195 research outputs found
The Construction of Sorkin Triangulations
Some time ago, Sorkin (1975) reported investigations of the time evolution
and initial value problems in Regge calculus, for one triangulation each of the
manifolds and . Here we display the simple, local characteristic
of those triangulations which underlies the structure found by Sorkin, and
emphasise its general applicability, and therefore the general validity of
Sorkin's conclusions. We also make some elementary observations on the
resulting structure of the time evolution and initial value problems in Regge
calculus, and add some comments and speculations.Comment: 5 pages (plus one figure not included, available from author on
request), Plain Tex, no local preprint number (Only change: omitted
"\magnification" command now replaced
Regge calculus in the canonical form
(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The
constraints are classified, classical and quantum consequences are discussed.
As basic variables connection matrices and antisymmetric area tensors are used
supplemented with appropriate bilinear constraints. In these variables the
action can be made quasipolinomial with as the only deviation from
polinomiality. In comparison with analogous formalism in the continuum theory
classification of constraints changes: some of them disappear, the part of I
class constraints including Hamiltonian one become II class (and vice versa,
some new constraints arise and some II class constraints become I class). As a
result, the number of the degrees of freedom coincides with the number of links
in 3-dimensional leaf of foliation. Moreover, in empty space classical dynamics
is trivial: the scale of timelike links become zero and spacelike links are
constant.Comment: 24 pages,Plain LaTeX,BINP 93-4
Discrete quantum gravity in the framework of Regge calculus formalism
An approach to the discrete quantum gravity based on the Regge calculus is
discussed which was developed in a number of our papers. Regge calculus is
general relativity for the subclass of general Riemannian manifolds called
piecewise flat ones. Regge calculus deals with the discrete set of variables,
triangulation lengths, and contains continuous general relativity as a
particular limiting case when the lengths tend to zero. In our approach the
quantum length expectations are nonzero and of the order of Plank scale
. This means the discrete spacetime structure on these scales.Comment: LaTeX, 16 pages, to appear in JET
A fully (3+1)-D Regge calculus model of the Kasner cosmology
We describe the first discrete-time 4-dimensional numerical application of
Regge calculus. The spacetime is represented as a complex of 4-dimensional
simplices, and the geometry interior to each 4-simplex is flat Minkowski
spacetime. This simplicial spacetime is constructed so as to be foliated with a
one parameter family of spacelike hypersurfaces built of tetrahedra. We
implement a novel two-surface initial-data prescription for Regge calculus, and
provide the first fully 4-dimensional application of an implicit decoupled
evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on
the Kasner cosmology --- a cosmology which embodies generic features of the
collapse of many cosmological models. We (1) reproduce the continuum solution
with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps,
(2) demonstrate stable evolution, (3) preserve the standard deviation of
spatial homogeneity to less than 10^{-10} and (4) explicitly display the
existence of diffeomorphism freedom in Regge calculus. We also present the
second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio
Regge Calculus as a Fourth Order Method in Numerical Relativity
The convergence properties of numerical Regge calculus as an approximation to
continuum vacuum General Relativity is studied, both analytically and
numerically. The Regge equations are evaluated on continuum spacetimes by
assigning squared geodesic distances in the continuum manifold to the squared
edge lengths in the simplicial manifold. It is found analytically that,
individually, the Regge equations converge to zero as the second power of the
lattice spacing, but that an average over local Regge equations converges to
zero as (at the very least) the third power of the lattice spacing. Numerical
studies using analytic solutions to the Einstein equations show that these
averages actually converge to zero as the fourth power of the lattice spacing.Comment: 14 pages, LaTeX, 8 figures mailed in separate file or email author
directl
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
From covariant to canonical formulations of discrete gravity
Starting from an action for discretized gravity we derive a canonical
formalism that exactly reproduces the dynamics and (broken) symmetries of the
