Dynamics of the Tippe Top via Routhian Reduction

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.Comment: 16 pages, 7 figures, added reference. Typos corrected and a forgotten term in de linearized system is adde

Three-dimensional stability of Burgers vortices

Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number $Re = \Gamma/\nu$, where $\Gamma$ is the total circulation of the vortex and $\nu$ is the kinematic viscosity. The purpose of this paper is to show that Burgers vortex is asymptotically stable with respect to general three-dimensional perturbations, for all values of the Reynolds number. This definitive result subsumes earlier studies by various authors, which were either restricted to small Reynolds numbers or to two-dimensional perturbations. Our proof relies on the crucial observation that the linearized operator at Burgers vortex has a simple and very specific dependence upon the axial variable. This allows to reduce the full linearized equations to a vectorial two-dimensional problem, which can be treated using an extension of the techniques developped in earlier works. Although Burgers vortices are found to be stable for all Reynolds numbers, the proof indicates that perturbations may undergo an important transient amplification if $Re$ is large, a phenomenon that was indeed observed in numerical simulations.Comment: 31 pages, no figur

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions

Feinglosite, a new mineral related to brackebuschite, from Tsumeb, Namibia

Feinglosite, the zinc analog of arsenbrackebuschite, was found lining a cavity in a sample of massive chalcocite from Tsumeb, Namibia. In this cavity it is assocd. with wulfenite, anglesite and goethite. The mean of seven electron-microprobe analyses (wt.%) is: PbO 61.4, ZnO 7.3, FeO 1.8, As2O5 22.1, SO3, 5.3, H2O (by difference) [2.1], total = [100.00]%, leading to the ideal formula: Pb2(Zn,Fe)[(As,S)O4]2\ub7H2O. Feinglosite is monoclinic, space group P21 or P21/m, with unit-cell parameters a=8.973(6), b=5.955(3), c=7.766(6) \uc5, \u3b2=112.20(6)\ub0, with Z = 2. The strongest five reflections of the X-ray powder diffraction pattern are [d in \uc5 (I) (hkl)]: 4.85 (50) (110), 3.246 (100) (112), 2.988 (60) (301), 2.769 (60) (300/211), 2.107 (50) (321). The mineral is pale olive-green, transparent, sectile, and has a white streak and adamantine luster. It overgrows clusters of goethite crystals and forms globular microcryst. aggregates up to 0.5-0.75 mm in size. The hardness on Mohs scale is 4-5; the mean micro-indentation hardness is 263 at VHN100. Its calcd. d. is 6.52 g cm-3. The mineral is pale brownish gray in reflected light (when compared with goethite). Visible spectrum reflectance data are presented. Feinglosite is named for Mark N. Feinglos who first recognized the mineral on a specimen of chalcocite in his collection

Ketorolac trometamol for postoperative analgesia after orthopaedic surgery

We have compared the postoperative morphine requirements and analgesic efficacy of four doses of i.m. ketorolac 30 mg administered 6-hourly with placebo in a double-blind study of patients undergoing major or minor orthopaedic surgery. During the 24-h postoperative study period which began at the end of surgery, patients were prescribed i.m. morphine 10 mg as required 2-hourly and assessments were made of pain at 4 and 24 h. After major surgery, the median morphine consumption over 24 h was 10 mg in patients who received ketorolac, compared with 30 mg in those who received placebo (P = 0.008). Visual analogue pain scores and verbal pain assessments were better than placebo at 4 h (P = 0.028 and P = 0.008, respectively), but were not statistically different between the groups at 24 h. Overall assessment of pain was similar in both groups who had undergone major surgery. In the minor surgery groups, median morphine consumption was 0 mg in patients who received ketorolac, compared with 10 mg in those given placebo (ns). Visual analogue pain scores at 24 h after surgery were significantly less in patients who had received ketorolac compared with placebo (P = 0.046) and the overall assessment of pain relief was better in the ketorolac group (P = 0.0007). Mandatory administration of ketorolac appeared to be of benefit in both major and minor orthopaedic surgery, although the principal effects were reduction in requirement for supplementary morphine for major surgery and better overall analgesia for minor surger

Existence and Stability of Viscous Vortices

International audienceVorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the archetype of which is the self-similar Lamb-Oseen vortex. In three dimensions, amplification of vorticity due to stretching can counterbalance viscous dissipation and produce stable tubular vortices. This phenomenon is illustrated in a famous model originally proposed by Burgers, where a straight vortex tube is produced by a linear uniaxial strain field. In real flows vortex lines are usually not straight, and can even form closed curves, as in the case of axisymmetric vortex rings which are very common in nature and in laboratory experiments. The aim of this chapter is to review a few rigorous results concerning existence and stability of viscous vortices in simple geometries