7,727 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
Multispace and Multilevel BDDC
BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl
Studies of waveform requirements for intermediate mass-ratio coalescence searches with advanced detectors
The coalescence of a stellar-mass compact object into an intermediate-mass
black hole (intermediate mass-ratio coalescence; IMRAC) is an important
astrophysical source for ground-based gravitational-wave interferometers in the
so-called advanced configuration. However, the ability to carry out effective
matched-filter based searches for these systems is limited by the lack of
reliable waveforms. Here we consider binaries in which the intermediate-mass
black hole has mass in the range 24 - 200 solar masses with a stellar-mass
companion having masses in the range 1.4 - 18.5 solar masses. In addition, we
constrain the mass ratios, q, of the binaries to be in the range 1/140 < q <
1/10 and we restrict our study to the case of circular binaries with
non-spinning components. We investigate the relative contribution to the
signal-to-noise ratio (SNR) of the three different phases of the coalescence:
inspiral, merger and ringdown. We show that merger and ringdown contribute to a
substantial fraction of the total SNR over a large portion of the mass
parameter space, although in a limited portion the SNR is dominated by the
inspiral phase. We further identify three regions in the IMRAC mass-space in
which: (i) inspiral-only searches could be performed with losses in detection
rates L in the range 10% < L < 27%, (ii) searches based on inspiral-only
templates lead to a loss in detection rates in the range 27% < L < 50%$, and
(iii) templates that include merger and ringdown are essential to prevent
losses in detection rates greater than 50%. We investigate the effectiveness
with which the inspiral-only portion of the IMRAC waveform space is covered by
comparing several existing waveform families in this regime. Our results
reinforce the importance of extensive numerical relativity simulations of
IMRACs and the need for further studies of suitable approximation schemes in
this mass range.Comment: 10 pages, 3 figure
Directory of aerospace safety specialized information sources
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Two-photon interference with two independent pseudo-thermal sources
The nature of two-photon interference is a subject that has aroused renewed
interest in recent years and is still under debate. In this paper we report the
first observation of two-photon interference with independent pseudo-thermal
sources in which sub-wavelength interference is observed. The phenomenon may be
described in terms of the classical statistical distribution of the two sources
and their optical transfer functions.Comment: Phys. Rev. A 74, 053807 (2006
Phase dynamics of a multimode Bose condensate controlled by decay
The relative phase between two uncoupled BE condensates tends to attain a
specific value when the phase is measured. This can be done by observing their
decay products in interference. We discuss exactly solvable models for this
process in cases where competing observation channels drive the phases to
different sets of values. We treat the case of two modes which both emit into
the input ports of two beam splitters, and of a linear or circular chain of
modes. In these latter cases, the transitivity of relative phase becomes an
issue
Quantum information processing using frequency control of impurity spins in diamond
Spin degrees of freedom of charged nitrogen-vacancy (NV) centers in
diamond have large decoherence times even at room temperature, can be
initialized and read out using optical fields, and are therefore a promising
candidate for solid state qubits. Recently, quantum manipulations of NV-
centers using RF fields were experimentally realized. In this paper we show;
first, that such operations can be controlled by varying the frequency of the
signal, instead of its amplitude, and NV- centers can be selectively
addressed even with spacially uniform RF signals; second, that when several \NV
- centers are placed in an off-resonance optical cavity, a similar application
of classical optical fields provides a controlled coupling and enables a
universal two-qubit gate (CPHASE). RF and optical control together promise a
scalable quantum computing architecture
A Transactional Analysis of Interaction Free Measurements
The transactional interpretation of quantum mechanics is applied to the
"interaction-free" measurement scenario of Elitzur and Vaidman and to the
Quantum Zeno Effect version of the measurement scenario by Kwiat, et al. It is
shown that the non-classical information provided by the measurement scheme is
supplied by the probing of the intervening object by incomplete offer and
confirmation waves that do not form complete transactions or lead to real
interactions.Comment: Accepted for publication in Foundations of Physics Letter
Role of spatial coherence in polarization tomography
We analyze an experimental setup in which a quasi-monochromatic spatially
coherent beam of light is used to probe a paraxial optical scatterer. We
discuss the effect of the spatial coherence of the probe beam on the Mueller
matrix representing the scatterer. We show that according to the degree of
spatial coherence of the beam, the \emph{same} scattering system can be
represented by \emph{different} Mueller matrices. This result should serve as a
warning for experimentalists.Comment: 3 pages, 1 figur
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