34,314 research outputs found
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA
Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods
Feature extraction and dimensionality reduction are important tasks in many
fields of science dealing with signal processing and analysis. The relevance of
these techniques is increasing as current sensory devices are developed with
ever higher resolution, and problems involving multimodal data sources become
more common. A plethora of feature extraction methods are available in the
literature collectively grouped under the field of Multivariate Analysis (MVA).
This paper provides a uniform treatment of several methods: Principal Component
Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis
(CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions
derived by means of the theory of reproducing kernel Hilbert spaces. We also
review their connections to other methods for classification and statistical
dependence estimation, and introduce some recent developments to deal with the
extreme cases of large-scale and low-sized problems. To illustrate the wide
applicability of these methods in both classification and regression problems,
we analyze their performance in a benchmark of publicly available data sets,
and pay special attention to specific real applications involving audio
processing for music genre prediction and hyperspectral satellite images for
Earth and climate monitoring
Subtraction-noise projection in gravitational-wave detector networks
In this paper, we present a successful implementation of a subtraction-noise
projection method into a simple, simulated data analysis pipeline of a
gravitational-wave search. We investigate the problem to reveal a weak
stochastic background signal which is covered by a strong foreground of
compact-binary coalescences. The foreground which is estimated by matched
filters, has to be subtracted from the data. Even an optimal analysis of
foreground signals will leave subtraction noise due to estimation errors of
template parameters which may corrupt the measurement of the background signal.
The subtraction noise can be removed by a noise projection. We apply our
analysis pipeline to the proposed future-generation space-borne Big Bang
Observer (BBO) mission which seeks for a stochastic background of primordial
GWs in the frequency range Hz covered by a foreground of
black-hole and neutron-star binaries. Our analysis is based on a simulation
code which provides a dynamical model of a time-delay interferometer (TDI)
network. It generates the data as time series and incorporates the analysis
pipeline together with the noise projection. Our results confirm previous ad
hoc predictions which say that BBO will be sensitive to backgrounds with
fractional energy densities below Comment: 54 pages, 15 figure
Gravitational conundrum? Dynamical mass segregation versus disruption of binary stars in dense stellar systems
Upon their formation, dynamically cool (collapsing) star clusters will,
within only a few million years, achieve stellar mass segregation for stars
down to a few solar masses, simply because of gravitational two-body
encounters. Since binary systems are, on average, more massive than single
stars, one would expect them to also rapidly mass segregate dynamically.
Contrary to these expectations and based on high-resolution Hubble Space
Telescope observations, we show that the compact, 15-30 Myr-old Large
Magellanic Cloud cluster NGC 1818 exhibits tantalizing hints at the >= 2 sigma
level of significance (> 3 sigma if we assume a power-law secondary-to-primary
mass-ratio distribution) of an increasing fraction of F-star binary systems
(with combined masses of 1.3-1.6 Msun) with increasing distance from the
cluster center, specifically between the inner 10 to 20" (approximately
equivalent to the cluster's core and half-mass radii) and the outer 60 to 80".
If confirmed, this will offer support of the theoretically predicted but thus
far unobserved dynamical disruption processes of the significant population of
'soft' binary systems---with relatively low binding energies compared to the
kinetic energy of their stellar members---in star clusters, which we have
access to here by virtue of the cluster's unique combination of youth and high
stellar density.Comment: Accepted for publication in The Astrophysical Journal; 19 pages in
AASTeX format; 3 figure
Optimal inference in a class of regression models
We consider the problem of constructing confidence intervals (CIs) for a
linear functional of a regression function, such as its value at a point, the
regression discontinuity parameter, or a regression coefficient in a linear or
partly linear regression. Our main assumption is that the regression function
is known to lie in a convex function class, which covers most smoothness and/or
shape assumptions used in econometrics. We derive finite-sample optimal CIs and
sharp efficiency bounds under normal errors with known variance. We show that
these results translate to uniform (over the function class) asymptotic results
when the error distribution is not known. When the function class is
centrosymmetric, these efficiency bounds imply that minimax CIs are close to
efficient at smooth regression functions. This implies, in particular, that it
is impossible to form CIs that are tighter using data-dependent tuning
parameters, and maintain coverage over the whole function class. We specialize
our results to inference on the regression discontinuity parameter, and
illustrate them in simulations and an empirical application.Comment: 39 pages plus supplementary material
Weak Lensing by High-Redshift Clusters of Galaxies - I: Cluster Mass Reconstruction
We present the results of a weak lensing survey of six high-redshift (z >
0.5), X-ray selected clusters of galaxies. We have obtained ultra-deep R-band
images of each cluster with the Keck Telescope, and have measured a weak
lensing signal from each cluster. From the background galaxy ellipticities we
create two-dimensional maps of the surface mass density of each cluster. We
find that the substructure seen in the mass reconstructions typically agree
well with substructure in both the cluster galaxy distributions and X-ray
images of the clusters. We also measure the one-dimensional radial profiles of
the lensing signals and fit these with both isothermal spheres and "universal"
CDM profiles. We find that the more massive clusters are less compact and not
as well fit by isothermal spheres as the less massive clusters, possibly
indicating that they are still in the process of collapse.Comment: 43 pages, 15 figures, uses aastex, submitted to ApJ 4 color plates
produced here as jpg's, larger versions of the jpgs can be found at
http://www.mpa-garching.mpg.de/~clow
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