The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas

This article reviews the recent developments in the theory of generalised hydrodynamics (GHD) with emphasis on the repulsive one-dimensional Bose gas. We discuss the implications of GHD on the mechanisms of thermalisation in integrable quantum many-body systems as well as its ability to describe far-from-equilibrium behaviour of integrable and near integrable systems in a variety of quantum quench scenarios. We outline the experimental tests of GHD in cold-atom gases and its benchmarks with other microscopic theoretical approaches. Finally, we offer some perspectives on the future direction of the development of GHD.Comment: 13 pages, 10 figure

Light-curve modelling constraints on the obliquities and aspect angles of the young Fermi pulsars

In more than four years of observation the Large Area Telescope on board the Fermi satellite has identified pulsed $\gamma$-ray emission from more than 80 young pulsars, providing light curves with high statistics. Fitting the observations with geometrical models can provide estimates of the magnetic obliquity $\alpha$ and aspect angle $\zeta$, yielding estimates of the radiation beaming factor and luminosity. Using $\gamma$-ray emission geometries (Polar Cap, Slot Gap, Outer Gap, One Pole Caustic) and radio emission geometry, we fit $\gamma$-ray light curves for 76 young pulsars and we jointly fit their $\gamma$-ray plus radio light curves when possible. We find that a joint radio plus $\gamma$-ray fit strategy is important to obtain ($\alpha$, $\zeta$) estimates that can explain simultaneous radio and $\gamma$-ray emission. The intermediate-to-high altitude magnetosphere models, Slot Gap, Outer Gap, and One pole Caustic, are favoured in explaining the observations. We find no evolution of $\alpha$ on a time scale of a million years. For all emission geometries our derived $\gamma$-ray beaming factors are generally less than one and do not significantly evolve with the spin-down power. A more pronounced beaming factor vs. spin-down power correlation is observed for Slot Gap model and radio-quiet pulsars and for the Outer Gap model and radio-loud pulsars. For all models, the correlation between $\gamma$-ray luminosity and spin-down power is consistent with a square root dependence. The $\gamma$-ray luminosities obtained by using our beaming factors not exceed the spin-down power. This suggests that assuming a beaming factor of one for all objects, as done in other studies, likely overestimates the real values. The data show a relation between the pulsar spectral characteristics and the width of the accelerator gap that is consistent with the theoretical prediction for the Slot Gap model.Comment: 90 pages, 80 figures (63 in Appendices), accepted for publication in Astronomy and Astrophysic

Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor retains the nonnegative curvature in the case that the deformation starts at a normal homogeneous metric. We classify triples of groups (H,K,G) where nonnegative curvature is maintained for small deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a complete classification in case the subgroup H has full rank and an almost complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat

The economics of rabbit control in Central Otago: A preliminary analysis

With contributions by J.M. Williams, J. Bell and T.M. Broad, Agricultural Research Division, Ministry of Agriculture and Fisheries. Prepared under contract for Agricultural Research Division Ministry of Agriculture and Fisheries, WellingtonThis paper reports a preliminary examination of the economic efficiency and equity implications of recent rabbit control policies and programmes. The Alexandra Pest Destruction Board in Central Otago was used as a case study. Public and private expenditure data on rabbit control were collected and analysed for the period 1974-75 through 1981-82. Control programme benefits were estimated using data obtained in a survey of runholders and from historical production records. Programme costs were developed from actual expenditure data on control operations and administration based on Board records. While the estimated benefits are much less precise in comparison to programme costs, the results of the cost-benefit analysis suggest that significant cost savings can be achieved in meeting the stated objectives of current pest management policies. In particular, the level of annual expenditure in recent years on those lands which can be regarded as good natural habitat for the feral rabbit does not appear to be warranted, since such land types have an inherently low productive capacity and could not sustain the present level of control input on a 'user pays' basis. Although certain public benefits (e.g., land and water conservation) were not estimated, such benefits would have to be quite large to justify recent levels of annual taxpayer input into APDB control operations. The incidence of programme costs under present policy shows that most of the burden is borne by the tax-paying public. The report concludes with some suggestions to appraise these implications more accurately for regional and national public policy

Magneto-optical Kerr Effect Studies of Square Artificial Spin Ice

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically-defined array of single-domain ferromagnetic islands. We find that the anisotropic inter-island interactions lead to a non-monotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.Comment: Physical Review B, Rapid Communications (in press

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe

G328.4+0.2 : A large and luminous Crab-like supernova remnant

We report on radio continuum and HI observations of the radio source G328.4+0.2 using the Australia Telescope Compact Array. Our results confirm G328.4+0.2 to be a filled-center nebula with no surrounding shell, showing significant linear polarization and an almost flat spectral index. These results lead us to conclude that G328.4+0.2 is a Crab-like, or ``plerionic'', supernova remnant (SNR), presumably powered by an unseen central pulsar. HI absorption towards G328.4+0.2 puts a lower limit on its distance of 17.4 +/- 0.9 kpc, making it the largest (D=25 pc) and most luminous (L_R = 3e35 erg/s) Crab-like SNR in the Galaxy. We infer G328.4+0.2 to be significantly older than the Crab Nebula, but powered by a pulsar which is fast spinning (P<20 ms) and which has a comparatively low magnetic field (B<1e12 G). We propose G328.4+0.2, G74.9+1.2 and N157B as a distinct group of large-diameter, high-luminosity Crab-like SNRs, all powered by fast-spinning low-field pulsars.Comment: 7 pages, 3 embedded EPS figures, uses emulateapj.sty. Accepted to ApJ. Abstract corrected so that distance is now in kpc, not pc

Two Large HI Shells in the Outer Galaxy near l=279 degrees

As part of a survey of HI 21-cm emission in the Southern Milky Way, we have detected two large shells in the interstellar neutral hydrogen near l=279 deg. The center velocities are +36 and +59 km/s, which puts the shells at kinematic distances of 7 and 10 kpc. The larger shell is about 610 pc in diameter and very empty, with density contrast of at least 15 between the middle and the shell walls. It has expansion velocity of about 20 km/s and swept up mass of several million solar masses. The energy indicated by the expansion may be as high as 2.4 X 10^53 ergs. We estimate its age to be 15 to 20 million years. The smaller shell has diameter of about 400 pc, expansion velocity about 10 km/s and swept up mass of about 10^6 solar masses. Morphologically both regions appear to be shells, with high density regions mostly surrounding the voids, although the first appears to have channels of low density which connect with the halo above and below the HI layer. They lie on the edge of the Carina arm, which suggests that they may be expanding horizontally into the interarm region as well as vertically out of the disk. If this interpretation is correct, this is the first detection of an HI chimney which has blown out of both sides of the disk.Comment: 21 pages, 14 jpeg figures, accepted for publication in A

Design Considerations for Efficient and Effective Microarray Studies

This paper describes the theoretical and practical issues in experimental design for gene expression microarrays. Specifically, this paper (1) discusses the basic principles of design (randomization, replication, and blocking) as they pertain to microarrays, and (2) provides some general guidelines for statisticians designing microarray studies

Grazing Collisions of Black Holes via the Excision of Singularities

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes $m$ are separated a distance $\approx10m$ and with impact parameter $\approx2m$. Initial data are based on superposed, boosted (velocity $\approx0.5c$) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to $t \approx 35m$ are obtained in which two initially separate apparent horizons are present for $t\approx3.8m$. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.Comment: 2 References corrected, reference to figure update