5,513 research outputs found
BDDC and FETI-DP under Minimalist Assumptions
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary
simple abstract form. It is shown that their properties can be obtained from
only on a very small set of algebraic assumptions. The presentation is purely
algebraic and it does not use any particular definition of method components,
such as substructures and coarse degrees of freedom. It is then shown that
P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC
preconditioned operators are of the same algebraic form, and the standard
condition number bound carries over to arbitrary abstract operators of this
form. The equality of eigenvalues of BDDC and FETI-DP also holds in the
minimalist abstract setting. The abstract framework is explained on a standard
substructuring example.Comment: 11 pages, 1 figure, also available at
http://www-math.cudenver.edu/ccm/reports
Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case
The objective of this paper is to show how the recently proposed method by
Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to
a case of real polynomial equation solving. Our main result concerns the
problem of finding one representative point for each connected component of a
real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a
method for symbolically solving a zero-dimensional polynomial equation system
in the affine (and toric) case. Its main feature is the use of adapted data
structure: Arithmetical networks and straight-line programs. The algorithm
solves any affine zero-dimensional equation system in non-uniform sequential
time that is polynomial in the length of the input description and an
adequately defined {\em affine degree} of the equation system. Replacing the
affine degree of the equation system by a suitably defined {\em real degree} of
certain polar varieties associated to the input equation, which describes the
hypersurface under consideration, and using straight-line program codification
of the input and intermediate results, we obtain a method for the problem
introduced above that is polynomial in the input length and the real degree.Comment: Late
Signal-to-noise ratio of Gaussian-state ghost imaging
The signal-to-noise ratios (SNRs) of three Gaussian-state ghost imaging
configurations--distinguished by the nature of their light sources--are
derived. Two use classical-state light, specifically a joint signal-reference
field state that has either the maximum phase-insensitive or the maximum
phase-sensitive cross correlation consistent with having a proper
representation. The third uses nonclassical light, in particular an entangled
signal-reference field state with the maximum phase-sensitive cross correlation
permitted by quantum mechanics. Analytic SNR expressions are developed for the
near-field and far-field regimes, within which simple asymptotic approximations
are presented for low-brightness and high-brightness sources. A high-brightness
thermal-state (classical phase-insensitive state) source will typically achieve
a higher SNR than a biphoton-state (low-brightness, low-flux limit of the
entangled-state) source, when all other system parameters are equal for the two
systems. With high efficiency photon-number resolving detectors, a
low-brightness, high-flux entangled-state source may achieve a higher SNR than
that obtained with a high-brightness thermal-state source.Comment: 12 pages, 4 figures. This version incorporates additional references
and a new analysis of the nonclassical case that, for the first time,
includes the complete transition to the classical signal-to-noise ratio
asymptote at high source brightnes
On the measure of nonclassicality of field states
The degree of nonclassicality of states of a field mode is analysed
considering both phase-space and distance-type measures of nonclassicality. By
working out some general examples, it is shown explicitly that the phase-space
measure is rather sensitive to superposition of states, with finite
superpositions possessing maximum nonclassical depth (the highest degree of
nonclassicality) irrespective to the nature of the component states. Mixed
states are also discussed and examples with nonclassical depth varying between
the minimum and the maximum allowed values are exhibited. For pure Gaussian
states, it is demonstrated that distance-type measures based on the
Hilbert-Schmidt metric are equivalent to the phase-space measure. Analyzing
some examples, it is shown that distance-type measures are efficient to
quantify the degree of nonclassicality of non-Gaussian pure states.Comment: Latex, 21 pages, 1 figur
Natural orbits of atomic Cooper pairs in a nonuniform Fermi gas
We examine the basic mode structure of atomic Cooper pairs in an
inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasi-particle
vacuum, the single particle density matrix and the anomalous density matrix
share the same set of eigenfunctions. These eigenfunctions correspond to
natural pairing orbits associated with the BCS ground state. We investigate
these orbits for a Fermi gas in a spherical harmonic trap, and construct the
wave function of a Cooper pair in the form of Schmidt decomposition. The issue
of spatial quantum entanglement between constituent atoms in a pair is
addressed.Comment: 14 pages, 4 figures, submitted to Phys. Rev.
Effects of resin coating methods and other variables on physical properties of glass-fabric reinforced polyesters
On the Interpretation of Supernova Light Echo Profiles and Spectra
The light echo systems of historical supernovae in the Milky Way and local
group galaxies provide an unprecedented opportunity to reveal the effects of
asymmetry on observables, particularly optical spectra. Scattering dust at
different locations on the light echo ellipsoid witnesses the supernova from
different perspectives and the light consequently scattered towards Earth
preserves the shape of line profile variations introduced by asymmetries in the
supernova photosphere. However, the interpretation of supernova light echo
spectra to date has not involved a detailed consideration of the effects of
outburst duration and geometrical scattering modifications due to finite
scattering dust filament dimension, inclination, and image point-spread
function and spectrograph slit width. In this paper, we explore the
implications of these factors and present a framework for future resolved
supernova light echo spectra interpretation, and test it against Cas A and SN
1987A light echo spectra. We conclude that the full modeling of the dimensions
and orientation of the scattering dust using the observed light echoes at two
or more epochs is critical for the correct interpretation of light echo
spectra. Indeed, without doing so one might falsely conclude that differences
exist when none are actually present.Comment: 18 pages, 22 figures, accepted for publication in Ap
Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry
Transmission spectra of metallic films or membranes perforated by arrays of
subwavelength slits or holes have been widely interpreted as resonance
absorption by surface plasmon polaritons (SPPs). Alternative interpretations
involving evanescent waves diffracted on the surface have also been proposed.
These two approaches lead to divergent predictions for some surface wave
properties. Using far-field interferometry, we have carried out a series of
measurements on elementary one-dimensional (1-D) subwavelength structures with
the aim of testing key properties of the surface waves and comparing them to
predictions of these two points of view
The stationary phase point method for transitional scattering: diffractive radio scintillation for pulsar
The stationary phase point (SPP) method in one-dimensional case is introduced
to treat the diffractive scintillation. From weak scattering, where the SPP
number N=1, to strong scattering (N1), via transitional scattering regime
(N2,3), we find that the modulation index of intensity experiences the
monotonically increasing from 0 to 1 with the scattering strength,
characterized by the ratio of Fresnel scale \rf to diffractive scale
\rdiff.Comment: Hanas Meeting paper, appear in ChJAA, 2006, 6, Su
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