1,320 research outputs found
Exhaust jet wake and thrust characteristics of several nozzles designed for VTOL DOWNWASH suppression. Tests in and out of ground effect with 70 deg F and 1200 deg F nozzle discharge temperatures
Jet wake degradation and thrust characteristics of exhaust nozzles designed for VTOL downwash suppression and fuselage and ground effect
A new proof of the Bianchi type IX attractor theorem
We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state. The
`Bianchi type IX attractor theorem' states that the past asymptotic behavior of
generic type IX solutions is governed by Bianchi type I and II vacuum states
(Mixmaster attractor). We give a comparatively short and self-contained new
proof of this theorem. The proof we give is interesting in itself, but more
importantly it illustrates and emphasizes that type IX is special, and to some
extent misleading when one considers the broader context of generic models
without symmetries.Comment: 26 pages, 5 figure
Spherically symmetric relativistic stellar structures
We investigate relativistic spherically symmetric static perfect fluid models
in the framework of the theory of dynamical systems. The field equations are
recast into a regular dynamical system on a 3-dimensional compact state space,
thereby avoiding the non-regularity problems associated with the
Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space
thus obtained is used to derive qualitative features and to prove theorems
about mass-radius properties. The perfect fluids we discuss are described by
barotropic equations of state that are asymptotically polytropic at low
pressures and, for certain applications, asymptotically linear at high
pressures. We employ dimensionless variables that are asymptotically homology
invariant in the low pressure regime, and thus we generalize standard work on
Newtonian polytropes to a relativistic setting and to a much larger class of
equations of state. Our dynamical systems framework is particularly suited for
numerical computations, as illustrated by several numerical examples, e.g., the
ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe
A Phase Space Approach to Gravitational Enropy
We examine the definition S = ln Omega as a candidate "gravitational entropy"
function. We calculate its behavior for gravitationl and density perturbations
in closed, open and flat cosmologies and find that in all cases it increases
monotonically. Using the formalism to calculate the gravitational entropy
produced during inflation gives the canonical answer. We compare the behavior
of S with the behavior of the square of the Weyl tensor. Applying the formalism
to black holes has proven more problematical.Comment: Talk delivered at South African Relativistic Cosmology Symposium, Feb
1999. Some new results over Rothman and Anninos 97. To appear in GRG, 17
page
Asymptotic self-similarity breaking at late times in cosmology
We study the late time evolution of a class of exact anisotropic cosmological
solutions of Einstein's equations, namely spatially homogeneous cosmologies of
Bianchi type VII with a perfect fluid source. We show that, in contrast to
models of Bianchi type VII which are asymptotically self-similar at late
times, Bianchi VII models undergo a complicated type of self-similarity
breaking. This symmetry breaking affects the late time isotropization that
occurs in these models in a significant way: if the equation of state parameter
satisfies the models isotropize as regards the shear
but not as regards the Weyl curvature. Indeed these models exhibit a new
dynamical feature that we refer to as Weyl curvature dominance: the Weyl
curvature dominates the dynamics at late times. By viewing the evolution from a
dynamical systems perspective we show that, despite the special nature of the
class of models under consideration, this behaviour has implications for more
general models.Comment: 29 page
Integration of the Friedmann equation for universes of arbitrary complexity
An explicit and complete set of constants of the motion are constructed
algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models
consisting of an arbitrary number of non-interacting species. The inheritance
of constants of the motion from simpler models as more species are added is
stressed. It is then argued that all FLRW models admit what amounts to a unique
candidate for a gravitational epoch function (a dimensionless scalar invariant
derivable from the Riemann tensor without differentiation which is monotone
throughout the evolution of the universe). The same relations that lead to the
construction of constants of the motion allow an explicit evaluation of this
function. In the simplest of all models, the CDM model, it is shown
that the epoch function exists for all models with , but for
almost no models with .Comment: Final form to appear in Physical Review D1
Hip osteoarthritis: patients with complex comorbidities can make exceptional improvements following intensive exercise and education.
A 71-year-old man presenting with hip osteoarthritis, with a complex range of comorbidities was referred by his general practitioner to CHAIN (Cycling against Hip PAIN), a 6 week programme developed to aid self-management of hip osteoarthritis through exercise, education and advice, as defined by the National Institute for Health and Care Excellence (NICE) guidelines. Significant improvements were seen in Oxford hip score, the Hip disability and Osteoarthritis Outcome Score (HOOS) - function score, sit-to-stand test, timed up and go test, pain scores and hip flexion. There was also a weight loss of 2.1 kg. The man reported 'an amazing difference' in his affected hip and leg, and improved fitness. Many clinicians would have questioned the man's suitability for the programme due to his coexisting medical conditions. This case study shows that patients may be much more able than we think to achieve significant improvement with exercise
Self-similar Bianchi models: I. Class A models
We present a study of Bianchi class A tilted cosmological models admitting a
proper homothetic vector field together with the restrictions, both at the
geometrical and dynamical level, imposed by the existence of the simply
transitive similarity group. The general solution of the symmetry equations and
the form of the homothetic vector field are given in terms of a set of
arbitrary integration constants. We apply the geometrical results for tilted
perfect fluids sources and give the general Bianchi II self-similar solution
and the form of the similarity vector field. In addition we show that
self-similar perfect fluid Bianchi VII models and irrotational Bianchi
VI models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit
Linear Complexity Lossy Compressor for Binary Redundant Memoryless Sources
A lossy compression algorithm for binary redundant memoryless sources is
presented. The proposed scheme is based on sparse graph codes. By introducing a
nonlinear function, redundant memoryless sequences can be compressed. We
propose a linear complexity compressor based on the extended belief
propagation, into which an inertia term is heuristically introduced, and show
that it has near-optimal performance for moderate block lengths.Comment: 4 pages, 1 figur
Area Regge Calculus and Discontinuous Metrics
Taking the triangle areas as independent variables in the theory of Regge
calculus can lead to ambiguities in the edge lengths, which can be interpreted
as discontinuities in the metric. We construct solutions to area Regge calculus
using a triangulated lattice and find that on a spacelike hypersurface no such
discontinuity can arise. On a null hypersurface however, we can have such a
situation and the resulting metric can be interpreted as a so-called refractive
wave.Comment: 18 pages, 1 figur
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