7,884 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
Insights into neutralization of animal viruses gained from study of influenza virus
It has long been known that the binding of antibodies to viruses can result in a loss of infectivity, or neutralization, but little is understood of the mechanism or mechanisms of this process. This is probably because neutralization is a multifactorial phenomenon depending upon the nature of the virus itself, the particular antigenic site involved, the isotype of immunoglobulin and the ratio of virus to immunoglobulin (see below). Thus not only is it likely that neutralization of one virus will differ from another but that changing the circumstances of neutralization can change the mechanism itself. To give coherence to the topic we are concentrating this review on one virus, influenza type A which is itself well studied and reasonably well understood [1–3]. Reviews of the older literature can be found in references 4 to 7
The geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem
The most promising way to compute the gravitational waves emitted by binary
black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques
fail, is a quasistationary approximation introduced by Detweiler and being
pursued by Price and others. In this approximation the outgoing gravitational
waves at infinity and downgoing gravitational waves at the holes' horizons are
replaced by standing waves so as to guarantee that the spacetime has a helical
Killing vector field. Because the horizon generators will not, in general, be
tidally locked to the holes' orbital motion, the standing waves will destroy
the horizons, converting the black holes into naked singularities that resemble
black holes down to near the horizon radius. This paper uses a spherically
symmetric, scalar-field model problem to explore in detail the following BBH
issues: (i) The destruction of a horizon by the standing waves. (ii) The
accuracy with which the resulting naked singularity resembles a black hole.
(iii) The conversion of the standing-wave spacetime (with a destroyed horizon)
into a spacetime with downgoing waves by the addition of a ``radiation-reaction
field''. (iv) The accuracy with which the resulting downgoing waves agree with
the downgoing waves of a true black-hole spacetime (with horizon). The model
problem used to study these issues consists of a Schwarzschild black hole
endowed with spherical standing waves of a scalar field. It is found that the
spacetime metric of the singular, standing-wave spacetime, and its
radiation-reaction-field-constructed downgoing waves are quite close to those
for a Schwarzschild black hole with downgoing waves -- sufficiently close to
make the BBH quasistationary approximation look promising for
non-tidally-locked black holes.Comment: 12 pages, 6 figure
Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
We examine whether metrological resolution beyond coherent states is a
nonclassical effect. We show that this is true for linear detection schemes but
false for nonlinear schemes, and propose a very simple experimental setup to
test it. We find a nonclassicality criterion derived from quantum Fisher
information.Comment: 4 pages, 1 figur
Quantum Zeno Effect for Exponentially Decaying Systems
The quantum Zeno effect -- suppression of decay by frequent measurements --
was believed to occur only when the response of the detector is so quick that
the initial tiny deviation from the exponential decay law is detectable.
However, we show that it can occur even for exactly exponentially decaying
systems, for which this condition is never satisfied, by considering a
realistic case where the detector has a finite energy band of detection. The
conventional theories correspond to the limit of an infinite bandwidth. This
implies that the Zeno effect occurs more widely than expected so far.Comment: 4 pages, 3 figure
Independent nonclassical tests for states and measurements in the same experiment
We show that one single experiment can test simultaneously and independently
both the nonclassicality of states and measurements by the violation or
fulfillment of classical bounds on the statistics. Nonideal measurements
affected by imperfections can be characterized by two bounds depending on
whether we test the ideal measurement or the real one.Comment: 9 pages, 3 figures. Proceedings of 17th CEWQO 201
Ordered Measurements of Permutationally-Symmetric Qubit Strings
We show that any sequence of measurements on a permutationally-symmetric
(pure or mixed) multi-qubit string leaves the unmeasured qubit substring also
permutationally-symmetric. In addition, we show that the measurement
probabilities for an arbitrary sequence of single-qubit measurements are
independent of how many unmeasured qubits have been lost prior to the
measurement. Our results are valuable for quantum information processing of
indistinguishable particles by post-selection, e.g. in cases where the results
of an experiment are discarded conditioned upon the occurrence of a given event
such as particle loss. Furthermore, our results are important for the design of
adaptive-measurement strategies, e.g. a series of measurements where for each
measurement instance, the measurement basis is chosen depending on prior
measurement results.Comment: 13 page
Cooperative effects in Josephson junctions in a cavity in the strong coupling regime
We analyze the behavior of systems of two and three qubits made by Josephson
junctions, treated in the two level approximation, driven by a radiation mode
in a cavity. The regime we consider is a strong coupling one recently
experimentally reached for a single junction. Rabi oscillations are obtained
with the frequency proportional to integer order Bessel functions in the limit
of a large photon number, similarly to the case of the single qubit. A
selection rule is derived for the appearance of Rabi oscillations. A quantum
amplifier built with a large number of Josephson junctions in a cavity in the
strong coupling regime is also described.Comment: 9 pages, no figures. Version accepted for publication in Physical
Review
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