16,504 research outputs found
A nonlinear detection algorithm for periodic signals in gravitational wave detectors
We present an algorithm for the detection of periodic sources of
gravitational waves with interferometric detectors that is based on a special
symmetry of the problem: the contributions to the phase modulation of the
signal from the earth rotation are exactly equal and opposite at any two
instants of time separated by half a sidereal day; the corresponding is true
for the contributions from the earth orbital motion for half a sidereal year,
assuming a circular orbit. The addition of phases through multiplications of
the shifted time series gives a demodulated signal; specific attention is given
to the reduction of noise mixing resulting from these multiplications. We
discuss the statistics of this algorithm for all-sky searches (which include a
parameterization of the source spin-down), in particular its optimal
sensitivity as a function of required computational power. Two specific
examples of all-sky searches (broad-band and narrow-band) are explored
numerically, and their performances are compared with the stack-slide technique
(P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.
GW method with the self-consistent Sternheimer equation
We propose a novel approach to quasiparticle GW calculations which does not
require the computation of unoccupied electronic states. In our approach the
screened Coulomb interaction is evaluated by solving self-consistent
linear-response Sternheimer equations, and the noninteracting Green's function
is evaluated by solving inhomogeneous linear systems. The frequency-dependence
of the screened Coulomb interaction is explicitly taken into account. In order
to avoid the singularities of the screened Coulomb interaction the calculations
are performed along the imaginary axis, and the results are analytically
continued to the real axis through Pade' approximants. As a proof of concept we
implemented the proposed methodology within the empirical pseudopotential
formalism and we validated our implementation using silicon as a test case. We
examine the advantages and limitations of our method and describe promising
future directions.Comment: 18 pages, 6 figure
A unified pseudo- framework
The pseudo- is an algorithm for estimating the angular power and
cross-power spectra that is very fast and, in realistic cases, also nearly
optimal. The algorithm can be extended to deal with contaminant deprojection
and purification, and can therefore be applied in a wide variety of
scenarios of interest for current and future cosmological observations. This
paper presents NaMaster, a public, validated, accurate and easy-to-use software
package that, for the first time, provides a unified framework to compute
angular cross-power spectra of any pair of spin-0 or spin-2 fields,
contaminated by an arbitrary number of linear systematics and requiring - or
-mode purification, both on the sphere or in the flat-sky approximation. We
describe the mathematical background of the estimator, including all the
features above, and its software implementation in NaMaster. We construct a
validation suite that aims to resemble the types of observations that
next-generation large-scale structure and ground-based CMB experiments will
face, and use it to show that the code is able to recover the input power
spectra in the most complex scenarios with no detectable bias. NaMaster can be
found at https://github.com/LSSTDESC/NaMaster, and is provided with
comprehensive documentation and a number of code examples.Comment: 27 pages, 17 figures, accepted in MNRAS. Code can be found at
https://github.com/LSSTDESC/NaMaste
3D weak lensing with spin wavelets on the ball
We construct the spin flaglet transform, a wavelet transform to analyze spin
signals in three dimensions. Spin flaglets can probe signal content localized
simultaneously in space and frequency and, moreover, are separable so that
their angular and radial properties can be controlled independently. They are
particularly suited to analyzing of cosmological observations such as the weak
gravitational lensing of galaxies. Such observations have a unique 3D
geometrical setting since they are natively made on the sky, have spin angular
symmetries, and are extended in the radial direction by additional distance or
redshift information. Flaglets are constructed in the harmonic space defined by
the Fourier-Laguerre transform, previously defined for scalar functions and
extended here to signals with spin symmetries. Thanks to various sampling
theorems, both the Fourier-Laguerre and flaglet transforms are theoretically
exact when applied to bandlimited signals. In other words, in numerical
computations the only loss of information is due to the finite representation
of floating point numbers. We develop a 3D framework relating the weak lensing
power spectrum to covariances of flaglet coefficients. We suggest that the
resulting novel flaglet weak lensing estimator offers a powerful alternative to
common 2D and 3D approaches to accurately capture cosmological information.
While standard weak lensing analyses focus on either real or harmonic space
representations (i.e., correlation functions or Fourier-Bessel power spectra,
respectively), a wavelet approach inherits the advantages of both techniques,
where both complicated sky coverage and uncertainties associated with the
physical modeling of small scales can be handled effectively. Our codes to
compute the Fourier-Laguerre and flaglet transforms are made publicly
available.Comment: 24 pages, 4 figures, version accepted for publication in PR
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