11,693 research outputs found
Gravitational energy as dark energy: Concordance of cosmological tests
We provide preliminary quantitative evidence that a new solution to averaging
the observed inhomogeneous structure of matter in the universe [gr-qc/0702082,
arxiv:0709.0732], may lead to an observationally viable cosmology without
exotic dark energy. We find parameters which simultaneously satisfy three
independent tests: the match to the angular scale of the sound horizon detected
in the cosmic microwave background anisotropy spectrum; the effective comoving
baryon acoustic oscillation scale detected in galaxy clustering statistics; and
type Ia supernova luminosity distances. Independently of the supernova data,
concordance is obtained for a value of the Hubble constant which agrees with
the measurement of the Hubble Key team of Sandage et al [astro-ph/0603647].
Best-fit parameters include a global average Hubble constant H_0 = 61.7
(+1.2/-1.1) km/s/Mpc, a present epoch void volume fraction of f_{v0} = 0.76
(+0.12/-0.09), and an age of the universe of 14.7 (+0.7/-0.5) billion years as
measured by observers in galaxies. The mass ratio of non-baryonic dark matter
to baryonic matter is 3.1 (+2.5/-2.4), computed with a baryon-to-photon ratio
that concords with primordial lithium abundances.Comment: 4 pages, 2 figures; v2 improved statistics, references added, to
appear in ApJ Letter
Steady state theory of current transfer
Current transfer is defined as a charge transfer process where the
transferred charge carries information about its original motion. We have
recently suggested that such transfer causes the asymmetry observed in electron
transfer induced by circularly polarized light through helical wires. This
paper presents the steady state theory of current transfer within a tight
binding model of coupled wires systems. The efficiency of current transfer is
quantified in terms of the calculated asymmetry in the system response to a
steady current imposed on one of the wires, with respect to the imposed current
direction.Comment: 25 pages, 14 figure
The empirical accuracy of uncertain inference models
Uncertainty is a pervasive feature of the domains in which expert systems are designed to function. Research design to test uncertain inference methods for accuracy and robustness, in accordance with standard engineering practice is reviewed. Several studies were conducted to assess how well various methods perform on problems constructed so that correct answers are known, and to find out what underlying features of a problem cause strong or weak performance. For each method studied, situations were identified in which performance deteriorates dramatically. Over a broad range of problems, some well known methods do only about as well as a simple linear regression model, and often much worse than a simple independence probability model. The results indicate that some commercially available expert system shells should be used with caution, because the uncertain inference models that they implement can yield rather inaccurate results
Continuous phase amplification with a Sagnac interferometer
We describe a weak value inspired phase amplification technique in a Sagnac
interferometer. We monitor the relative phase between two paths of a slightly
misaligned interferometer by measuring the average position of a split-Gaussian
mode in the dark port. Although we monitor only the dark port, we show that the
signal varies linearly with phase and that we can obtain similar sensitivity to
balanced homodyne detection. We derive the source of the amplification both
with classical wave optics and as an inverse weak value.Comment: 5 pages, 4 figures, previously submitted for publicatio
Adaptation Algorithm and Theory Based on Generalized Discrepancy
We present a new algorithm for domain adaptation improving upon a discrepancy
minimization algorithm previously shown to outperform a number of algorithms
for this task. Unlike many previous algorithms for domain adaptation, our
algorithm does not consist of a fixed reweighting of the losses over the
training sample. We show that our algorithm benefits from a solid theoretical
foundation and more favorable learning bounds than discrepancy minimization. We
present a detailed description of our algorithm and give several efficient
solutions for solving its optimization problem. We also report the results of
several experiments showing that it outperforms discrepancy minimization
Multilevel convergence analysis of multigrid-reduction-in-time
This paper presents a multilevel convergence framework for
multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid
estimates. The framework provides a priori upper bounds on the convergence of
MGRIT V- and F-cycles, with different relaxation schemes, by deriving the
respective residual and error propagation operators. The residual and error
operators are functions of the time stepping operator, analyzed directly and
bounded in norm, both numerically and analytically. We present various upper
bounds of different computational cost and varying sharpness. These upper
bounds are complemented by proposing analytic formulae for the approximate
convergence factor of V-cycle algorithms that take the number of fine grid time
points, the temporal coarsening factors, and the eigenvalues of the time
stepping operator as parameters.
The paper concludes with supporting numerical investigations of parabolic
(anisotropic diffusion) and hyperbolic (wave equation) model problems. We
assess the sharpness of the bounds and the quality of the approximate
convergence factors. Observations from these numerical investigations
demonstrate the value of the proposed multilevel convergence framework for
estimating MGRIT convergence a priori and for the design of a convergent
algorithm. We further highlight that observations in the literature are
captured by the theory, including that two-level Parareal and multilevel MGRIT
with F-relaxation do not yield scalable algorithms and the benefit of a
stronger relaxation scheme. An important observation is that with increasing
numbers of levels MGRIT convergence deteriorates for the hyperbolic model
problem, while constant convergence factors can be achieved for the diffusion
equation. The theory also indicates that L-stable Runge-Kutta schemes are more
amendable to multilevel parallel-in-time integration with MGRIT than A-stable
Runge-Kutta schemes.Comment: 26 pages; 17 pages Supplementary Material
On the Propagation of Slip Fronts at Frictional Interfaces
The dynamic initiation of sliding at planar interfaces between deformable and
rigid solids is studied with particular focus on the speed of the slip front.
Recent experimental results showed a close relation between this speed and the
local ratio of shear to normal stress measured before slip occurs (static
stress ratio). Using a two-dimensional finite element model, we demonstrate,
however, that fronts propagating in different directions do not have the same
dynamics under similar stress conditions. A lack of correlation is also
observed between accelerating and decelerating slip fronts. These effects
cannot be entirely associated with static local stresses but call for a dynamic
description. Considering a dynamic stress ratio (measured in front of the slip
tip) instead of a static one reduces the above-mentioned inconsistencies.
However, the effects of the direction and acceleration are still present. To
overcome this we propose an energetic criterion that uniquely associates,
independently on the direction of propagation and its acceleration, the slip
front velocity with the relative rise of the energy density at the slip tip.Comment: 15 pages, 6 figure
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