4,537 research outputs found
Eguchi-Hanson Solitons in Odd Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added
feature of having Lorentzian signatures. They are asymptotic to
(A)dS. In the AdS case their energy is negative relative to that of
pure AdS. We present perturbative evidence in 5 dimensions that such metrics
are the states of lowest energy in their asymptotic class, and present a
conjecture that this is generally true for all such metrics. In the dS case
these solutions have a cosmological horizon. We show that their mass at future
infinity is less than that of pure dS.Comment: 26 pages, Late
Finding Pairwise Intersections Inside a Query Range
We study the following problem: preprocess a set O of objects into a data
structure that allows us to efficiently report all pairs of objects from O that
intersect inside an axis-aligned query range Q. We present data structures of
size and with query time
time, where k is the number of reported pairs, for two classes of objects in
the plane: axis-aligned rectangles and objects with small union complexity. For
the 3-dimensional case where the objects and the query range are axis-aligned
boxes in R^3, we present a data structures of size and query time . When the objects and
query are fat, we obtain query time using storage
1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations
We use the, covariant and gauge-invariant, 1+1+2 formalism developed by
Clarkson and Barrett, and develop new techniques, to decouple electromagnetic
(EM) perturbations on arbitrary locally rotationally symmetric (LRS)
space-times. Ultimately, we derive 3 decoupled complex equations governing 3
complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized
for LRS space-times, whereas the remaining two are new generalizations of the
Bardeen-Press (BP) equations. This is achieved by first using linear algebra
techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2
form which is conducive to decoupling. This new complex system immediately
yields the generalized RW equation, and furthermore, we also derive a decoupled
equation governing a newly defined complex EM 2-vector. Subsequently, a further
decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed,
allowing us to decompose the complex EM 2-vector, and its governing equations,
into spin-weighted scalars, giving rise to the generalized BP equations
Symmetries of a class of nonlinear fourth order partial differential equations
In this paper we study symmetry reductions of a class of nonlinear fourth
order partial differential equations \be u_{tt} = \left(\kappa u + \gamma
u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2,
\ee where , , , and are constants. This
equation may be thought of as a fourth order analogue of a generalization of
the Camassa-Holm equation, about which there has been considerable recent
interest. Further equation (1) is a ``Boussinesq-type'' equation which arises
as a model of vibrations of an anharmonic mass-spring chain and admits both
``compacton'' and conventional solitons. A catalogue of symmetry reductions for
equation (1) is obtained using the classical Lie method and the nonclassical
method due to Bluman and Cole. In particular we obtain several reductions using
the nonclassical method which are no} obtainable through the classical method
Prospecting Period Measurements with LSST - Low Mass X-ray Binaries as a Test Case
The Large Synoptic Survey Telescope (LSST) will provide for unbiased sampling
of variability properties of objects with mag 24. This should allow for
those objects whose variations reveal their orbital periods (), such
as low mass X-ray binaries (LMXBs) and related objects, to be examined in much
greater detail and with uniform systematic sampling. However, the baseline LSST
observing strategy has temporal sampling that is not optimised for such work in
the Galaxy. Here we assess four candidate observing strategies for measurement
of in the range 10 minutes to 50 days. We simulate multi-filter
quiescent LMXB lightcurves including ellipsoidal modulation and stochastic
flaring, and then sample these using LSST's operations simulator (OpSim) over
the (mag, ) parameter space, and over five sightlines sampling a range
of possible reddening values. The percentage of simulated parameter space with
correctly returned periods ranges from 23 %, for the current baseline
strategy, to 70 % for the two simulated specialist strategies. Convolving
these results with a distribution, a modelled Galactic spatial
distribution and reddening maps, we conservatively estimate that the most
recent version of the LSST baseline strategy will allow determination
for 18 % of the Milky Way's LMXB population, whereas strategies that do
not reduce observations of the Galactic Plane can improve this dramatically to
32 %. This increase would allow characterisation of the full binary
population by breaking degeneracies between suggested distributions
in the literature. Our results can be used in the ongoing assessment of the
effectiveness of various potential cadencing strategies.Comment: Replacement after addressing minor corrections from the referee -
mainly improvements in clarificatio
The Surface Morphology of Normal and Atherosclerotic Coronary Arteries in Male Macaca Fascicularis and the Effect of Coronary Angiography
Selective coronary angiography is one of the procedures used frequently in the diagnosis and management of coronary artery disease. Macaca fascicularis monkeys were used to study the effects of coronary angiography on coronary artery surface morphology. Fourteen M. fascicularis were fed either an atherogenic diet (0.34 mg of cholesterol/kcal and 40 to 43% of the calories as fat) for six to nine months or a control diet. For six of these animals the Judkin method of selective left coronary angiography was done 24 h prior to necropsy. The ascending aorta, right coronary artery, left circumflex (LCX), left anterior descending (LAD) and left main (LM) coronary arteries were examined using scanning electron microscopy (SEM). The animals fed an atherogenic diet had 27% of the ascending aorta and 7% of the coronary arteries covered with raised lesions. The surface of these coronary arteries differed from those of animals fed a control diet in that the surface appeared smoother and often had numerous adherent leukocytes. The animals undergoing coronary angiography had 25% of the ascending aorta and 10% of the LM surface injured by the catheter. These areas were denuded of endothelium and covered with adherent platelets. There were no morphologic changes observed by SEM following angiography within the LCX or LAD arteries. Thus even in a setting of hypercholesterolemia exposure to contrast media during the coronary angiography procedure did not lead to surface alterations
The Hamiltonian Structure of the Second Painleve Hierarchy
In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable depending on n
parameters denoted by and . We introduce new
canonical coordinates and obtain Hamiltonians for the and
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates
On Scaling Solutions with a Dissipative Fluid
We study the asymptotic behaviour of scaling solutions with a dissipative
fluid and we show that, contrary to recent claims, the existence of stable
accelerating attractor solution which solves the `energy' coincidence problem
depends crucially on the chosen equations of state for the thermodynamical
variables. We discuss two types of equations of state, one which contradicts
this claim, and one which supports it.Comment: 8 pages and 5 figures; to appear in Class. Quantum Gra
1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes
We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and
Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on
non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times.
Ultimately, we show how to derive six real decoupled equations governing the
total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new,
and result from expanding the complex EM 2-vector which we defined in
\cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then
able to show that there are four precise combinations of the amplitudes that
decouple, two of these are polar perturbations whereas the remaining two are
axial. The remaining two decoupled equations are the generalized Regge-Wheeler
equations which were developed previously in \cite{Betschart2004}, and these
govern the two EM scalar harmonic amplitudes. However, our analysis generalizes
this by including a full description and classification of energy-momentum
sources, such as charges and currents.Comment: 9 page
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