12,479 research outputs found
The practical implementation of fatigue requirements to military aircraft and helicopters in the United Kingdom
The methods adopted in the United Kingdom to ensure the structural integrity of military aeroplanes and helicopters from the fatigue point of view are described. The procedure adopted from the writing of the specification to the monitoring of fatigue life in service are presented along with the requirements to be met and the way in which they are satisfied. Some of the outstanding problems that remain to be solved are indicated
A model problem for conformal parameterizations of the Einstein constraint equations
We investigate the possibility that the conformal and conformal thin sandwich
(CTS) methods can be used to parameterize the set of solutions of the vacuum
Einstein constraint equations. To this end we develop a model problem obtained
by taking the quotient of certain symmetric data on conformally flat tori.
Specializing the model problem to a three-parameter family of conformal data we
observe a number of new phenomena for the conformal and CTS methods. Within
this family, we obtain a general existence theorem so long as the mean
curvature does not change sign. When the mean curvature changes sign, we find
that for certain data solutions exist if and only if the transverse-traceless
tensor is sufficiently small. When such solutions exist, there are generically
more than one. Moreover, the theory for mean curvatures changing sign is shown
to be extremely sensitive with respect to the value of a coupling constant in
the Einstein constraint equations.Comment: 40 pages, 4 figure
Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints
The Einstein constraint equations have been the subject of study for more
than fifty years. The introduction of the conformal method in the 1970's as a
parameterization of initial data for the Einstein equations led to increased
interest in the development of a complete solution theory for the constraints,
with the theory for constant mean curvature (CMC) spatial slices and closed
manifolds completely developed by 1995. The first general non-CMC existence
result was establish by Holst et al. in 2008, with extensions to rough data by
Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC
theory remains mostly open; moreover, recent work of Maxwell on specific
symmetry models sheds light on fundamental non-uniqueness problems with the
conformal method as a parameterization in non-CMC settings. In parallel with
these mathematical developments, computational physicists have uncovered
surprising behavior in numerical solutions to the extended conformal thin
sandwich formulation of the Einstein constraints. In particular, numerical
evidence suggests the existence of multiple solutions with a quadratic fold,
and a recent analysis of a simplified model supports this conclusion. In this
article, we examine this apparent bifurcation phenomena in a methodical way,
using modern techniques in bifurcation theory and in numerical homotopy
methods. We first review the evidence for the presence of bifurcation in the
Hamiltonian constraint in the time-symmetric case. We give a brief introduction
to the mathematical framework for analyzing bifurcation phenomena, and then
develop the main ideas behind the construction of numerical homotopy, or
path-following, methods in the analysis of bifurcation phenomena. We then apply
the continuation software package AUTO to this problem, and verify the presence
of the fold with homotopy-based numerical methods.Comment: 13 pages, 4 figures. Final revision for publication, added material
on physical implication
Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics
In this article we develop some new existence results for the Einstein
constraint equations using the Lichnerowicz-York conformal rescaling method.
The mean extrinsic curvature is taken to be an arbitrary smooth function
without restrictions on the size of its spatial derivatives, so that it can be
arbitrarily far from constant. The rescaled background metric belongs to the
positive Yamabe class, and the freely specifiable part of the data given by the
traceless-transverse part of the rescaled extrinsic curvature and the matter
fields are taken to be sufficiently small, with the matter energy density not
identically zero. Using topological fixed-point arguments and global barrier
constructions, we then establish existence of solutions to the constraints. Two
recent advances in the analysis of the Einstein constraint equations make this
result possible: A new type of topological fixed-point argument without
smallness conditions on spatial derivatives of the mean extrinsic curvature,
and a new construction of global super-solutions for the Hamiltonian constraint
that is similarly free of such conditions on the mean extrinsic curvature. For
clarity, we present our results only for strong solutions on closed manifolds.
However, our results also hold for weak solutions and for other cases such as
compact manifolds with boundary; these generalizations will appear elsewhere.
The existence results presented here for the Einstein constraints are
apparently the first such results that do not require smallness conditions on
spatial derivatives of the mean extrinsic curvature.Comment: 4 pages, no figures, accepted for publication in Physical Review
Letters. (Abstract shortenned and other minor changes reflecting v4 version
of arXiv:0712.0798
Progress report on the relativistic three-particle quantization condition
We describe recent work on the relativistic three-particle quantization
condition, generalizing and applying the original formalism of Hansen and
Sharpe, and of Brice\~no, Hansen and Sharpe. In particular, we sketch three
recent developments: the generalization of the formalism to include K-matrix
poles; the numerical implementation of the quantization condition in the
isotropic approximation; and ongoing work extending the description of the
three-particle divergence-free K matrix beyond the isotropic approximation.Comment: 7 pages, 1 figure, Proceedings of Lattice 201
High-flux beam source for cold, slow atoms or molecules
We demonstrate and characterize a high-flux beam source for cold, slow atoms
or molecules. The desired species is vaporized using laser ablation, then
cooled by thermalization in a cryogenic cell of buffer gas. The beam is formed
by particles exiting a hole in the buffer gas cell. We characterize the
properties of the beam (flux, forward velocity, temperature) for both an atom
(Na) and a molecule (PbO) under varying buffer gas density, and discuss
conditions for optimizing these beam parameters. Our source compares favorably
to existing techniques of beam formation, for a variety of applications.Comment: 5 Pages, 4 figure
The prevalence of medical reasons for non-participation in the Scottish breast and bowel cancer screening programmes
Objective: Increasing uptake of cancer screening is a priority for health systems internationally, however, some patients may not attend because they are undergoing active treatment for the cancer of interest or have other medical reasons that mean participation would be inappropriate. This study aims to quantify the proportion of non-participants who have a medical reason for not attending cancer screening.<p></p>
Methods: Medical reasons for not participating in breast and bowel screening were defined a priori on the basis of a literature review and expert opinion. The notes of 700 patients at two GP practices in Scotland were reviewed, to ascertain the prevalence of medical reasons amongst non-participants. Simple proportions and confidence intervals were calculated.<p></p>
Results: 17.4% of breast and 2.3% of bowel screening non-participants had a medical reason to not participate. The two most common reasons were previous breast cancer follow up (8.86%) and recent mammogram (6.57%).<p></p>
Conclusion: These patients may not benefit from screening while also being distressed by receiving an invitation. This issue also makes accurate monitoring and target-setting for improving uptake difficult. Further work is needed to estimate robustly the extent to which medical reasons account for screening non-participation in a larger population.<p></p>
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