Completeness of the Trajectories of Particles Coupled to a General Force Field

We analyze the extendability of the solutions to a certain second order differential equation on a Riemannian manifold $(M,g)$, which is defined by a general class of forces (both prescribed on $M$ or depending on the velocity). The results include the general time-dependent anholonomic case, and further refinements for autonomous systems or forces derived from a potential are obtained. These extend classical results for Lagrangian and Hamiltonian systems. Several examples show the optimality of the assumptions as well as the applicability of the results, including an application to relativistic pp-waves.Comment: Archive for Rational Mechanics and Analysis (to appear

The Dynamics of a Rigid Body in Potential Flow with Circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte

Degree of entanglement for two qubits

In this paper, we present a measure to quantify the degree of entanglement for two qubits in a pure state.Comment: 5 page

Simultaneous Magneto-Optical Trapping of Two Lithium Isotopes

We confine 4 10^8 fermionic 6Li atoms simultaneously with 9 10^9 bosonic 7Li atoms in a magneto-optical trap based on an all-semiconductor laser system. We optimize the two-isotope sample for sympathetic evaporative cooling. This is an essential step towards the production of a quantum-degenerate gas of fermionic lithium atoms.Comment: 4 pages, 3 figure

Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements

We present new determinations of the cosmic expansion history from red-envelope galaxies. We have obtained for this purpose high-quality spectra with the Keck-LRIS spectrograph of red-envelope galaxies in 24 galaxy clusters in the redshift range 0.2 < z < 1.0. We complement these Keck spectra with high-quality, publicly available archival spectra from the SPICES and VVDS surveys. We improve over our previous expansion history measurements in Simon et al. (2005) by providing two new determinations of the expansion history: H(z) = 97 +- 62 km/sec/Mpc at z = 0.5 and H(z) = 90 +- 40 km/sec/Mpc at z = 0.8. We discuss the uncertainty in the expansion history determination that arises from uncertainties in the synthetic stellar-population models. We then use these new measurements in concert with cosmic-microwave-background (CMB) measurements to constrain cosmological parameters, with a special emphasis on dark-energy parameters and constraints to the curvature. In particular, we demonstrate the usefulness of direct H(z) measurements by constraining the dark- energy equation of state parameterized by w0 and wa and allowing for arbitrary curvature. Further, we also constrain, using only CMB and H(z) data, the number of relativistic degrees of freedom to be 4 +- 0.5 and their total mass to be < 0.2 eV, both at 1-sigma.Comment: Submitted to JCA

Modelling thirty-day mortality in the acute respiratory distress syndrome (ARDS) in an adult ICU

Publisher's copy made available with the permission of the publisher © Australian Society of AnaesthetistsVariables predicting thirty-day outcome from Acute Respiratory Distress Syndrome (ARDS) were analysed using Cox regression structured for time-varying covariates. Over a three-year period, 1996-1998, consecutive patients with ARDS (bilateral chest X-ray opacities, PaO₂/FiO₂ ratio of <200 and an acute precipitating event) were identified using a prospective computerized data base in a university teaching hospital ICU. The cohort, 106 mechanically ventilated patients, was of mean (SD) age 63.5 (15.5) years and 37% were female. Primary lung injury occurred in 45% and 24% were postoperative. ICU-admission day APACHE II score was 25 (8); ARDS onset time from ICU admission was 1 day (median: range 0-16) and 30 day mortality was 41% (95% CI: 33%-51%). At ARDS onset, PaO₂/FiO₂ ratio was 92 (31), 81% had four-quadrant chest X-ray opacification and lung injury score was 2.75 (0.45). Average mechanical ventilator tidal volume was 10.3 ml/ predicted kg weight. Cox model mortality predictors (hazard ratio, 95% CI) were: APACHE II score, 1.15 (1.09-1.21); ARDS lag time (days), 0.72 (0.58-0.89); direct versus indirect injury, 2.89 (1.45-5.76); PaO₂/FiO₂ ratio, 0.98 (0.97-0.99); operative versus non-operative category, 0.24 (0.09-0.63). Time-varying effects were evident for PaO₂/FiO₂ ratio, operative versus non-operative category and ventilator tidal volume assessed as a categorical predictor with a cut-point of 8 ml/kg predicted weight (mean tidal volumes, 7.1 (1.9) vs 10.7 (1.6) ml/kg predicted weight). Thirty-day survival was improved for patients ventilated with lower tidal volumes. Survival predictors in ARDS were multifactorial and related to patient-injury-time interaction and level of mechanical ventilator tidal volume.J. L. Moran, P. J. Solomon, V. Fox, M. Salagaras, P. J. Williams, K. Quinlan, A. D. Berstenhttp://www.aaic.net.au/Article.asp?D=200332

Comprehensive lung injury pathology induced by mTOR inhibitors

Molecular Targets in Oncology[Abstract] Interstitial lung disease is a rare side effect of temsirolimus treatment in renal cancer patients. Pulmonary fibrosis is characterised by the accumulation of extracellular matrix collagen, fibroblast proliferation and migration, and loss of alveolar gas exchange units. Previous studies of pulmonary fibrosis have mainly focused on the fibro-proliferative process in the lungs. However, the molecular mechanism by which sirolimus promotes lung fibrosis remains elusive. Here, we propose an overall cascade hypothesis of interstitial lung diseases that represents a common, partly underlying synergism among them as well as the lung pathogenesis side effects of mammalian target of rapamycin inhibitors