The river model of black holes

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.Comment: 16 pages, 4 figures. The introduction now refers to the paper of Unruh (1981) and the extensive work on analog black holes that it spawned. Thanks to many readers for feedback that called attention to our omissions. Submitted to the American Journal of Physic

An Evaluation of a Behaviour Assessment to Determine the Suitability of Shelter Dogs for Rehoming

We evaluated a scheme for assessing shelter dog behaviour, which used 28 tests and rated responses from 0 (positive response) to 5 (fear, tonic immobility, or escape attempts). The assessment was evaluated for 236 dogs, and was repeated by a different assessor for 39 dogs approximately 80 days after rehoming to determine relevance of individual test components. A new owner survey evaluated satisfaction with the dog. A total of 130 of 236 dogs passed (score ≤ 70), 24 scored 71–80 (referred for behavioural modification), and 82 (score > 80) failed. Scores were mainly unaffected by dog type and environmental variables, but decreased if dog faeces from a previous test was present in the arena during a test. Shelter tests only correlated with repeat tests if there was no direct contact with assessors. Adopters were satisfied with their dogs, despite reporting some behaviour problems. The shelter assessment was therefore robust against most outside influences but did not predict responses to people well

Penrose Diagram for a Transient Black Hole

A Penrose diagram is constructed for a spatially coherent black hole that smoothly begins an accretion, then excretes symmetrically as measured by a distant observer, with the initial and final states described by a metric of Minkowski form. Coordinate curves on the diagram are computationally derived. Causal relationships between space-time regions are briefly discussed. The life cycle of the black hole demonstrably leaves asymptotic observers in an unaltered Minkowski space-time of uniform conformal scale.Comment: 14 pages, 9 figures, spelling correction

Management of Bleeding Associated with Malignant Wounds

Abstract Bleeding malignant wounds in palliative care patients can be anxiety-provoking for patients, their caregivers, and healthcare providers, and can be difficult to manage. We present the case of a 60-year-old man with a bleeding neck wound due to squamous cell carcinoma of the hypopharynx admitted to our inpatient palliative care unit. Management of bleeding included local wound care measures and psychosocial support for the patient and his wife. We review therapeutic approaches to managing bleeding malignant wounds with the aim of providing clinically useful information.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98457/1/jpm%2E2011%2E0286.pd

Lubiprostone ameliorates the cystic fibrosis mouse intestinal phenotype

<p>Abstract</p> <p>Background</p> <p>Cystic fibrosis (CF) is caused by mutations in the <it>CFTR </it>gene that impair the function of CFTR, a cAMP-regulated anion channel. In the small intestine loss of CFTR function creates a dehydrated, acidic luminal environment which is believed to cause an accumulation of mucus, a phenotype characteristic of CF. CF mice have small intestinal bacterial overgrowth, an altered innate immune response, and impaired intestinal transit. We investigated whether lubiprostone, which can activate the CLC2 Cl^-channel, would improve the intestinal phenotype in CF mice.</p> <p>Methods</p> <p><it>Cftr^tm1UNC</it>(CF) and wildtype (WT) littermate mice on the C57BL/6J background were used. Lubiprostone (10 μg/kg-day) was administered by gavage for two weeks. Mucus accumulation was estimated from crypt lumen widths in periodic acid-Schiff base, Alcian blue stained sections. Luminal bacterial load was measured by qPCR for the bacterial 16<it>S </it>gene. Gastric emptying and small intestinal transit in fasted mice were assessed using gavaged rhodamine dextran. Gene expression was evaluated by Affymetrix Mouse430 2.0 microarray and qRT-PCR.</p> <p>Results</p> <p>Crypt width in control CF mice was 700% that of WT mice (<it>P </it>< 0.001). Lubiprostone did not affect WT crypt width but, unexpectedly, increased CF crypt width 22% (<it>P </it>= 0.001). Lubiprostone increased bacterial load in WT mice to 490% of WT control levels (<it>P </it>= 0.008). Conversely, lubiprostone decreased bacterial overgrowth in CF mice by 60% (<it>P </it>= 0.005). Lubiprostone increased gastric emptying at 20 min postgavage in both WT (<it>P </it>< 0.001) and CF mice (<it>P </it>< 0.001). Lubiprostone enhanced small intestinal transit in WT mice (<it>P </it>= 0.024) but not in CF mice (<it>P </it>= 0.377). Among other innate immune markers, expression of mast cell genes was elevated 4-to 40-fold in the CF intestine as compared to WT, and lubiprostone treatment of CF mice decreased expression to WT control levels.</p> <p>Conclusions</p> <p>These results indicate that lubiprostone has some benefits for the CF intestinal phenotype, especially on bacterial overgrowth and the innate immune response. The unexpected observation of increased mucus accumulation in the crypts of lubiprostone-treated CF mice suggests the possibility that lubiprostone increases mucus secretion.</p

Symmetries of Differential Equations via Cartan's Method of Equivalence

We formulate a method of computing invariant 1-forms and structure equations of symmetry pseudo-groups of differential equations based on Cartan's method of equivalence and the moving coframe method introduced by Fels and Olver. Our apparoach does not require a preliminary computation of infinitesimal defining systems, their analysis and integration, and uses differentiation and linear algebra operations only. Examples of its applications are given.Comment: 15 pages, LaTeX 2.0

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Winding number order in the Haldane model with interactions

We study the Haldane model with nearest–neighbor interactions. This model is physically motivated by the associated implementation with ultracold atoms. We show that the topological phase of the interacting model can be characterized by a physically observable winding number. The robustness of this number extends well beyond the topological insulator phase towards attractive and repulsive interactions that are comparable to the kinetic energy scale of the model. We identify and characterize the relevant phases of the model as a function of the interaction strength