The Angular Momentum Distribution within Halos in Different Dark Matter Models

We study the angular momentum profile of dark matter halos for a statistical sample drawn from a set of high-resolution cosmological simulations of $256^3$ particles. Two typical Cold Dark Matter (CDM) models have been analyzed, and the halos are selected to have at least $3\times 10^4$ particles in order to reliably measure the angular momentum profile. In contrast with the recent claims of Bullock et al., we find that the degree of misalignment of angular momentum within a halo is very high. About 50 percent of halos have more than 10 percent of halo mass in the mass of negative angular momentum $j$. After the mass of negative $j$ is excluded, the cumulative mass function $M(<j)$ follows approximately the universal function proposed by Bullock et al., though we still find a significant fraction of halos ($\sim 50$) which exhibit systematic deviations from the universal function. Our results, however, are broadly in good agreement with a recent work of van den Bosch et al.. We also study the angular momentum profile of halos in a Warm Dark Matter (WDM) model and a Self-Interacting Dark Matter (SIDM) model. We find that the angular momentum profile of halos in the WDM is statistically indistinguishable from that in the CDM model, but the angular momentum of halos in the SIDM is reduced by the self-interaction of dark matter.Comment: 23 pages, 10 figures, 2 tables. Revised version, added a new table, accepted for publication in MNRA

Mathematical and computational studies of equilibrium capillary free surfaces

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated

Blue flag with yellow tiger? Flags, authenticity and identity

The Flag of the Formosa Republic in the collection of the National Taiwan Museum is a national icon. It is a copy of one made in 1895 to mark the formation of a new Taiwanese republic; this replica, described in a contemporary newspaper account as an exact copy, was made in Japan in 1909. The painted flag was an intriguing puzzle. Instrumental analysis and a close study of the flag itself and of surviving historic photographs and records were used to try to establish whether what looked like later additions and repairs were actually part of the original construction. An international team of conservators and scientists from Taiwan, the UK, the USA and Germany carried out the investigation and the conservation treatment. Although dye analysis was inconclusive and it has not yet been possible to ascertain the original colour, it was felt that an addition in the upper right corner and some of the repairs could well be part of the original construction and these were left in situ though other repairs were removed. The paper lining was removed, revealing that the flag was painted on both sides. The fabric was cleaned using a vacuum suction table, while the paint surface was cleaned with swabs. The flag was supported using an adhesive treatment with Lascaux acrylic resin

Evolution of the rates of mass wasting and fluvial sediment transfer from the epicentral area of the 1999, Mw 7.6 earthquake

The 1999 Chichi earthquake (Mw=7.6) triggered more than 20,000 landslides in the epicentral area in central west Taiwan, and subsequent typhoons have caused an even larger number of slope failures. As a result, the suspended sediment load of the epi- central Choshui River has increased dramatically. Measurements of suspended sedi- ment at a downstream gauging station indicate that the unit sediment concentration increased about six times due to the earthquake, and decreased exponentially due to flushing by subsequent typhoons. The e-folding time scale of the seismic perturbation of sediment transfer in the Choshui River is 3-5 years. Based on this estimate of the de- cay of the erosional response to the earthquake, a mass balance can be calculated for the earthquake, including co-seismic uplift and subsidence, post-seismic relaxation, and erosion. This mass balance shows that the Chi-Chi earthquake has acted to build ridge topography in the hanging wall of the fault, but in the far field, some destruc- tion of topography has occurred. However, our estimate of seismically-driven erosion may be incomplete. A detailed analysis of landsliding in the Chenyoulan tributary of the Choshui River indicates that most co-and post seismic landslide debris remains on hillslopes within the catchment. Recent typhoons have continued to cause high rates of landsliding high in the landscape, but rates of mass wasting near the stream net- work have decreased. The full geomorphic response to the Chi-Chi earthquake may be much larger, and more protracted than indicated by river gauging data

General Kerr-NUT-AdS Metrics in All Dimensions

The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables \mu_i that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate reparameterisation in which the \mu_i variables are replaced by [D/2]-1 unconstrained coordinates y_\alpha, and having the remarkable property that the Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The coordinates r and y_\alpha now appear in a very symmetrical way in the metric, leading to an immediate generalisation in which we can introduce [D/2]-1 NUT parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst (D-2)/2 are non-trivial in even dimensions. This gives the most general Kerr-NUT-AdS metric in $D$ dimensions. We find that in all dimensions D\ge4 there exist discrete symmetries that involve inverting a rotation parameter through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with over-rotating parameters are equivalent to under-rotating metrics. We also consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.Comment: Latex, 24 pages, minor typos correcte