32,766 research outputs found
A Fast and Accurate Algorithm for Spherical Harmonic Analysis on HEALPix Grids with Applications to the Cosmic Microwave Background Radiation
The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used
extensively in astrophysics for data collection and analysis on the sphere. The
scheme was originally designed for studying the Cosmic Microwave Background
(CMB) radiation, which represents the first light to travel during the early
stages of the universe's development and gives the strongest evidence for the
Big Bang theory to date. Refined analysis of the CMB angular power spectrum can
lead to revolutionary developments in understanding the nature of dark matter
and dark energy. In this paper, we present a new method for performing
spherical harmonic analysis for HEALPix data, which is a central component to
computing and analyzing the angular power spectrum of the massive CMB data
sets. The method uses a novel combination of a non-uniform fast Fourier
transform, the double Fourier sphere method, and Slevinsky's fast spherical
harmonic transform (Slevinsky, 2019). For a HEALPix grid with pixels
(points), the computational complexity of the method is , with an initial set-up cost of . This compares
favorably with runtime complexity of the current methods
available in the HEALPix software when multiple maps need to be analyzed at the
same time. Using numerical experiments, we demonstrate that the new method also
appears to provide better accuracy over the entire angular power spectrum of
synthetic data when compared to the current methods, with a convergence rate at
least two times higher
Testing the Accuracy and Stability of Spectral Methods in Numerical Relativity
The accuracy and stability of the Caltech-Cornell pseudospectral code is
evaluated using the KST representation of the Einstein evolution equations. The
basic "Mexico City Tests" widely adopted by the numerical relativity community
are adapted here for codes based on spectral methods. Exponential convergence
of the spectral code is established, apparently limited only by numerical
roundoff error. A general expression for the growth of errors due to finite
machine precision is derived, and it is shown that this limit is achieved here
for the linear plane-wave test. All of these tests are found to be stable,
except for simulations of high amplitude gauge waves with nontrivial shift.Comment: Final version, as published in Phys. Rev. D; 13 pages, 16 figure
Wavelet domain Bayesian denoising of string signal in the cosmic microwave background
An algorithm is proposed for denoising the signal induced by cosmic strings
in the cosmic microwave background (CMB). A Bayesian approach is taken, based
on modeling the string signal in the wavelet domain with generalized Gaussian
distributions. Good performance of the algorithm is demonstrated by simulated
experiments at arcminute resolution under noise conditions including primary
and secondary CMB anisotropies, as well as instrumental noise.Comment: 16 pages, 11 figures. Version 2 matches version accepted for
publication in MNRAS. Changes include substantial clarifications on our
approach and a significant reduction of manuscript lengt
Exact reconstruction with directional wavelets on the sphere
A new formalism is derived for the analysis and exact reconstruction of
band-limited signals on the sphere with directional wavelets. It represents an
evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999)
and Wiaux et al. (2005). The translations of the wavelets at any point on the
sphere and their proper rotations are still defined through the continuous
three-dimensional rotations. The dilations of the wavelets are directly defined
in harmonic space through a new kernel dilation, which is a modification of an
existing harmonic dilation. A family of factorized steerable functions with
compact harmonic support which are suitable for this kernel dilation is firstly
identified. A scale discretized wavelet formalism is then derived, relying on
this dilation. The discrete nature of the analysis scales allows the exact
reconstruction of band-limited signals. A corresponding exact multi-resolution
algorithm is finally described and an implementation is tested. The formalism
is of interest notably for the denoising or the deconvolution of signals on the
sphere with a sparse expansion in wavelets. In astrophysics, it finds a
particular application for the identification of localized directional features
in the cosmic microwave background (CMB) data, such as the imprint of
topological defects, in particular cosmic strings, and for their reconstruction
after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for
publication in MNRAS. Version 3 (identical to version 2) posted for code
release announcement - "Steerable scale discretised wavelets on the sphere" -
S2DW code available for download at
http://www.mrao.cam.ac.uk/~jdm57/software.htm
Interpolation in waveform space: enhancing the accuracy of gravitational waveform families using numerical relativity
Matched-filtering for the identification of compact object mergers in
gravitational-wave antenna data involves the comparison of the data stream to a
bank of template gravitational waveforms. Typically the template bank is
constructed from phenomenological waveform models since these can be evaluated
