7,278 research outputs found
Limit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A
general limit curve theorem is formulated which includes the case of converging
curves with endpoints and the case in which the limit points assigned since the
beginning are one, two or at most denumerable. Some applications are
considered. It is proved that in chronological spacetimes, strong causality is
either everywhere verified or everywhere violated on maximizing lightlike
segments with open domain. As a consequence, if in a chronological spacetime
two distinct lightlike lines intersect each other then strong causality holds
at their points. Finally, it is proved that two distinct components of the
chronology violating set have disjoint closures or there is a lightlike line
passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio
Magnification relations for Kerr lensing and testing Cosmic Censorship
A Kerr black hole with mass parameter m and angular momentum parameter a
acting as a gravitational lens gives rise to two images in the weak field
limit. We study the corresponding magnification relations, namely the signed
and absolute magnification sums and the centroid up to post-Newtonian order. We
show that there are post-Newtonian corrections to the total absolute
magnification and centroid proportional to a/m, which is in contrast to the
spherically symmetric case where such corrections vanish. Hence we also propose
a new set of lensing observables for the two images involving these
corrections, which should allow measuring a/m with gravitational lensing. In
fact, the resolution capabilities needed to observe this for the Galactic black
hole should in principle be accessible to current and near-future
instrumentation. Since a/m >1 indicates a naked singularity, a most interesting
application would be a test of the Cosmic Censorship conjecture. The technique
used to derive the image properties is based on the degeneracy of the Kerr lens
and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple
physical explanation for this degeneracy is also given.Comment: 13 pages, version 2: references added, minor changes. To appear in
Phys. Rev.
A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole
Consider, in the domain of outer communication of a Kerr-Newman black hole, a
point (observation event) and a timelike curve (worldline of light source).
Assume that the worldline of the source (i) has no past end-point, (ii) does
not intersect the caustic of the past light-cone of the observation event, and
(iii) goes neither to the horizon nor to infinity in the past. We prove that
then for infinitely many positive integers k there is a past-pointing lightlike
geodesic of (Morse) index k from the observation event to the worldline of the
source, hence an observer at the observation event sees infinitely many images
of the source. Moreover, we demonstrate that all lightlike geodesics from an
event to a timelike curve in the domain of outer communication are confined to
a certain spherical shell. Our characterization of this spherical shell shows
that in the Kerr-Newman spacetime the occurrence of infinitely many images is
intimately related to the occurrence of centrifugal-plus-Coriolis force
reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy
Effects of Corner Geometry and Adiabatic Extensions on Heat Transfer through a Differentially Heated Square Cavity
This study is concerned with heat transfer by natural convection in a differentially heated square cavity. The purpose is to explore numerically the effects of the corner geometry and adiabatic extensions on heat transfer through the sidewalls. Two sets of simulations have been carried out in this study. The first set is concerned with steady-state calculations with different corner shapes, and the second set considers both steady-state and transient heat transfer with adiabatic extensions of various dimensions. The numerical results are presented in this paper
Painleve-Gullstrand Coordinates for the Kerr Solution
We construct a coordinate system for the Kerr solution, based on the zero
angular momentum observers dropped from infinity, which generalizes the
Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr
metric can then be interpreted as describing space flowing on a (curved)
Riemannian 3-manifold. The stationary limit arises as the set of points on this
manifold where the speed of the flow equals the speed of light, and the
horizons as the set of points where the radial speed equals the speed of light.
A deeper analysis of what is meant by the flow of space reveals that the
acceleration of free-falling objects is generally not in the direction of this
flow. Finally, we compare the new coordinate system with the closely related
Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign
error in the expression of the function delta correcte
Titanium solubility in olivine in the system TiO2âMgOâSiO2: no evidence for an ultra-deep origin of Ti-bearing olivine
3D Simulations of MHD Jet Propagation Through Uniform and Stratified External Environments
We present a set of high-resolution 3D MHD simulations of steady light,
supersonic jets, exploring the influence of jet Mach number and the ambient
medium on jet propagation and energy deposition over long distances. The
results are compared to simple self-similar scaling relations for the
morphological evolution of jet-driven structures and to previously published 2D
simulations. For this study we simulated the propagation of light jets with
internal Mach numbers 3 and 12 to lengths exceeding 100 initial jet radii in
both uniform and stratified atmospheres.
