14,946 research outputs found
Tractability of multivariate problems for standard and linear information in the worst case setting: part II
We study QPT (quasi-polynomial tractability) in the worst case setting for
linear tensor product problems defined over Hilbert spaces. We assume that the
domain space is a reproducing kernel Hilbert space so that function values are
well defined. We prove QPT for algorithms that use only function values under
the three assumptions:
1) the minimal errors for the univariate case decay polynomially fast to
zero,
2) the largest singular value for the univariate case is simple and
3) the eigenfunction corresponding to the largest singular value is a
multiple of the function value at some point.
The first two assumptions are necessary for QPT. The third assumption is
necessary for QPT for some Hilbert spaces
"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
We present a new 3D general relativistic hydrodynamics code for simulations
of stellar core collapse to a neutron star, as well as pulsations and
instabilities of rotating relativistic stars. It uses spectral methods for
solving the metric equations, assuming the conformal flatness approximation for
the three-metric. The matter equations are solved by high-resolution
shock-capturing schemes. We demonstrate that the combination of a finite
difference grid and a spectral grid can be successfully accomplished. This
"Mariage des Maillages" (French for grid wedding) approach results in high
accuracy of the metric solver and allows for fully 3D applications using
computationally affordable resources, and ensures long term numerical stability
of the evolution. We compare our new approach to two other, finite difference
based, methods to solve the metric equations. A variety of tests in 2D and 3D
is presented, involving highly perturbed neutron star spacetimes and
(axisymmetric) stellar core collapse, demonstrating the ability to handle
spacetimes with and without symmetries in strong gravity. These tests are also
employed to assess gravitational waveform extraction, which is based on the
quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests
and grid setu
The optimal polarizations for achieving maximum contrast in radar images
There is considerable interest in determining the optimal polarizations that maximize contrast between two scattering classes in polarimetric radar images. A systematic approach is presented for obtaining the optimal polarimetric matched filter, i.e., that filter which produces maximum contrast between two scattering classes. The maximization procedure involves solving an eigenvalue problem where the eigenvector corresponding to the maximum contrast ratio is an optimal polarimetric matched filter. To exhibit the physical significance of this filter, it is transformed into its associated transmitting and receiving polarization states, written in terms of horizontal and vertical vector components. For the special case where the transmitting polarization is fixed, the receiving polarization which maximizes the contrast ratio is also obtained. Polarimetric filtering is then applies to synthetic aperture radar images obtained from the Jet Propulsion Laboratory. It is shown, both numerically and through the use of radar imagery, that maximum image contrast can be realized when data is processed with the optimal polarimeter matched filter
Determination of the magnetic anisotropy axes of single-molecule magnets
Simple methods are presented allowing the determination of the magnetic
anisotropy axes of a crystal of a single-molecule magnet (SMM). These methods
are used to determine an upper bound of the easy axis tilts in a standard
Mn12-Ac crystal. The values obtained in the present study are significately
smaller than those reported in recent high frequency electron paramagnetic
resonance (HF-EPR) studies which suggest distributions of hard-axes tilts.Comment: 10 pages, 6 figure
Radius Dependent Luminosity Evolution of Blue Galaxies in GOODS-N
We examine the radius-luminosity (R-L) relation for blue galaxies in the Team
Keck Redshift Survey (TKRS) of GOODS-N. We compare with a volume-limited, Sloan
Digital Sky Survey sample and find that the R-L relation has evolved to lower
surface brightness since z=1. Based on the detection limits of GOODS this can
not be explained by incompleteness in low surface-brightness galaxies. Number
density arguments rule out a pure radius evolution. It can be explained by a
radius dependent decline in B-band luminosity with time. Assuming a linear
shift in M_B with z, we use a maximum likelihood method to quantify the
evolution. Under these assumptions, large (R_{1/2} > 5 kpc), and intermediate
sized (3 < R_{1/2} < 5 kpc) galaxies, have experienced Delta M_B =1.53
(-0.10,+0.13) and 1.65 (-0.18, +0.08) magnitudes of dimming since z=1. A simple
exponential decline in star formation with an e-folding time of 3 Gyr can
result in this amount of dimming. Meanwhile, small galaxies, or some subset
thereof, have experienced more evolution, 2.55 (+/- 0.38) magnitudes. This
factor of ten decline in luminosity can be explained by sub-samples of
starbursting dwarf systems that fade rapidly, coupled with a decline in burst
strength or frequency. Samples of bursting, luminous, blue, compact galaxies at
intermediate redshifts have been identified by various previous studies. If
there has been some growth in galaxy size with time, these measurements are
upper limits on luminosity fading.Comment: 34 Total pages, 15 Written pages, 19 pages of Data Table, 13 Figures,
accepted for publication in Ap
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