Two physical characteristics of numerical apparent horizons

This article translates some recent results on quasilocal horizons into the language of $(3+1)$ general relativity so as to make them more useful to numerical relativists. In particular quantities are described which characterize how quickly an apparent horizon is evolving and how close it is to either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in response to referees comments to improve clarity and fix typos. One reference adde

Excitation of the odd-parity quasi-normal modes of compact objects

The gravitational radiation generated by a particle in a close unbounded orbit around a neutron star is computed as a means to study the importance of the $w$ modes of the neutron star. For simplicity, attention is restricted to odd parity (``axial'') modes which do not couple to the neutron star's fluid modes. We find that for realistic neutron star models, particles in unbounded orbits only weakly excite the $w$ modes; we conjecture that this is also the case for astrophysically interesting sources of neutron star perturbations. We also find that for cases in which there is significant excitation of quadrupole $w$ modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.

Phase Separation in Lix_xFePO4_4 Induced by Correlation Effects

We report on a significant failure of LDA and GGA to reproduce the phase stability and thermodynamics of mixed-valence Li$_x$FePO$_4$ compounds. Experimentally, Li$_x$FePO$_4$ compositions ($0 \leq x \leq 1$) are known to be unstable and phase separate into Li FePO$_4$ and FePO$_4$. However, first-principles calculations with LDA/GGA yield energetically favorable intermediate compounds an d hence no phase separation. This qualitative failure of LDA/GGA seems to have its origin in the LDA/GGA self-interaction which de localizes charge over the mixed-valence Fe ions, and is corrected by explicitly considering correlation effects in this material. This is demonstrated with LDA+U calculations which correctly predict phase separation in Li$_x$FePO$_4$ for $U-J \gtrsim 3.5$eV. T he origin of the destabilization of intermediate compounds is identified as electron localization and charge ordering at different iron sites. Introduction of correlation also yields more accurate electrochemical reaction energies between FePO$_4$/Li$_x$FePO$_ 4$ and Li/Li$^+$ electrodes.Comment: 12 pages, 5 figures, Phys. Rev. B 201101R, 200

Feasibility study: investigation of car park-based V2G services in the UK central hub

The increasing uptake of electric vehicles, and the established practice of long-term parking at stations and airports, offers an opportunity to develop a flexible approach to help with the energy storage dilemma. This paper investigates the feasibility of using a number of EV batteries as an energy storage and grid balancing solution within the UK Central Hub area. Here, the capital cost of the vehicle is a sunk cost to the EV owner. The potential income generated, or discount on long-term parking, is an additional benefit of ownership. This paper considers the income available to a small and large size car park from the different market mechanisms to offer grid support in the UK and contrasts this with the complexity and costs of the EV charging infrastructure required within these types of scheme

Superconductors are topologically ordered

We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e. that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the ``$BF$'' type and its elementary quantization. On manifolds with boundaries, the $BF$ action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the $BF$ action describes the topological order in several other physically distinct systems thus providing an example of topological universality

Revising the Local Bubble Model due to Solar Wind Charge Exchange X-ray Emission

The hot Local Bubble surrounding the solar neighborhood has been primarily studied through observations of its soft X-ray emission. The measurements were obtained by attributing all of the observed local soft X-rays to the bubble. However, mounting evidence shows that the heliosphere also produces diffuse X-rays. The source is solar wind ions that have received an electron from another atom. The presence of this alternate explanation for locally produced diffuse X-rays calls into question the existence and character of the Local Bubble. This article addresses these questions. It reviews the literature on solar wind charge exchange (SWCX) X-ray production, finding that SWCX accounts for roughly half of the observed local 1/4 keV X-rays found at low latitudes. This article also makes predictions for the heliospheric O VI column density and intensity, finding them to be smaller than the observational error bars. Evidence for the continued belief that the Local Bubble contains hot gas includes the remaining local 1/4 keV intensity, the observed local O VI column density, and the need to fill the local region with some sort of plasma. If the true Local Bubble is half as bright as previously thought, then its electron density and thermal pressure are 1/square-root(2) as great as previously thought, and its energy requirements and emission measure are 1/2 as great as previously thought. These adjustments can be accommodated easily, and, in fact, bring the Local Bubble's pressure more in line with that of the adjacent material. Suggestions for future work are made.Comment: 9 pages, refereed, accepted for publication in the proceedings of the "From the Outer Heliosphere to the Local Bubble: Comparisons of New Observations with Theory" conference and in Space Science Review

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

The Influence of the effect of solute on the thermodynamic driving force on grain refinement of Al alloys

Grain refinement is known to be strongly affected by the solute in cast alloys. Addition of some solute can reduce grain size considerably while others have a limited effect. This is usually attributed to the constitutional supercooling which is quantified by the growth restriction factor, Q. However, one factor that has not been considered is whether different solutes have differing effects on the thermodynamic driving force for solidification. This paper reveals that addition of solute reduces the driving force for solidification for a given undercooling, and that for a particular Q value, it is reduced more substantially when adding eutectic-forming solutes than peritectic-forming elements. Therefore, compared with the eutectic-forming solutes, addition of peritectic-forming solutes into Al alloys not only possesses a higher initial nucleation rate resulted from the larger thermodynamic driving force for solidification, but also promotes nucleation within the constitutionally supercooled zone during growth. As subsequent nucleation can occur at smaller constitutional supercoolings for peritectic-forming elements, a smaller grain size is thus produced. The very small constitutional supercooling required to trigger subsequent nucleation in alloys containing Ti is considered as a major contributor to its extraordinary grain refining efficiency in cast Al alloys even without the deliberate addition of inoculants.The Australian Research Council (ARC DP10955737)

Genuine Correlations of Like-Sign Particles in Hadronic Z0 Decays

Correlations among hadrons with the same electric charge produced in Z0 decays are studied using the high statistics data collected from 1991 through 1995 with the OPAL detector at LEP. Normalized factorial cumulants up to fourth order are used to measure genuine particle correlations as a function of the size of phase space domains in rapidity, azimuthal angle and transverse momentum. Both all-charge and like-sign particle combinations show strong positive genuine correlations. One-dimensional cumulants initially increase rapidly with decreasing size of the phase space cells but saturate quickly. In contrast, cumulants in two- and three-dimensional domains continue to increase. The strong rise of the cumulants for all-charge multiplets is increasingly driven by that of like-sign multiplets. This points to the likely influence of Bose-Einstein correlations. Some of the recently proposed algorithms to simulate Bose-Einstein effects, implemented in the Monte Carlo model PYTHIA, are found to reproduce reasonably well the measured second- and higher-order correlations between particles with the same charge as well as those in all-charge particle multiplets.Comment: 26 pages, 6 figures, Submitted to Phys. Lett.