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$_{d+1}/Z_p$. 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 $O(n({\rm polylog} n))$ and with query time $O((k+1)({\rm polylog} n))$ 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 $O(n\sqrt{n}({\rm polylog} n))$ and query time $O((\sqrt{n}+k)({\rm polylog} n))$. When the objects and query are fat, we obtain $O((k+1)({\rm polylog} n))$ query time using $O(n({\rm polylog} n))$ 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 $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ 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 $r$ mag $<$ 24. This should allow for those objects whose variations reveal their orbital periods ($P_{orb}$), 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 $P_{orb}$ 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, $P_{orb}$) 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 $\sim$23 %, for the current baseline strategy, to $\sim$70 % for the two simulated specialist strategies. Convolving these results with a $P_{orb}$ distribution, a modelled Galactic spatial distribution and reddening maps, we conservatively estimate that the most recent version of the LSST baseline strategy will allow $P_{orb}$ determination for $\sim$18 % of the Milky Way's LMXB population, whereas strategies that do not reduce observations of the Galactic Plane can improve this dramatically to $\sim$32 %. This increase would allow characterisation of the full binary population by breaking degeneracies between suggested $P_{orb}$ 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 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 $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ 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

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

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