Site percolation and random walks on d-dimensional Kagome lattices

The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site percolation thresholds are calculated numerically for d= 3, 4, 5, and 6. The scaling of these thresholds as a function of dimension d, or alternatively q, is different than for hypercubic lattices: p_c ~ 2/q instead of p_c ~ 1/(q-1). The latter is the Bethe approximation, which is usually assumed to hold for all lattices in high dimensions. A series expansion is calculated, in order to understand the different behaviour of the Kagome' lattice. The return probability of a random walker on these lattices is also shown to scale as 2/q. For bond percolation on d-dimensional diamond lattices these results imply p_c ~ 1/(q-1).Comment: 11 pages, LaTeX, 8 figures (EPS format), submitted to J. Phys.

A Dynamical Systems Approach to Schwarzschild Null Geodesics

The null geodesics of a Schwarzschild black hole are studied from a dynamical systems perspective. Written in terms of Kerr-Schild coordinates, the null geodesic equation takes on the simple form of a particle moving under the influence of a Newtonian central force with an inverse-cubic potential. We apply a McGehee transformation to these equations, which clearly elucidates the full phase space of solutions. All the null geodesics belong to one of four families of invariant manifolds and their limiting cases, further characterized by the angular momentum L of the orbit: for |L|>|L_c|, (1) the set that flow outward from the white hole, turn around, then fall into the black hole, (2) the set that fall inward from past null infinity, turn around outside the black hole to continue to future null infinity, and for |L|<|L_c|, (3) the set that flow outward from the white hole and continue to future null infinity, (4) the set that flow inward from past null infinity and into the black hole. The critical angular momentum Lc corresponds to the unstable circular orbit at r=3M, and the homoclinic orbits associated with it. There are two additional critical points of the flow at the singularity at r=0. Though the solutions of geodesic motion and Hamiltonian flow we describe here are well known, what we believe is a novel aspect of this work is the mapping between the two equivalent descriptions, and the different insights each approach can give to the problem. For example, the McGehee picture points to a particularly interesting limiting case of the class (1) that move from the white to black hole: in the limit as L goes to infinity, as described in Schwarzschild coordinates, these geodesics begin at r=0, flow along t=constant lines, turn around at r=2M, then continue to r=0. During this motion they circle in azimuth exactly once, and complete the journey in zero affine time.Comment: 14 pages, 3 Figure

Black hole tidal problem in the Fermi normal coordinates

We derive a tidal potential for a self-gravitating fluid star orbiting Kerr black hole along a timelike geodesic extending previous works by Fishbone and Marck. In this paper, the tidal potential is calculated up to the third and fourth-order terms in $R/r$, where $R$ is the stellar radius and $r$ the orbital separation, in the Fermi-normal coordinate system following the framework developed by Manasse and Misner. The new formulation is applied for determining the tidal disruption limit (Roche limit) of corotating Newtonian stars in circular orbits moving on the equatorial plane of Kerr black holes. It is demonstrated that the third and fourth-order terms quantitatively play an important role in the Roche limit for close orbits with R/r \agt 0.1. It is also indicated that the Roche limit of neutron stars orbiting a stellar-mass black hole near the innermost stable circular orbit may depend sensitively on the equation of state of the neutron star.Comment: Correct typo

SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE

It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a non-rotating black hole is presented. The generalization to the case of the Kerr solution is presented too.Comment: 11 pages, 2 PostScript figures (available as uuencoded compressed tar file), uses epsfig.tex). Accepted on February 1995 for publication in Classical and Quantum Gravit

The Giant X-Ray Flare of NGC 5905: Tidal Disruption of a Star, a Brown Dwarf, or a Planet?

We model the 1990 giant X-ray flare of the quiescent galaxy NGC 5905 as the tidal disruption of a star by a supermassive black hole. From the observed rapid decline of the luminosity, over a timescale of a few years, we argue that the flare was powered by the fallback of debris rather than subsequent accretion via a thin disk. The fallback model allows constraints to be set on the black hole mass and the mass of debris. The latter must be very much less than a solar mass to explain the very low luminosity of the flare. The observations can be explained either as the partial stripping of the outer layers of a low-mass main sequence star or as the disruption of a brown dwarf or a giant planet. We find that the X-ray emission in the flare must have originated within a small patch rather than over the entire torus of circularized material surrounding the black hole. We suggest that the patch corresponds to the ``bright spot'' where the stream of returning debris impacts the torus. Interestingly, although the peak luminosity of the flare was highly sub-Eddington, the peak flux from the bright spot was close to the Eddington limit. We speculate on the implications of this result for observations of other flare events.Comment: 25 pages, including 5 figure

