9,155 research outputs found
Implementing an apparent-horizon finder in three dimensions
Locating apparent horizons is not only important for a complete understanding
of numerically generated spacetimes, but it may also be a crucial component of
the technique for evolving black-hole spacetimes accurately. A scheme proposed
by Libson et al., based on expanding the location of the apparent horizon in
terms of symmetric trace-free tensors, seems very promising for use with
three-dimensional numerical data sets. In this paper, we generalize this scheme
and perform a number of code tests to fully calibrate its behavior in
black-hole spacetimes similar to those we expect to encounter in solving the
binary black-hole coalescence problem. An important aspect of the
generalization is that we can compute the symmetric trace-free tensor expansion
to any order. This enables us to determine how far we must carry the expansion
to achieve results of a desired accuracy. To accomplish this generalization, we
describe a new and very convenient set of recurrence relations which apply to
symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures
Spacetime Symmetries and Kepler's Third Law
The curved spacetime geometry of a system of two point masses moving on a
circular orbit has a helical symmetry. We show how Kepler's third law for
circular motion, and its generalization in post-Newtonian theory, can be
recovered from a simple, covariant condition on the norm of the associated
helical Killing vector field. This unusual derivation can be used to illustrate
some concepts of prime importance in a general relativity course, including
those of Killing field, covariance, coordinate dependence, and gravitational
redshift.Comment: 11 pages, 3 figures; minor changes and text improvements; matches
version to appear in Class. Quant. Gra
Markov and Neural Network Models for Prediction of Structural Deterioration of Stormwater Pipe Assets
Storm-water pipe networks in Australia are designed to convey water from rainfall and surface runoff. They do not transport sewerage. Their structural deterioration is progressive with aging and will eventually cause pipe collapse with consequences of service interruption. Predicting structural condition of pipes provides vital information for asset management to prevent unexpected failures and to extend service life. This study focused on predicting the structural condition of storm-water pipes with two objectives. The first objective is the prediction of structural condition changes of the whole network of storm-water pipes by a Markov model at different times during their service life. This information can be used for planning annual budget and estimating the useful life of pipe assets. The second objective is the prediction of structural condition of any particular pipe by a neural network model. This knowledge is valuable in identifying pipes that are in poor condition for repair actions. A case study with closed circuit television inspection snapshot data was used to demonstrate the applicability of these two models
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.
The beginnings of geography teaching and research in the University of Glasgow: the impact of J.W. Gregory
J.W. Gregory arrived in Glasgow from Melbourne in 1904 to take up the post of foundation Professor of Geology in the University of Glasgow. Soon after his arrival in Glasgow he began to push for the setting up of teaching in Geography in Glasgow, which came to pass in 1909 with the appointment of a Lecturer in Geography. This lecturer was based in the Department of Geology in the University's East Quad. Gregory's active promotion of Geography in the University was matched by his extensive writing in the area, in textbooks, journal articles and popular books. His prodigious output across a wide range of subject areas is variably accepted today, with much of his geomorphological work being judged as misguided to varying degrees. His 'social science' publications - in the areas of race, migration, colonisation and economic development of Africa and Australia - espouse a viewpoint that is unacceptable in the twenty-first century. Nonetheless, that viewpoint sits squarely within the social and economic traditions of Gregory's era, and he was clearly a key 'Establishment' figure in natural and social sciences research in the first half of the twentieth century. The establishment of Geography in the University of Glasgow remains enduring testimony of J.W. Gregory's energy, dedication and foresight
Solving the Initial Value Problem of two Black Holes
We solve the elliptic equations associated with the Hamiltonian and momentum
constraints, corresponding to a system composed of two black holes with
arbitrary linear and angular momentum. These new solutions are based on a
Kerr-Schild spacetime slicing which provides more physically realistic
solutions than the initial data based on conformally flat metric/maximal
slicing methods. The singularity/inner boundary problems are circumvented by a
new technique that allows the use of an elliptic solver on a Cartesian grid
where no points are excised, simplifying enormously the numerical problem.Comment: 4 pages, 3 figures. Minor corrections, some points clarified, and one
reference added. To appear in Phys. Rev. Let
Softening of Cu-O bond stretching phonon in tetragonal HgBaCuO
Phonons in nearly optimally doped HgBaCuO were studied by
inelastic X-ray scattering. The dispersion of the low energy modes is well
described by a shell model, while the Cu-O bond stretching mode at high energy
shows strong softening towards the zone boundary, which deviates strongly from
the model. This seems to be common in the hole-doped high-
superconducting cuprates, and, based on this work, not related to a lattice
distortion specific to each material.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let
Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions
We prove the uniqueness theorem for asymptotically flat static vacuum black
hole solutions in higher dimensional space-times. We also construct infinitely
many non-asymptotically flat regular static black holes on the same spacetime
manifold with the same spherical topology.Comment: to appear in Progress of Theoretical Physics Supplement No. 14
Localised and nonlocalised structures in nonlinear lattices with fermions
We discuss the quasiclassical approximation for the equations of motions of a
nonlinear chain of phonons and electrons having phonon mediated hopping.
Describing the phonons and electrons as even and odd grassmannian functions and
using the continuum limit we show that the equations of motions lead to a
Zakharov-like system for bosonic and fermionic fields. Localised and
nonlocalised solutions are discussed using the Hirota bilinear formalism.
Nonlocalised solutions turn out to appear naturally for any choice of wave
parameters. The bosonic localised solution has a fermionic dressing while the
fermionic one is an oscillatory localised field. They appear only if some
constraints on the dispersion are imposed. In this case the density of fermions
is a strongly localised travelling wave. Also it is shown that in the multiple
scales approach the emergent equation is linear. Only for the resonant case we
get a nonlinear fermionic Yajima-Oikawa system. Physical implications are
discussed.Comment: 7 pages, LaTeX, no figures. to appear in Europhysics Latter
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