for an arbitrary choice of physical parameters. Recently it has been proposed
that singular value decomposition (SVD) can be used to reduce the number of
templates required for detection. As we show here, another benefit of SVD is
its removal of biases from the phenomenological templates along with a
corresponding improvement in their ability to represent waveform signals
obtained from numerical relativity (NR) simulations. Using these ideas, we
present a method that calibrates a reduced SVD basis of phenomenological
waveforms against NR waveforms in order to construct a new waveform approximant
with improved accuracy and faithfulness compared to the original
phenomenological model. The new waveform family is given numerically through
the interpolation of the projection coefficients of NR waveforms expanded onto
the reduced basis and provides a generalized scheme for enhancing
phenomenological models.Comment: 10 pages, 7 figure
Calibration of optical tweezers with positional detection in the back-focal-plane
We explain and demonstrate a new method of force- and position-calibration
for optical tweezers with back-focal-plane photo detection. The method combines
power spectral measurements of thermal motion and the response to a sinusoidal
motion of a translation stage. It consequently does not use the drag
coefficient of the trapped ob ject as an input. Thus, neither the viscosity,
nor the size of the trapped ob ject, nor its distance to nearby surfaces need
to be known. The method requires only a low level of instrumentation and can be
applied in situ in all spatial dimensions. It is both accurate and precise:
true values are returned, with small error-bars. We tested this experimentally,
near and far from surfaces. Both position- and force-calibration were accurate
to within 3%. To calibrate, we moved the sample with a piezo-electric
translation stage, but the laser beam could be moved instead, e.g. by
acousto-optic deflectors. Near surfaces, this precision requires an improved
formula for the hydrodynamical interaction between an infinite plane and a
micro-sphere in non-constant motion parallel to it. We give such a formula.Comment: Submitted to: Review of Scientific Instruments. 13 pages, 5 figures.
Appendix added (hydrodynamically correct calibration
Resampling to accelerate cross-correlation searches for continuous gravitational waves from binary systems
Continuous-wave (CW) gravitational waves (GWs) call for
computationally-intensive methods. Low signal-to-noise ratio signals need
templated searches with long coherent integration times and thus fine
parameter-space resolution. Longer integration increases sensitivity. Low-mass
x-ray binaries (LMXBs) such as Scorpius X-1 (Sco X-1) may emit accretion-driven
CWs at strains reachable by current ground-based observatories. Binary orbital
parameters induce phase modulation. This paper describes how resampling
corrects binary and detector motion, yielding source-frame time series used for
cross-correlation. Compared to the previous, detector-frame, templated
cross-correlation method, used for Sco X-1 on data from the first Advanced LIGO
observing run (O1), resampling is about 20x faster in the costliest,
most-sensitive frequency bands. Speed-up factors depend on integration time and
search setup. The speed could be reinvested into longer integration with a
forecast sensitivity gain, 20 to 125 Hz median, of approximately 51%, or from
20 to 250 Hz, 11%, given the same per-band cost and setup. This paper's timing
model enables future setup optimization. Resampling scales well with longer
integration, and at 10x unoptimized cost could reach respectively 2.83x and
2.75x median sensitivities, limited by spin-wandering. Then an O1 search could
yield a marginalized-polarization upper limit reaching torque-balance at 100
Hz. Frequencies from 40 to 140 Hz might be probed in equal observing time with
2x improved detectors.Comment: 28 pages, 7 figures, 3 table
Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect
The quantum Hall effect is necessarily accompanied by low-energy excitations
localized at the edge of a two-dimensional electron system. For the case of
electrons interacting via the long-range Coulomb interaction, these excitations
are edge magnetoplasmons. We address the time evolution of localized
edge-magnetoplasmon wave packets. On short times the wave packets move along
the edge with classical E cross B drift. We show that on longer times the wave
packets can have properties similar to those of the Rydberg wave packets that
are produced in atoms using short-pulsed lasers. In particular, we show that
edge-magnetoplasmon wave packets can exhibit periodic revivals in which a
dispersed wave packet reassembles into a localized one. We propose the study of
edge-magnetoplasmon wave packets as a tool to investigate dynamical properties
of integer and fractional quantum-Hall edges. Various scenarios are discussed
for preparing the initial wave packet and for detecting it at a later time. We
comment on the importance of magnetoplasmon-phonon coupling and on quantum and
thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was
originally 3Mbyte and had to be bitmapped for submission to archive; in the
process it acquired distracting artifacts, to upload the better version, see
http://physics.indiana.edu/~uli/publ/projects.htm
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