Early outcome of facial reconstructive surgery abroad: a comparative study

Every year, many medical missions are undertaken in the developing world but there is almost a universal lack of outcome data on the quality of these missions. The present study compares early clinical outcome and complication rate in two consecutive missions (facial reconstruction) undertaken to Ethiopia in 2007 and 2008. The object was to establish if measures adopted following feedback from the first mission led to improvement of the results. A significant improvement was observed in early clinical outcome and there were less severe complications in the 2008 compared to the 2007 mission. On both occasions, significantly more complications were experienced after complex compared to simple procedures. Despite improved outcome in 2008, 50% of the complex cases had an unfavourable clinical result. The data suggest that early outcome studies are a useful method of critically evaluating the quality of surgical mission. The unsatisfactory outcome of complex procedures underlines the need for feedback on the quality of these missions

Nursing Care and Patient Safety: Visualizing Medication Organization, Storage and Distribution with Photographic Research Methods

In this qualitative study, we adapted photographic research methods from earlier nursing research to identify factors related to organization, storage and distribution that could lead to errors in the selection, preparation and administration of medications. The research excerpt presented here was developed in a clinical unit of an urban Brazilian public hospital. The research participants were nurses working at that unit and students from the two final semesters of the Undergraduate Nursing Course. We collected digital photographs of the medication system and subsequently used photo elicitation to review the images with research participants, so as to obtain their perceptions and narratives of working with medications in the unit. We report selected findings here on the organization, storage and distribution of medications, which indicate there is room to improve the safety of the medication system.En este estudio cualitativo, se adoptó el método de investigación fotográfica de estudios anteriores, para identificar factores relacionados a la organización, acondicionamiento y distribución, los que podrían conducir a errores en la selección, preparación y administración de medicamentos. Esta parte de la investigación que se presenta fue desarrollada en una unidad de clínica médica de un Hospital Público, en Brasil. Los participantes de la investigación fueron enfermeros que trabajaban en aquella unidad y estudiantes de los dos últimos semestres del Curso de Graduación en Enfermería. Fueron obtenidas fotografías digitales del sistema de medicación y subsecuentemente, se obtuvieron las fotos para analizar las imágenes con los participantes de la investigación, a fin de obtener sus percepciones y narrativas al respecto del trabajo con medicamentos en aquella unidad. Se presenta una selección de los principales hallazgos de la investigación sobre organización, acondicionamiento y distribución de medicamentos, indicando que hay espacio para mejorar la seguridad del sistema de medicación.Neste estudo qualitativo, adaptou-se o método de pesquisa fotográfica de estudos anteriores, para identificar fatores relacionados à organização, acondicionamento e distribuição que poderiam levar a erros na seleção, preparo e administração de medicamentos. O recorte da pesquisa apresentado foi desenvolvido em unidade de clínica médica de um hospital público, Brasil. Os participantes da pesquisa foram enfermeiros que trabalhavam naquela unidade e acadêmicos dos dois últimos semestres do curso de graduação em Enfermagem. Obtiveram-se fotografias digitais do sistema de medicação e, subsequentemente, utilizou-se a elicitação das fotos para rever imagens com os participantes da pesquisa, a fim de obter suas percepções e narrativas a respeito do trabalho com medicamentos, naquela unidade. Apresenta-se uma seleção dos principais achados da pesquisa sobre organização, acondicionamento e distribuição de medicamentos, indicando que há espaço para melhorar a segurança do sistema de medicação

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid, and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Tidal disruption occurs at orbital radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma ray bursts which may result from such disruption.Comment: 29 pages including 8 figures. Minor changes and update. To appear in ApJ, March 20, 2000 (Vol.532, #1

Burst dynamics during drainage displacements in porous media: Simulations and experiments

We investigate the burst dynamics during drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical distribution of pressure drops scales according to other systems exhibiting self-organized criticality. The pressure signal was calculated by a network model that properly simulates drainage displacements. We compare our results with corresponding experiments.Comment: 7 pages, 4 figures. Submitted to Europhys. Let