gravitational-wave stochastic background contains a dipole
intensity anisotropy whose origin (like that of the Cosmic Background
Radiation) is motion of our local system, then that anisotropy will be
observable by the advanced LIGO detector (with 90% confidence in one year of
observation) if \Omega_{gw} > 5.3 \times 10^{-8} h_{100}^{-2}. We also study
the signal produced by stochastic sources distributed in the same way as the
luminous matter in the galactic disk, and in the same way as the galactic halo.
The anisotropy due to sources distributed as the galactic disk or as the
galactic halo will be observable by the advanced LIGO detector (with 90%
confidence in one year of observation) if \Omega_{gw} > 1.8 \times 10^{-10}
h_{100}^{-2} or \Omega_{gw} > 6.7 \times 10^{-8} h_{100}^{-2}, respectively.Comment: 25 pages, Latex with RevTeX and epsfig, now includes S/N ratio
calculations, expected response from anisotropy due to local motion & sources
in galax
Effective source approach to self-force calculations
Numerical evaluation of the self-force on a point particle is made difficult
by the use of delta functions as sources. Recent methods for self-force
calculations avoid delta functions altogether, using instead a finite and
extended "effective source" for a point particle. We provide a review of the
general principles underlying this strategy, using the specific example of a
scalar point charge moving in a black hole spacetime. We also report on two new
developments: (i) the construction and evaluation of an effective source for a
scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii)
the successful implementation of hyperboloidal slicing that significantly
improves on previous treatments of boundary conditions used for
effective-source-based self-force calculations. Finally, we identify some of
the key issues related to the effective source approach that will need to be
addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at
Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG
special issue - 22 pages, 8 figure
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