covariant formalism. For linearized Regge calculus on a flat background --
which exhibits exact gauge symmetries -- we derive local and first class
constraints for arbitrary triangulated Cauchy surfaces. These constraints have
a clear geometric interpretation and are a first step towards obtaining
anomaly--free constraint algebras for canonical lattice gravity. Taking higher
order dynamics into account the symmetries of the action are broken. This
results in consistency conditions on the background gauge parameters arising
from the lowest non--linear equations of motion. In the canonical framework the
constraints to quadratic order turn out to depend on the background gauge
parameters and are therefore pseudo constraints. These considerations are
important for connecting path integral and canonical quantizations of gravity,
in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version +
updated references
The IDvIP Trial: A two-centre randomised double-blind controlled trial comparing intramuscular diamorphine and intramuscular pethidine for labour analgesia
<p>Abstract</p> <p>Background</p> <p>Intramuscular pethidine is routinely used throughout the UK for labour analgesia. Studies have suggested that pethidine provides little pain relief in labour and has a number of side effects affecting mother and neonate. It can cause nausea, vomiting and dysphoria in mothers and can cause reduced fetal heart rate variability and accelerations. Neonatal effects include respiratory depression and impaired feeding. There are few large studies comparing the relative side effects and efficacy of different opioids in labour. A small trial comparing intramuscular pethidine with diamorphine, showed diamorphine to have some benefits over pethidine when used for labour analgesia but the study did not investigate the adverse effects of either opioid.</p> <p>Methods</p> <p>The Intramuscular Diamorphine versus Intramuscular Pethidine (IDvIP) trial is a randomised double-blind two centre controlled trial comparing intramuscular diamorphine and pethidine regarding their analgesic efficacy in labour and their side effects in mother, fetus and neonate. Information about the trial will be provided to women in the antenatal period or in early labour. Consent and recruitment to the trial will be obtained when the mother requests opioid analgesia. The sample size requirement is 406 women with data on primary outcomes. The maternal primary outcomes are pain relief during the first 3 hours after trial analgesia and specifically pain relief after 60 minutes. The neonatal primary outcomes are need for resuscitation and Apgar Score <7 at 1 minute. The secondary outcomes are an additional measure of pain relief, maternal sedation, nausea and vomiting, maternal oxygen saturation, satisfaction with analgesia, whether method of analgesia would be used again, use of Entonox, umbilical arterial and venous pH, fetal heart rate, meconium staining, time from delivery to first breath, Apgar scores at 5 mins, naloxone requirement, transfer to neonatal intensive care unit, neonatal haemoglobin oxygen saturation at 30, 60, 90, and 120 mins after delivery, and neonatal sedation and feeding behaviour during first 2 hours.</p> <p>Discussion</p> <p>If the trial demonstrates that diamorphine provides better analgesia with fewer side effects in mother and neonate this could lead to a change in national practice and result in diamorphine becoming the preferred intramuscular opioid for analgesia in labour.</p> <p>Trial Registration</p> <p><a href="http://www.controlled-trials.com/ISRCTN14898678">ISRCTN14898678</a></p> <p>Eudra No: 2006-003250-18, REC Reference No: 06/Q1702/95, MHRA Authorisation No: 1443/0001/001-0001, NIHR UKCRN reference 6895, RfPB grant PB-PG-0407-13170_IR5</p
Recommended from our members
Brief Report: Schema Consistent Misinformation Effects in Eyewitnesses with Autism Spectrum Disorder
A number of studies have demonstrated schema-related misinformation effects in typical individuals, but no research to date has examined this with witnesses with autism spectrum disorder (ASD), despite their impaired ability to generate core elements that define everyday events. After witnessing slides depicting a bank robbery, 16 adults with ASD and 16 matched comparison individuals were exposed to post-event misinformation that was either schema typical or atypical. Consistent with previous work, the comparison group went onto report more schema typical misinformation than atypical misinformation. However, so too did the ASD group, suggesting that individuals with ASD do have understanding of the causal links between events, persons and actions, an important finding from both theoretical and applied perspectives
- âŠ