8,063 research outputs found
Initial data transients in binary black hole evolutions
We describe a method for initializing characteristic evolutions of the
Einstein equations using a linearized solution corresponding to purely outgoing
radiation. This allows for a more consistent application of the characteristic
(null cone) techniques for invariantly determining the gravitational radiation
content of numerical simulations. In addition, we are able to identify the {\em
ingoing} radiation contained in the characteristic initial data, as well as in
the initial data of the 3+1 simulation. We find that each component leads to a
small but long lasting (several hundred mass scales) transient in the measured
outgoing gravitational waves.Comment: 18 pages, 4 figure
Cauchy boundaries in linearized gravitational theory
We investigate the numerical stability of Cauchy evolution of linearized
gravitational theory in a 3-dimensional bounded domain. Criteria of robust
stability are proposed, developed into a testbed and used to study various
evolution-boundary algorithms. We construct a standard explicit finite
difference code which solves the unconstrained linearized Einstein equations in
the 3+1 formulation and measure its stability properties under Dirichlet,
Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability
of a specific evolution-boundary algorithm under random constraint violating
initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte
High-powered Gravitational News
We describe the computation of the Bondi news for gravitational radiation. We
have implemented a computer code for this problem. We discuss the theory behind
it as well as the results of validation tests. Our approach uses the
compactified null cone formalism, with the computational domain extending to
future null infinity and with a worldtube as inner boundary. We calculate the
appropriate full Einstein equations in computational eth form in (a) the
interior of the computational domain and (b) on the inner boundary. At future
null infinity, we transform the computed data into standard Bondi coordinates
and so are able to express the news in terms of its standard and
polarization components. The resulting code is stable and
second-order convergent. It runs successfully even in the highly nonlinear
case, and has been tested with the news as high as 400, which represents a
gravitational radiation power of about .Comment: 24 pages, 4 figures. To appear in Phys. Rev.
Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin- Models
We apply the microscopic coupled-cluster method (CCM) to the spin-
models on both the one-dimensional chain and the two-dimensional square
lattice. Based on a systematic approximation scheme of the CCM developed by us
previously, we carry out high-order {\it ab initio} calculations using
computer-algebraic techniques. The ground-state properties of the models are
obtained with high accuracy as functions of the anisotropy parameter.
Furthermore, our CCM analysis enables us to study their quantum critical
behavior in a systematic and unbiased manner.Comment: (to appear in PRL). 4 pages, ReVTeX, two figures available upon
request. UMIST Preprint MA-000-000
Cauchy-characteristic Evolution of Einstein-Klein-Gordon Systems
A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon
system with spherical symmetry is presented. Initial data are specified on the
union of a space-like and null hypersurface. The development of the data is
obtained with the combination of a constrained Cauchy evolution in the interior
domain and a characteristic evolution in the exterior, asymptotically flat
region. The matching interface between the space-like and characteristic
foliations is constructed by imposing continuity conditions on metric,
extrinsic curvature and scalar field variables, ensuring smoothness across the
matching surface. The accuracy of the method is established for all ranges of
, most notably, with a detailed comparison of invariant observables
against reference solutions obtained with a calibrated, global, null algorithm.Comment: Submitted to Phys. Rev. D, 16 pages, revtex, 7 figures available at
http://nr.astro.psu.edu:8080/preprints.htm
Numerical relativity with characteristic evolution, using six angular patches
The characteristic approach to numerical relativity is a useful tool in
evolving gravitational systems. In the past this has been implemented using two
patches of stereographic angular coordinates. In other applications, a
six-patch angular coordinate system has proved effective. Here we investigate
the use of a six-patch system in characteristic numerical relativity, by
comparing an existing two-patch implementation (using second-order finite
differencing throughout) with a new six-patch implementation (using either
second- or fourth-order finite differencing for the angular derivatives). We
compare these different codes by monitoring the Einstein constraint equations,
numerically evaluated independently from the evolution. We find that, compared
to the (second-order) two-patch code at equivalent resolutions, the errors of
the second-order six-patch code are smaller by a factor of about 2, and the
errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue
New results for virial coefficients of hard spheres in D dimensions
We present new results for the virial coefficients B_k with k <= 10 for hard
spheres in dimensions D=2,...,8.Comment: 10 pages, 5 figures, to appear in conference proceedings of STATPHYS
2004 in Pramana - Journal of Physic
Phase Transitions in the Spin-Half J_1--J_2 Model
The coupled cluster method (CCM) is a well-known method of quantum many-body
theory, and here we present an application of the CCM to the spin-half J_1--J_2
quantum spin model with nearest- and next-nearest-neighbour interactions on the
linear chain and the square lattice. We present new results for ground-state
expectation values of such quantities as the energy and the sublattice
magnetisation. The presence of critical points in the solution of the CCM
equations, which are associated with phase transitions in the real system, is
investigated. Completely distinct from the investigation of the critical
points, we also make a link between the expansion coefficients of the
ground-state wave function in terms of an Ising basis and the CCM ket-state
correlation coefficients. We are thus able to present evidence of the
breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which
is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any
bipartite lattice. For the square lattice, our best estimates of the points at
which the sign rule breaks down and at which the phase transition from the
antiferromagnetic phase to the frustrated phase occurs are, respectively, given
(to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure
High-quality variational wave functions for small 4He clusters
We report a variational calculation of ground state energies and radii for
4He_N droplets (3 \leq N \leq 40), using the atom-atom interaction HFD-B(HE).
The trial wave function has a simple structure, combining two- and three-body
correlation functions coming from a translationally invariant
configuration-interaction description, and Jastrow-type short-range
correlations. The calculated ground state energies differ by around 2% from the
diffusion Monte Carlo results.Comment: 5 pages, 1 ps figure, REVTeX, submitted to Phys. Rev.
Orbital evolution of a test particle around a black hole: Indirect determination of the self force in the post Newtonian approximation
Comparing the corrections to Kepler's law with orbital evolution under a self
force, we extract the finite, already regularized part of the latter in a
specific gauge. We apply this method to a quasi-circular orbit around a
Schwarzschild black hole of an extreme mass ratio binary, and determine the
first- and second-order conservative gravitational self force in a post
Newtonian expansion. We use these results in the construction of the
gravitational waveform, and revisit the question of the relative contribution
of the self force and spin-orbit coupling.Comment: 5 pages, 2 figure
- …