Joins for (Augmented) Simplicial Sets

We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.Comment: 8 page

The damping of gravitational waves in dust

We examine a simple model of interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of gravitational wave when passing through media. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.Comment: 7 pages, accepted to Phys. Sc

A Mach line panel method for computing the linearized supersonic flow over planar wings

A method is described for solving the linearized supersonic flow over planar wings using panels bounded by two families of Mach lines. Polynomial distributions of source and doublet strength lead to simple, closed form solutions for the aerodynamic influence coefficients, and a nearly triangular matrix yields rapid solutions for the singularity parameters. The source method was found to be accurate and stable both for analysis and design boundary conditions. Similar results were obtained with the doublet method for analysis boundary conditions on the portion of the wing downstream of the supersonic leading edge, but instabilities in the solution occurred for the region containing a portion of the subsonic leading edge. Research on the method was discontinued before this difficulty was resolved

Moving frames for cotangent bundles

Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy

Development of learning objectives for neurology in a veterinary curriculum: part I: undergraduates

Background With an increasing caseload of veterinary neurology patients in first opinion practice, there is a requirement to establish relevant learning objectives for veterinary neurology encompassing knowledge, skills and attitudes for veterinary undergraduate students in Europe. With help of experts in veterinary neurology from the European College of Veterinary Neurology (ECVN) and the European Society of Veterinary Neurology (ESVN) a survey of veterinary neurologic learning objectives using a modified Delphi method was conducted. The first phase comprised the development of a draft job description and learning objectives by a working group established by the ECVN. In the second phase, a quantitative questionnaire (multiple choice, Likert scale and free text) covering 140 learning objectives and subdivided into 8 categories was sent to 341 ESVN and ECVN members and a return rate of 62% (n = 213/341) was achieved. Results Of these 140 learning objectives ECVN Diplomates and ESVN members considered 42 (30%) objectives as not necessary for standard clinical veterinary neurology training, 94 (67%) were graded to be learned at a beginner level and 4 (3%) at an advanced level. The following objectives were interpreted as the most important day one skills: interpret laboratory tests, perform a neurological examination and establish a neuroanatomical localization. In this survey the three most important diseases of the central nervous system included epilepsy, intervertebral disc disease and inflammatory diseases. The three most important diseases of the peripheral nervous system included polyradiculoneuritis, myasthenia gravis and toxic neuropathies. Conclusions The results of this study should help to reform the veterinary curriculum regarding neurology and may reduce the phenomenon of “Neurophobia”.</p

Distance-redshift from an optical metric that includes absorption

We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a "transverse" conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon's optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure

Killing vectors and anisotropy

We consider an action that can generate fluids with three unequal stresses for metrics with a spacelike Killing vector. The parameters in the action are directly related to the stress anisotropies. The field equations following from the action are applied to an anisotropic cosmological expansion and an extension of the Gott-Hiscock cosmic string

Spacetime perspective of Schwarzschild lensing

We propose a definition of an exact lens equation without reference to a background spacetime, and construct the exact lens equation explicitly in the case of Schwarzschild spacetime. For the Schwarzschild case, we give exact expressions for the angular-diameter distance to the sources as well as for the magnification factor and time of arrival of the images. We compare the exact lens equation with the standard lens equation, derived under the thin-lens-weak-field assumption (where the light rays are geodesics of the background with sharp bending in the lens plane, and the gravitational field is weak), and verify the fact that the standard weak-field thin-lens equation is inadequate at small impact parameter. We show that the second-order correction to the weak-field thin-lens equation is inaccurate as well. Finally, we compare the exact lens equation with the recently proposed strong-field thin-lens equation, obtained under the assumption of straight paths but without the small angle approximation, i.e., with allowed large bending angles. We show that the strong-field thin-lens equation is remarkably accurate, even for lightrays that take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.