1,750 research outputs found
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
RUNNING SHOE STIFFNESS:THE EFFECT ON WALKING GAIT
Sports shoes can be grouped into various categories based on their stability, protection capabilities, traction, impact characteristics and stiffness. The majority of shoe tests involve measures of traction and impact. Few studies have examined shoe sole stiffness. Therefore, the purpose of this study was to assess shoe sole stiffness by a materials testing procedure, and then examine the effect of shoe stiffness on walking gait. A damped oscillation technique, previously used on muscle-tendon complexes, was utilised to calculate the stiffness and the damping factor of six types of running shoes. The shoes used different rnidsole components which included air sacs, gel sacs, ethylene vinyl acetate (EVA), and kevlar reinforcing. Two shoes at the extremes of the range were then selected from the materials test results for use in the subsequent gait analysis. Nine males ranging in age from 25 to 45 years (mean =36 years) participated in the experiment. Heights ranged from 186cm to 176cm (mean=182cm) and weights ranged from 72.5kg to 89kg (mean=8lkg). No subjects had any musculoskeletal problems affecting the lower limb. Two dimensional video data were collected on the right leg using an Ariel Video Analysis system sampling at 50 Hz, as subjects walked at 5.1 km/hr on a motor driven treadmill. Markers were placed on the greater trochanter, lateral condyle of the femur, lateral malleolus of the fibular, the heel of the shoe and on the shoe at the level of the fifth metatarsal head. Three stride cycles were collected after the subjects had walked on the treadmill for one minute. Data were digitised and downloaded to FMAP software to calculate kinematic variables such as knee and ankle angle and knee and ankle angular velocity. Data were then normalised to 50 points and averaged across stride cycles and subjects. Although a comparison of the stiff and flexible shoes indicated no differences in the kinematic parameters (p>0.05), it may be that the muscles of the lower limb adjust their activity level for the stiffness of the shoe to maintain an invariant kinematic pattern
Cluster observations of non-time-continuous magnetosonic waves
Equatorial magnetosonic waves are normally observed as temporally
continuous sets of emissions lasting from minutes to hours. Recent
observations, however, have shown that this is not always the case. Using
Cluster data, this study identifies two distinct forms of these non-temporallycontinuous
emissions. The first, referred to as rising tone emissions, are characterised
by the systematic onset of wave activity at increasing proton gyroharmonic
frequencies. Sets of harmonic emissions (emission elements) are
observed to occur periodically in the region ±10◦ off the geomagnetic equator.
The sweep rate of these emissions maximises at the geomagnetic equator.
In addition, the ellipticity and propagation direction also change systematically
as Cluster crosses the geomagnetic equator. It is shown that the
observed frequency sweep rate is unlikely to result from the sideband instability
related to nonlinear trapping of suprathermal protons in the wave field.
The second form of emissions is characterised by the simultaneous onset of
activity across a range of harmonic frequencies. These waves are observed
at irregular intervals. Their occurrence correlates with changes in the spacecraft
potential, a measurement that is used as a proxy for electron densit
Seeking Evolution of Dark Energy
We study how observationally to distinguish between a cosmological constant
(CC) and an evolving dark energy with equation of state . We focus
on the value of redshift Z* at which the cosmic late time acceleration begins
and . Four are studied, including the
well-known CPL model and a new model that has advantages when describing the
entire expansion era. If dark energy is represented by a CC model with , the present ranges for and
imply that Z* = 0.743 with 4% error. We discuss the possible implications of a
model independent measurement of Z* with better accuracy.Comment: 9 pages, LaTeX, 5 figure
Friedmann-like equations for High Energy Area of Universe
In this paper, evolution of the high energy area of universe, through the
scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we
solve Einstein equations for 5D metric and 5D perfect fuid to derive
Friedmann-like equations. Then we obtain the evolution of scale factor and
energy density with respect to both space-like and time-like extra dimensions.
We obtain the novel equations for the space-like extra dimension and show that
the matter with zero pressure cannot exist in the bulk. Also, for dark energy
fuid and vacuum fluid, we have both accelerated expansion and contraction in
the bulk.Comment: 9 pages, Accepted to publication in IJTP 26 June 2012. arXiv admin
note: substantial text overlap with arXiv:1202.497
How to find the holonomy algebra of a Lorentzian manifold
Manifolds with exceptional holonomy play an important role in string theory,
supergravity and M-theory. It is explained how one can find the holonomy
algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de~Rham
and Wu decompositions, this problem is reduced to the case of locally
indecomposable manifolds. In the case of locally indecomposable Riemannian
manifolds, it is known that the holonomy algebra can be found from the analysis
of special geometric structures on the manifold. If the holonomy algebra
of a locally indecomposable
Lorentzian manifold of dimension is different from
, then it is contained in the similitude algebra
. There are 4 types of such holonomy algebras. Criterion
how to find the type of are given, and special geometric
structures corresponding to each type are described. To each
there is a canonically associated subalgebra
. An algorithm how to find
is provided.Comment: 15 pages; the final versio
An inverse approach to Einstein's equations for non-conducting fluids
We show that a flow (timelike congruence) in any type warped product
spacetime is uniquely and algorithmically determined by the condition of zero
flux. (Though restricted, these spaces include many cases of interest.) The
flow is written out explicitly for canonical representations of the spacetimes.
With the flow determined, we explore an inverse approach to Einstein's
equations where a phenomenological fluid interpretation of a spacetime follows
directly from the metric irrespective of the choice of coordinates. This
approach is pursued for fluids with anisotropic pressure and shear viscosity.
In certain degenerate cases this interpretation is shown to be generically not
unique. The framework developed allows the study of exact solutions in any
frame without transformations. We provide a number of examples, in various
coordinates, including spacetimes with and without unique interpretations. The
results and algorithmic procedure developed are implemented as a computer
algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev
Bulk Scale Factor at Very Early Universe
In this paper we propose a higher dimensional Cosmology based on FRW model
and brane-world scenario. We consider the warp factor in the brane-world
scenario as a scale factor in 5-dimensional generalized FRW metric, which is
called as bulk scale factor, and obtain the evolution of it with space-like and
time-like extra dimensions. It is then showed that, additional space-like
dimensions can produce exponentially bulk scale factor under repulsive strong
gravitational force in the empty universe at a very early stage.Comment: 7 pages, October 201
The Imprint of Gravitational Waves on the Cosmic Microwave Background
Long-wavelength gravitational waves can induce significant temperature
anisotropy in the cosmic microwave background. Distinguishing this from
anisotropy induced by energy density fluctuations is critical for testing
inflationary cosmology and theories of large-scale structure formation. We
describe full radiative transport calculations of the two contributions and
show that they differ dramatically at angular scales below a few degrees. We
show how anisotropy experiments probing large- and small-angular scales can
combine to distinguish the imprint due to gravitational waves.Comment: 11 pages, Penn Preprint-UPR-
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