98 research outputs found
Extrinsic Curvature and the Einstein Constraints
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian)
representation and conformal thin sandwich (Lagrangian) representation are
brought into complete conformity by the use of a decomposition of symmetric
tensors which involves a weight function. In stationary spacetimes, there is a
natural choice of the weight function such that the transverse traceless part
of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex
Corotating and irrotational binary black holes in quasi-circular orbits
A complete formalism for constructing initial data representing black-hole
binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in
general, true equilibrium binary configurations. However, when the timescale
for orbital decay is much longer than the orbital period, a binary can be
considered to be in quasi-equilibrium. If each black hole is assumed to be in
quasi-equilibrium, then a complete set of boundary conditions for all initial
data variables can be developed. These boundary conditions are applied on the
apparent horizon of each black hole, and in fact force a specified surface to
be an apparent horizon. A global assumption of quasi-equilibrium is also used
to fix some of the freely specifiable pieces of the initial data and to
uniquely fix the asymptotic boundary conditions. This formalism should allow
for the construction of completely general quasi-equilibrium black hole binary
initial data.Comment: 13 pages, no figures, revtex4; Content changed slightly to reflect
fact that regularized shift solutions do satisfy the isometry boundary
condition
Comparing initial-data sets for binary black holes
We compare the results of constructing binary black hole initial data with
three different decompositions of the constraint equations of general
relativity. For each decomposition we compute the initial data using a
superposition of two Kerr-Schild black holes to fix the freely specifiable
data. We find that these initial-data sets differ significantly, with the ADM
energy varying by as much as 5% of the total mass. We find that all
initial-data sets currently used for evolutions might contain unphysical
gravitational radiation of the order of several percent of the total mass. This
is comparable to the amount of gravitational-wave energy observed during the
evolved collision. More astrophysically realistic initial data will require
more careful choices of the freely specifiable data and boundary conditions for
both the metric and extrinsic curvature. However, we find that the choice of
extrinsic curvature affects the resulting data sets more strongly than the
choice of conformal metric.Comment: 18 pages, 12 figures, accepted for publication in Phys. Rev.
Comparing Criteria for Circular Orbits in General Relativity
We study a simple analytic solution to Einstein's field equations describing
a thin spherical shell consisting of collisionless particles in circular orbit.
We then apply two independent criteria for the identification of circular
orbits, which have recently been used in the numerical construction of binary
black hole solutions, and find that both yield equivalent results. Our
calculation illustrates these two criteria in a particularly transparent
framework and provides further evidence that the deviations found in those
numerical binary black hole solutions are not caused by the different criteria
for circular orbits.Comment: 4 pages; to appear in PRD as a Brief Report; added and corrected
reference
Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture
Sequences of initial-data sets representing binary black holes in
quasi-circular orbits have been used to calculate what may be interpreted as
the innermost stable circular orbit. These sequences have been computed with
two approaches. One method is based on the traditional
conformal-transverse-traceless decomposition and locates quasi-circular orbits
from the turning points in an effective potential. The second method uses a
conformal-thin-sandwich decomposition and determines quasi-circular orbits by
requiring the existence of an approximate helical Killing vector. Although the
parameters defining the innermost stable circular orbit obtained from these two
methods differ significantly, both approaches yield approximately the same
initial data, as the separation of the binary system increases. To help
understanding this agreement between data sets, we consider the case of initial
data representing a single boosted or spinning black hole puncture of the
Bowen-York type and show that the conformal-transverse-traceless and
conformal-thin-sandwich methods yield identical data, both satisfying the
conditions for the existence of an approximate Killing vector.Comment: 13 pages, 2 figure
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
We present a new many-parameter family of hyperbolic representations of
Einstein's equations, which we obtain by a straightforward generalization of
previously known systems. We solve the resulting evolution equations
numerically for a Schwarzschild black hole in three spatial dimensions, and
find that the stability of the simulation is strongly dependent on the form of
the equations (i.e. the choice of parameters of the hyperbolic system),
independent of the numerics. For an appropriate range of parameters we can
evolve a single 3D black hole to -- , and are
apparently limited by constraint-violating solutions of the evolution
equations. We expect that our method should result in comparable times for
evolutions of a binary black hole system.Comment: 11 pages, 2 figures, submitted to PR
Height and risk of death among men and women: aetiological implications of associations with cardiorespiratory disease and cancer mortality
OBJECTIVES: Height is inversely associated with cardiovascular disease mortality risk and has shown variable associations with cancer incidence and mortality. The interpretation of findings from previous studies has been constrained by data limitations. Associations between height and specific causes of death were investigated in a large general population cohort of men and women from the West of Scotland.
