19,457 research outputs found
Properties of Information Carrying Waves in Cosmology
Recently we studied the effects of information carrying waves propagating
through isotropic cosmologies. By information carrying we mean that the waves
have an arbitrary dependence on a function. We found that the waves introduce
shear and anisotropic stress into the universe. We then constructed explicit
examples of pure gravity wave perturbations for which the presence of this
anisotropic stress is essential and the null hypersurfaces playing the role of
the histories of the wave-fronts in the background space-time are shear-free.
Motivated by this result we now prove that these two properties are true for
all information carrying waves in isotropic cosmologies.Comment: 15 pages, Latex File, accepted for publication in Physical Review
Anatomy of Soft Tissues of the Spinal Canal
Background and Objectives.
Important issues regarding the spread of solutions in the epidural space and the anatomy of the site of action of spinal and epidural injections are unresolved. However, the detailed anatomy of the spinal canal has been incompletely determined. We therefore examined the microscopic anatomy of the spinal canal soft tissues, including relationships to the canal walls.
Methods.
Whole mounts were prepared of decalcified vertebral columns with undisturbed contents from three adult humans. Similar material was prepared from a macaque and baboon immediately on death to control for artifact of tissue change after death. Other tissues examined included nerve root and proximal spinal nerve complex and dorsal epidural fat obtained during surgery. Slides were examined by light microscopy at magnifications of 10-40Ă.
Results.
There is no fibrous tissue in the epidural space. The epidural fat is composed of uniform cells enclosed in a fine membrane. The dorsal fat is only attached to the canal wall in the dorsal midline and is often tenuously attached to the dura. The dura is joined to the canal wall only ventrally at the discs. Veins are evident predominantly in the ventral epidural space. Nerve roots are composed of multiple fascicles which disperse as they approach the dorsal root ganglion. An envelope of arachnoid encloses the roots near the site of exit from the dura.
Conclusions.
These features of the fat explain its semifluid consistency. Lack of substantial attachments to the dura facilitate movement of the dura relative to the canal wall and allow distribution of injected solution. Fibrous barriers are an unlikely explanation for asymmetric epidural anesthesia, but the midline fat could impede solution spread. Details of nerve-root structure and their envelope of pia-arachnoid membrane may be relevant to anesthetic action
Metric Perturbation Approach to Gravitational Waves in Isotropic Cosmologies
Gravitational waves in isotropic cosmologies were recently studied using the
gauge-invariant approach of Ellis-Bruni. We now construct the linearised metric
perturbations of the background Robertson-Walker space-time which reproduce the
results obtained in that study. The analysis carried out here also facilitates
an easy comparison with Bardeen.Comment: 29 pages, Latex file, accepted for publication in Physical Review
Shear-Free Gravitational Waves in an Anisotropic Universe
We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review
Gravitational Wave Propagation in Isotropic Cosmologies
We study the propagation of gravitational waves carrying arbitrary
information through isotropic cosmologies. The waves are modelled as small
perturbations of the background Robertson-Walker geometry. The perfect fluid
matter distribution of the isotropic background is, in general, modified by
small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl
tensor is radiative (i.e. type N in the Petrov classification), we construct
explicit examples for which the presence of the anisotropic stress is shown to
be essential and the histories of the wave-fronts in the background
Robertson-Walker geometry are shear-free null hypersurfaces. The examples
derived in this case are analogous to the Bateman waves of electromagnetic
theory.Comment: 27 pages, accepted for publication in Phys.Rev.
The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
We consider a non-autonomous dynamical system formed by coupling two
piecewise-smooth systems in \RR^2 through a non-autonomous periodic
perturbation. We study the dynamics around one of the heteroclinic orbits of
one of the piecewise-smooth systems. In the unperturbed case, the system
possesses two normally hyperbolic invariant manifolds of dimension two
with a couple of three dimensional heteroclinic manifolds between them. These
heteroclinic manifolds are foliated by heteroclinic connections between
tori located at the same energy levels. By means of the {\em impact map} we
prove the persistence of these objects under perturbation. In addition, we
provide sufficient conditions of the existence of transversal heteroclinic
intersections through the existence of simple zeros of Melnikov-like functions.
The heteroclinic manifolds allow us to define the {\em scattering map}, which
links asymptotic dynamics in the invariant manifolds through heteroclinic
connections. First order properties of this map provide sufficient conditions
for the asymptotic dynamics to be located in different energy levels in the
perturbed invariant manifolds. Hence we have an essential tool for the
construction of a heteroclinic skeleton which, when followed, can lead to the
existence of Arnol'd diffusion: trajectories that, on large time scales,
destabilize the system by further accumulating energy. We validate all the
theoretical results with detailed numerical computations of a mechanical system
with impacts, formed by the linkage of two rocking blocks with a spring
Astrophysical Effects of Scalar Dark Matter Miniclusters
We model the formation, evolution and astrophysical effects of dark compact
Scalar Miniclusters (``ScaMs''). These objects arise when a scalar field, with
an axion-like or Higgs-like potential, undergoes a second order phase
transition below the QCD scale. Such a scalar field may couple too weakly to
the standard model to be detectable directly through particle interactions, but
may still be detectable by gravitational effects, such as lensing and baryon
accretion by large, gravitationally bound miniclusters. The masses of these
objects are shown to be constrained by the Ly power spectrum to be less
than , but they may be as light as classical axion
miniclusters, of the order of . We simulate the formation and
nonlinear gravitational collapse of these objects around matter-radiation
equality using an N-body code, estimate their gravitational lensing properties,
and assess the feasibility of studying them using current and future lensing
experiments. Future MACHO-type variability surveys of many background sources
can reveal either high-amplification, strong lensing events, or measure density
profiles directly via weak-lensing variability, depending on ScaM parameters
and survey depth. However, ScaMs, due to their low internal densities, are
unlikely to be responsible for apparent MACHO events already detected in the
Galactic halo. A simple estimate is made of parameters that would give rise to
early structure formation; in principle, early stellar collapse could be
triggered by ScaMs as early as recombination, and significantly affect cosmic
reionization.Comment: 13 pages, 12 figures. Replaced to reflect published versio
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