194,852 research outputs found
Polynomial Meshes: Computation and Approximation
We present the software package WAM, written in Matlab, that generates Weakly
Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d
polynomial least squares and interpolation on compact sets with various geometries.
Possible applications range from data fitting to high-order methods for PDEs
Review of the mathematical foundations of data fusion techniques in surface metrology
The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed
A method for the estimation of p-mode parameters from averaged solar oscillation power spectra
A new fitting methodology is presented which is equally well suited for the
estimation of low-, medium-, and high-degree mode parameters from -averaged
solar oscillation power spectra of widely differing spectral resolution. This
method, which we call the "Windowed, MuLTiple-Peak, averaged spectrum", or
WMLTP Method, constructs a theoretical profile by convolving the weighted sum
of the profiles of the modes appearing in the fitting box with the power
spectrum of the window function of the observing run using weights from a
leakage matrix that takes into account both observational and physical effects,
such as the distortion of modes by solar latitudinal differential rotation. We
demonstrate that the WMLTP Method makes substantial improvements in the
inferences of the properties of the solar oscillations in comparison with a
previous method that employed a single profile to represent each spectral peak.
We also present an inversion for the internal solar structure which is based
upon 6,366 modes that we have computed using the WMLTP method on the 66-day
long 2010 SOHO/MDI Dynamics Run. To improve both the numerical stability and
reliability of the inversion we developed a new procedure for the
identification and correction of outliers in a frequency data set. We present
evidence for a pronounced departure of the sound speed in the outer half of the
solar convection zone and in the subsurface shear layer from the radial sound
speed profile contained in Model~S of Christensen-Dalsgaard and his
collaborators that existed in the rising phase of Solar Cycle~24 during
mid-2010
Infrared Observations During the Secondary Eclipse of HD 209458b: I. 3.6-Micron Occultation Spectroscopy Using the VLT
We search for an infrared signature of the transiting extrasolar planet HD
209458b during secondary eclipse. Our method, which we call `occultation
spectroscopy,' searches for the disappearance and reappearance of weak spectral
features due to the exoplanet as it passes behind the star and later reappears.
We argue that at the longest infrared wavelengths, this technique becomes
preferable to conventional `transit spectroscopy'. We observed the system in
the wing of the strong nu-3 band of methane near 3.6 microns during two
secondary eclipses, using the VLT/ISAAC spectrometer at a spectral resolution
of 3300. Our analysis, which utilizes a model template spectrum, achieves
sufficient precision to expect detection of the spectral structure predicted by
an irradiated, low-opacity (cloudless), low-albedo, thermochemical equilibrium
model for the exoplanet atmosphere. However, our observations show no evidence
for the presence of this spectrum from the exoplanet, with the statistical
significance of the non-detection depending on the timing of the secondary
eclipse, which depends on the assumed value for the orbital eccentricity. Our
results reject certain specific models of the atmosphere of HD 209458b as
inconsistent with our observations at the 3-sigma level, given assumptions
about the stellar and planetary parameters.Comment: 26 pages, 8 figures Accepted to Astrophysical Journa
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
Fast B-spline Curve Fitting by L-BFGS
We propose a novel method for fitting planar B-spline curves to unorganized
data points. In traditional methods, optimization of control points and foot
points are performed in two very time-consuming steps in each iteration: 1)
control points are updated by setting up and solving a linear system of
equations; and 2) foot points are computed by projecting each data point onto a
B-spline curve. Our method uses the L-BFGS optimization method to optimize
control points and foot points simultaneously and therefore it does not need to
perform either matrix computation or foot point projection in every iteration.
As a result, our method is much faster than existing methods
Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced
quantum phase transition between a semimetallic phase at weak disorder and a
diffusive-metallic phase at strong disorder. Despite considerable effort, both
numerically and analytically, the critical exponents and of this
phase transition are not known precisely. Here we report a numerical
calculation of the critical exponent using a minimal
single-Weyl node model and a finite-size scaling analysis of conductance. Our
high-precision numerical value for is incompatible with previous
numerical studies on tight-binding models and with one- and two-loop
calculations in an -expansion scheme. We further obtain
from the scaling of the conductivity with chemical potential
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