The propagating jets asymptotically deposit approximately half of their
energy flux as thermal energy in the ambient atmosphere, almost independent of
jet Mach number or the external density gradient. Nearly one-quarter of the jet
total energy flux goes directly into dissipative heating of the ICM, supporting
arguments for effective feedback from AGNs to cluster media. The remaining
energy resides primarily in the jet and cocoon structures. Despite having
different shock distributions and magnetic field features, global trends in
energy flow are similar among the different models.
As expected the jets advance more rapidly through stratified atmospheres than
uniform environments. The asymptotic head velocity in King-type atmospheres
shows little or no deceleration. This contrasts with jets in uniform media with
heads that are slowed as they propagate. This suggests that the energy
deposited by jets of a given length and power depends strongly on the structure
of the ambient medium. While our low-Mach jets are more easily disrupted, their
cocoons obey evolutionary scaling relations similar to the high-Mach jets.Comment: Accepted in ApJ, 32 pages, 18 figures, animations available from:
http://www.msi.umn.edu/Projects/twj/newsite/projects/radiojets/movies
Demography and disorders of the French Bulldog population under primary veterinary care in the UK in 2013
Abstract Background Despite its Gallic name, the French Bulldog is a breed of both British and French origin that was first recognised by The Kennel Club in 1906. The French Bulldog has demonstrated recent rapid rises in Kennel Club registrations and is now (2017) the second most commonly registered pedigree breed in the UK. However, the breed has been reported to be predisposed to several disorders including ocular, respiratory, neurological and dermatological problems. The VetCompass⢠Programme collates de-identified clinical data from primary-care veterinary practices in the UK for epidemiological research. Using VetCompass⢠clinical data, this study aimed to characterise the demography and common disorders of the general population of French Bulldogs under veterinary care in the UK. Results French Bulldogs comprised 2228 (0.49%) of 445,557 study dogs under veterinary care during 2013. Annual proportional birth rates showed that the proportional ownership of French Bulldog puppies rose steeply from 0.02% of the annual birth cohort attending VetCompass⢠practices in 2003 to 1.46% in 2013. The median age of the French Bulldogs overall was 1.3 years (IQR 0.6â2.5, range 0.0â13.0). The most common colours of French Bulldogs were brindle (solid or main) (32.36%) and fawn (solid or main) (29.9%). Of the 2228 French Bulldogs under veterinary care during 2013, 1612 (72.4%) had at least one disorder recorded. The most prevalent fine-level precision disorders recorded were otitis externa (14.0%, 95% CI: 12.6â15.5), diarrhoea (7.5%, 95% CI: 6.4â8.7), conjunctivitis (3.2%, 95% CI: 2.5â4.0), nails overlong (3.1%, 95% CI% 2.4â3.9) and skin fold dermatitis (3.0%, 95% CI% 2.3â3.8). The most prevalent disorder groups were cutaneous (17.9%, 95% CI: 16.3â19.6), enteropathy (16.7%, 95% CI: 15.2â18.3), aural (16.3%, 95% CI: 14.8â17.9), upper respiratory tract (12.7%, 95% CI: 11.3â14.1) and ophthalmological (10.5%, 95% CI: 9.3â11.9). Conclusions Ownership of French Bulldogs in the UK is rising steeply. This means that the disorder profiles reported in this study reflect a current young UK population and are likely to shift as this cohort ages. Otitis externa, diarrhoea and conjunctivitis were the most common disorders in French Bulldogs. Identification of health priorities based on VetCompass⢠data can support evidenceâbased reforms to improve health and welfare within the breed
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