Concircular tensors in Spaces of Constant Curvature: With Applications to Orthogonal Separation of The Hamilton-Jacobi Equation

We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic Hamilton-Jacobi equation are called separable. Specifically for spaces of constant curvature, we obtain canonical forms of concircular tensors modulo the action of the isometry group, we obtain the separable coordinates induced by irreducible concircular tensors, and we obtain warped products adapted to reducible concircular tensors. Using these results, we show how to enumerate the isometrically inequivalent orthogonal separable coordinates, construct the transformation from separable to Cartesian coordinates, and execute the Benenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separating natural Hamilton-Jacobi equations.Comment: Removed preamble and references to unpublished articles. Also made some minor changes in the bod

Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature

We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthogonal) separable coordinates in spaces of constant curvature using concircular tensors. This results in the construction of a special class of separable coordinates known as Kalnins-Eisenhart-Miller coordinates. Then we present the Benenti-Eisenhart-Kalnins-Miller separation algorithm, which uses concircular tensors to intrinsically search for Kalnins-Eisenhart-Miller coordinates which separate a given natural Hamilton-Jacobi equation. As a new application of the theory, we show how to obtain the separable coordinate systems in the two dimensional spaces of constant curvature, Minkowski and (Anti-)de Sitter space. We also apply the Benenti-Eisenhart-Kalnins-Miller separation algorithm to study the separability of the three dimensional Calogero-Moser and Morosi-Tondo systems

Continuous synthesis of pyridocarbazoles and initial photophysical and bioprobe characterization

Pyridocarbazoles when ligated to transition metals yield high affinity kinase inhibitors. While batch photocyclizations enable the synthesis of these heterocycles, the non-oxidative Mallory reaction only provides modest yields and difficult to purify mixtures. We demonstrate here that a flow-based Mallory cyclization provides superior results and enables observation of a clear isobestic point. The flow method allowed us to rapidly synthesize ten pyridocarbazoles and for the first time to document their interesting photophysical attributes. Preliminary characterization reveals that these molecules might be a new class of fluorescent bioprobe

Jet-induced cratering of a granular surface with application to lunar spaceports

The erosion of lunar soil by rocket exhaust plumes is investigated experimentally. This has identified the diffusion-driven flow in the bulk of the sand as an important but previously unrecognized mechanism for erosion dynamics. It has also shown that slow regime cratering is governed by the recirculation of sand in the widening geometry of the crater. Scaling relationships and erosion mechanisms have been characterized in detail for the slow regime. The diffusion-driven flow occurs in both slow and fast regime cratering. Because diffusion-driven flow had been omitted from the lunar erosion theory and from the pressure cratering theory of the Apollo and Viking era, those theories cannot be entirely correct.Comment: 13 pages, link to published version: http://cedb.asce.org/cgi/WWWdisplay.cgi?090000

National and subnational mortality effects of metabolic risk factors and smoking in Iran: a comparative risk assessment

<p>Abstract</p> <p>Background</p> <p>Mortality from cardiovascular and other chronic diseases has increased in Iran. Our aim was to estimate the effects of smoking and high systolic blood pressure (SBP), fasting plasma glucose (FPG), total cholesterol (TC), and high body mass index (BMI) on mortality and life expectancy, nationally and subnationally, using representative data and comparable methods.</p> <p>Methods</p> <p>We used data from the Non-Communicable Disease Surveillance Survey to estimate means and standard deviations for the metabolic risk factors, nationally and by region. Lung cancer mortality was used to measure cumulative exposure to smoking. We used data from the death registration system to estimate age-, sex-, and disease-specific numbers of deaths in 2005, adjusted for incompleteness using demographic methods. We used systematic reviews and meta-analyses of epidemiologic studies to obtain the effect of risk factors on disease-specific mortality. We estimated deaths and life expectancy loss attributable to risk factors using the comparative risk assessment framework.</p> <p>Results</p> <p>In 2005, high SBP was responsible for 41,000 (95% uncertainty interval: 38,000, 44,000) deaths in men and 39,000 (36,000, 42,000) deaths in women in Iran. High FPG, BMI, and TC were responsible for about one-third to one-half of deaths attributable to SBP in men and/or women. Smoking was responsible for 9,000 deaths among men and 2,000 among women. If SBP were reduced to optimal levels, life expectancy at birth would increase by 3.2 years (2.6, 3.9) and 4.1 years (3.2, 4.9) in men and women, respectively; the life expectancy gains ranged from 1.1 to 1.8 years for TC, BMI, and FPG. SBP was also responsible for the largest number of deaths in every region, with age-standardized attributable mortality ranging from 257 to 333 deaths per 100,000 adults in different regions.</p> <p>Discussion</p> <p>Management of blood pressure through diet, lifestyle, and pharmacological interventions should be a priority in Iran. Interventions for other metabolic risk factors and smoking can also improve population health.</p

Chronotype and environmental light exposure in a student population

In humans and most other species, changes in the intensity and duration of light provide a critical set of signals for the synchronisation of the circadian system to the astronomical day. The timing of activity within the 24 h day defines an individual’s chronotype, i.e. morning, intermediate or evening type. The aim of this study was to investigate the associations between environmental light exposure, due to geographical location, on the chronotype of university students. Over 6 000 university students from cities in the Northern Hemisphere (Oxford, Munich and Groningen) and Southern Hemisphere (Perth, Melbourne and Auckland) completed the Munich ChronoType Questionnaire. In parallel, light measures (daily irradiance, timing of sunrise and sunset) were compiled from satellite or ground stations at each of these locations. Our data shows that later mid-sleep point on free days (corrected for oversleep on weekends MFSsc) is associated with (i) residing further from the equator, (ii) a later sunset, (iii) spending more time outside and (iv) waking from sleep significantly after sunrise. However, surprisingly, MSFscdid not correlate with daily light intensity at the different geographical locations. Although these findings appear to contradict earlier studies suggesting that in the wider population increased light exposure is associated with an earlier chronotype, our findings are derived exclusively from a student population aged between 17 and 26 years. We therefore suggest that the age and occupation of our population increase the likelihood that these individuals will experience relatively little light exposure in the morning whilst encountering more light exposure later in the day, when light has a delaying effect upon the circadian system