Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

We formulate a conjecture about the structure of `upper lines' in the expansion of the colored Jones polynomial of a knot in powers of (q-1). The Melvin-Morton conjecture states that the bottom line in this expansion is equal to the inverse Alexander polynomial of the knot. We conjecture that the upper lines are rational functions whose denominators are powers of the Alexander polynomial. We prove this conjecture for torus knots and give experimental evidence that it is also true for other types of knots.Comment: 21 pages, 1 figure, LaTe

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

WS9.3 Reduced physical activity participation is associated with increased need for hospitalisation in adults with cystic fibrosis

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Metabolic profiling of diabetic cats in remission

Background: The majority of diabetic cats in remission have abnormal glucose tolerance, and approximately one third relapse within 1 year. Greater understanding of the metabolic characteristics of diabetic cats in remission, and predictors of relapse is required to effectively monitor and manage these cats. Objectives: To identify and compare differences in plasma metabolites between diabetic cats in remission and healthy control cats using a metabolomics approach. Secondly, to assess whether identified metabolites are predictors of diabetic relapse. Animals: Twenty cats in diabetic remission for a median of 101 days, and 22 healthy matched control cats. Methods: Cats were admitted to a clinic, and casual blood glucose was recorded. After a 24 h fast, blood glucose concentration was measured, then a blood sample was taken for metabolomic (GCMS and LCMS) analyses. Three hours later, a simplified intravenous glucose tolerance test (1 g glucose/kg) was performed. Cats were monitored for diabetes relapse for at least 9 months (270 days) after baseline testing. Results: Most cats in remission continued to display impaired glucose tolerance. Concentrations of 16 identified metabolites differed (P ≤ 0.05) between remission and control cats: 10 amino acids and stearic acid (all lower in remission cats), and glucose, glycine, xylitol, urea and carnitine (all higher in remission cats). Moderately close correlations were found between these 16 metabolites and variables assessing glycaemic responses (most |r| = 0.31 to 0.69). Five cats in remission relapsed during the study period. No metabolite was identified as a predictor of relapse. Conclusion and clinical importance: This study shows that cats in diabetic remission have abnormal metabolism

Elite male Flat jockeys display lower bone density and lower resting metabolic rate than their female counterparts: implications for athlete welfare

To test the hypothesis that daily weight-making is more problematic to health in male compared with female jockeys, we compared the bone-density and resting metabolic rate (RMR) in weight-matched male and female Flat-jockeys. RMR (kcal.kg-1 lean mass) was lower in males compared with females as well as lower bone-density Z-scores at the hip and lumbar spine. Data suggest the lifestyle of male jockeys’ compromise health more severely than females, possibly due to making-weight more frequently

Chern-Simons Invariants of Torus Links

We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.Comment: 20 pages, 5 figures; v2: minor changes, version submitted to AHP. The final publication is available at http://www.springerlink.com/content/a2614232873l76h6

Evaluation of MOSFETs for entrance dose dosimetry for 6 and 10 MV photons with a custom made build up cap

Copyright © 2007 ACPSEM. All rights reserved. The dcoument attached has been archived with permission from the publisher.Commercially available MOSFETs, Thomson and Nielsen TN502-RD, were evaluated for suitability as an entrance dose in vivo dosimeter for 6MV and 10MV. Detector response was normally distributed around a mean (skewness=-0.01±0.24, kurtosis=-0.09±0.48) with a mean of 110.6 mV/Gy, with a standard deviation of 2.4% at 0.86 Gy. The standard deviation of readings increased with decreasing dose and increased at a rate greater than inverse square. The linearity coefficient was 0.9999. No significant dependence on angle, field size, dose rate, energy or time was observed. As such, they would be useful for entrance dose in vivo dosimetry. With a custom made build up cap corrections were required for field size, wedge, beam energy and tray factors, showing that build up cap design is an important consideration for entrance dose in vivo dosimetry using MOSFETs.J. P. Morton, M. Bhat, A. Kovendy and T. Williamshttp://www.acpsem.org.au/journal/abstract/abstract_3002.html#abs0

Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

Chemostratigraphy of Neoproterozoic carbonates: implications for 'blind dating'

The delta C-13(carb) and Sr-87/Sr-86 secular variations in Neoproteozoic seawater have been used for the purpose of 'isotope stratigraphy' but there are a number of problems that can preclude its routine use. In particular, it cannot be used with confidence for 'blind dating'. The compilation of isotopic data on carbonate rocks reveals a high level of inconsistency between various carbon isotope age curves constructed for Neoproteozoic seawater, caused by a relatively high frequency of both global and local delta C-13(carb) fluctuations combined with few reliable age determinations. Further complication is caused by the unresolved problem as to whether two or four glaciations, and associated negative delta C-13(carb) excursions, can be reliably documented. Carbon isotope stratigraphy cannot be used alone for geological correlation and 'blind dating'. Strontium isotope stratigraphy is a more reliable and precise tool for stratigraphic correlations and indirect age determinations. Combining strontium and carbon isotope stratigraphy, several discrete ages within the 590-544 Myr interval, and two age-groups at 660-610 and 740-690 Myr can be resolved