1,493 research outputs found
An ADM 3+1 formulation for Smooth Lattice General Relativity
A new hybrid scheme for numerical relativity will be presented. The scheme
will employ a 3-dimensional spacelike lattice to record the 3-metric while
using the standard 3+1 ADM equations to evolve the lattice. Each time step will
involve three basic steps. First, the coordinate quantities such as the Riemann
and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM
equations are used to evolve the coordinate data, and finally, the coordinate
data is used to update the scalar data on the lattice (such as the leg
lengths). The scheme will be presented only for the case of vacuum spacetime
though there is no reason why it could not be extended to non-vacuum
spacetimes. The scheme allows any choice for the lapse function and shift
vectors. An example for the Kasner cosmology will be presented and it
will be shown that the method has, for this simple example, zero discretisation
error.Comment: 18 pages, plain TeX, 5 epsf figues, gzipped ps file also available at
http://newton.maths.monash.edu.au:8000/preprints/3+1-slgr.ps.g
Fast algorithms for computing defects and their derivatives in the Regge calculus
Any practical attempt to solve the Regge equations, these being a large
system of non-linear algebraic equations, will almost certainly employ a
Newton-Raphson like scheme. In such cases it is essential that efficient
algorithms be used when computing the defect angles and their derivatives with
respect to the leg-lengths. The purpose of this paper is to present details of
such an algorithm.Comment: 38 pages, 10 figure
Is the Regge Calculus a consistent approximation to General Relativity?
We will ask the question of whether or not the Regge calculus (and two
related simplicial formulations) is a consistent approximation to General
Relativity. Our criteria will be based on the behaviour of residual errors in
the discrete equations when evaluated on solutions of the Einstein equations.
We will show that for generic simplicial lattices the residual errors can not
be used to distinguish metrics which are solutions of Einstein's equations from
those that are not. We will conclude that either the Regge calculus is an
inconsistent approximation to General Relativity or that it is incorrect to use
residual errors in the discrete equations as a criteria to judge the discrete
equations.Comment: 27 pages, plain TeX, very belated update to match journal articl
Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method
We will present results of a numerical integration of a maximally sliced
Schwarzschild black hole using a smooth lattice method. The results show no
signs of any instability forming during the evolutions to t=1000m. The
principle features of our method are i) the use of a lattice to record the
geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM
equations to the lattice and iii) the use of the Bianchi identities to assist
in the computation of the curvatures. No other special techniques are used. The
evolution is unconstrained and the ADM equations are used in their standard
form.Comment: 47 pages including 26 figures, plain TeX, also available at
http://www.maths.monash.edu.au/~leo/preprint
Intrusive memories following disaster: Relationship with peritraumatic responses and later affect
Cognitive theories of posttraumatic stress disorder (PTSD) suggest that intrusive memories result from disrupted information processing during traumatic memory encoding and are characterized by fear, helplessness, and horror at recall. Existing naturalistic studies are limited by the absence of direct comparisons between specific moments that do and do not correspond to intrusive memories. We tested predictions from cognitive theories of PTSD by comparing peritraumatic responses during moments experienced as intrusive memories versus distressing moments of the same traumatic event from the same individual not experienced as intrusive memories. A further comparison was with highly distressing moments experienced during the same event by individuals without intrusive memories. We utilized a psychometrically generated model to distinguish different peritraumatic reactions. Moments experienced as intrusive memories were characterized by higher peritraumatic distress, immobility, cognitive overload, and somatic dissociation when compared both to distressing moments from the same individual that did not intrude and to the most distressing memories of individuals without intrusions. Exploratory analyses indicated that at recall, intrusive memories were characterized by higher levels of primary traumatic emotions such as anxiety, fear, and helplessness in comparison with nonintrusive memories. Findings from this novel naturalistic design support predictions made by cognitive theories of PTSD and have implications for research and preventative interventions targeting intrusive memories. (PsycInfo Database Record (c) 2021 APA, all rights reserved)
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
Optimised performance of the backward longswing on rings
Many elite gymnasts perform the straight arm backward longswing on rings in competition. Since points are deducted if gymnasts possess motion on completion of the movement, the ability to successfully perform the longswing to a stationary final handstand is of great importance. Sprigings et al. (1998) found that for a longswing initiated from a still handstand the optimum performance of an inelastic planar simulation model resulted in a residual swing of more than 3° in the final handstand.
For the present study, a three-dimensional simulation model of a gymnast swinging on rings, incorporating lateral arm movements used by gymnasts and mandatory apparatus elasticity, was used to investigate the possibility of performing a backward longswing initiated and completed in handstands with minimal swing. Root mean square differences between the actual and simulated performances for the orientations of the gymnast and rings cables, the combined cable tension and the extension of the gymnast were 3.2°, 1.0°, 270 N and 0.05 m respectively.
The optimised simulated performance initiated from a handstand with 2.1° of swing and using realistic changes to the gymnast's technique resulted in 0.6° of residual swing in the final handstand. The sensitivity of the backward longswing to perturbations in the technique used for the optimised performance was determined. For a final handstand with minimal residual swing (2°) the changes in body configuration must be timed to within 15 m s while a delay of 30 m s will result in considerable residual swing (7°)
Regge calculus and Ashtekar variables
Spacetime discretized in simplexes, as proposed in the pioneer work of Regge,
is described in terms of selfdual variables. In particular, we elucidate the
"kinematic" structure of the initial value problem, in which 3--space is
divided into flat tetrahedra, paying particular attention to the role played by
the reality condition for the Ashtekar variables. An attempt is made to write
down the vector and scalar constraints of the theory in a simple and
potentially useful way.Comment: 10 pages, uses harvmac. DFUPG 83/9
On the convergence of Regge calculus to general relativity
Motivated by a recent study casting doubt on the correspondence between Regge
calculus and general relativity in the continuum limit, we explore a mechanism
by which the simplicial solutions can converge whilst the residual of the Regge
equations evaluated on the continuum solutions does not. By directly
constructing simplicial solutions for the Kasner cosmology we show that the
oscillatory behaviour of the discrepancy between the Einstein and Regge
solutions reconciles the apparent conflict between the results of Brewin and
those of previous studies. We conclude that solutions of Regge calculus are, in
general, expected to be second order accurate approximations to the
corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations
added, several sections rewritten. 9 pages, 4 EPS figure
Effective stress-energy tensors, self-force, and broken symmetry
Deriving the motion of a compact mass or charge can be complicated by the
presence of large self-fields. Simplifications are known to arise when these
fields are split into two parts in the so-called Detweiler-Whiting
decomposition. One component satisfies vacuum field equations, while the other
does not. The force and torque exerted by the (often ignored) inhomogeneous
"S-type" portion is analyzed here for extended scalar charges in curved
spacetimes. If the geometry is sufficiently smooth, it is found to introduce
effective shifts in all multipole moments of the body's stress-energy tensor.
This greatly expands the validity of statements that the homogeneous R field
determines the self-force and self-torque up to renormalization effects. The
forces and torques exerted by the S field directly measure the degree to which
a spacetime fails to admit Killing vectors inside the body. A number of
mathematical results related to the use of generalized Killing fields are
therefore derived, and may be of wider interest. As an example of their
application, the effective shift in the quadrupole moment of a charge's
stress-energy tensor is explicitly computed to lowest nontrivial order.Comment: 22 pages, fixed typos and simplified discussio
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