DESIGN: Prospective observational study.
SETTING: Renfrew and Paisley, in the West of Scotland.
SUBJECTS: 7052 men and 8354 women aged 45-64 were recruited into a study in Renfrew and Paisley, in the West of Scotland, between 1972 and 1976. Detailed assessments of cardiovascular disease risk factors, morbidity and socioeconomic circumstances were made at baseline.
MAIN OUTCOME MEASURES: Deaths during 20 years of follow up classified into specific causes.
RESULTS: Over the follow up period 3347 men and 2638 women died. Height is inversely associated with all cause, coronary heart disease, stroke, and respiratory disease mortality among men and women. Adjustment for socioeconomic position and cardiovascular risk factors had little influence on these associations. Height is strongly associated with forced expiratory volume in one second (FEV1) and adjustment for FEV1 considerably attenuated the association between height and cardiorespiratory mortality. Smoking related cancer mortality is not associated with height. The risk of deaths from cancer unrelated to smoking tended to increase with height, particularly for haematopoietic, colorectal and prostate cancers. Stomach cancer mortality was inversely associated with height. Adjustment for socioeconomic position had little influence on these associations.
CONCLUSION: Height serves partly as an indicator of socioeconomic circumstances and nutritional status in childhood and this may underlie the inverse associations between height and adulthood cardiorespiratory mortality. Much of the association between height and cardiorespiratory mortality was accounted for by lung function, which is also partly determined by exposures acting in childhood. The inverse association between height and stomach cancer mortality probably reflects Helicobacter pylori infection in childhood resulting inor being associated withshorter height. The positive associations between height and several cancers unrelated to smoking could reflect the influence of calorie intake during childhood on the risk of these cancers
Pt clusters in BaKL zeolite: Characterization by transmission electron microscopy, hydrogen chemisorption, and X-ray absorption spectroscopy
Magnetic Field Generation in Stars
Enormous progress has been made on observing stellar magnetism in stars from
the main sequence through to compact objects. Recent data have thrown into
sharper relief the vexed question of the origin of stellar magnetic fields,
which remains one of the main unanswered questions in astrophysics. In this
chapter we review recent work in this area of research. In particular, we look
at the fossil field hypothesis which links magnetism in compact stars to
magnetism in main sequence and pre-main sequence stars and we consider why its
feasibility has now been questioned particularly in the context of highly
magnetic white dwarfs. We also review the fossil versus dynamo debate in the
context of neutron stars and the roles played by key physical processes such as
buoyancy, helicity, and superfluid turbulence,in the generation and stability
of neutron star fields.
Independent information on the internal magnetic field of neutron stars will
come from future gravitational wave detections. Thus we maybe at the dawn of a
new era of exciting discoveries in compact star magnetism driven by the opening
of a new, non-electromagnetic observational window.
We also review recent advances in the theory and computation of
magnetohydrodynamic turbulence as it applies to stellar magnetism and dynamo
theory. These advances offer insight into the action of stellar dynamos as well
as processes whichcontrol the diffusive magnetic flux transport in stars.Comment: 41 pages, 7 figures. Invited review chapter on on magnetic field
generation in stars to appear in Space Science Reviews, Springe
- …