Stable filtering procedures for nodal discontinuous Galerkin methods

We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre-Gauss-Lobatto quadrature. The theoretical discussion serves to re-contextualize stable filtering results for finite difference methods into the DG setting. It is shown that the stability of the filtering is equivalent to a particular contractivity condition borrowed from the analysis of so-called transmission problems. As such, the temporal stability proof relies on the fact that the underlying spatial discretization of the problem possesses a semi-discrete bound on the solution. Numerical tests are provided to verify and validate the underlying theoretical results.Comment: 14 pages, 3 figure

Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes

We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable coefficient initial boundary value problems can be formulated in simple and straightforward ways using high-order accurate operators of generalized summation-by-parts type. Encapsulated features on a single computational block or element may include polynomial bases, tensor products as well as curvilinear coordinate transformations. Moreover, through the use of inner product preserving interpolation or projection, the global summation-by-parts property in extended to arbitrary multi-block or multi-element meshes with non-conforming nodal interfaces

On the central symmetry of the circumstellar envelope of RS Cnc

We present a phenomenological study of CO(1-0) and CO(2-1) emission from the circumstellar envelope (CSE) of the Asymptotic Giant Branch (AGB) star RS\,Cnc. It reveals departures from central symmetry that turn out to be efficient tools for the exploration of some of the CSE properties. We use a wind model including a bipolar flow with a typical wind velocity of $\sim$8 km\,s$^{-1}$ decreasing to $\sim$2 km\,s$^{-1}$ near the equator to describe Doppler velocity spectral maps obtained by merging data collected at the IRAM Plateau de Bure Interferometer and Pico Veleta single dish radio telescope. Parameters describing the wind morphology and kinematics are obtained, together with the radial dependence of the gas temperature in the domain of the circumstellar envelope probed by the CO observations. Significant north-south central asymmetries are revealed by the analysis, which we quantify using a simple phenomenological description. The origin of such asymmetries is unclear.Comment: accepted for publication in Research in Astronomy and Astrophysics (RAA

HI and CO in the circumstellar environment of the S-type star RS Cnc

This paper presents interferometric and single-dish CO observations along with HI data obtained for the oxygen-rich semi-regular variable RS Cnc, in order to probe its circumstellar environment at different scales. With the Plateau de Bure Interferometer and the IRAM 30-m telescope, we detect both the CO(1-0) and the CO(2-1) rotational lines from RS Cnc. The line profiles are composite, with two components of half-width ~2 km/s and ~8 km/s respectively. Whereas the narrow velocity component seems to originate from an equatorial disk in the central part of the CO envelope, the broad component reveals a bipolar structure, with a north-south velocity gradient. In addition, we obtain new HI data on the source and around it in a field of almost 1 square degree. The HI line is centered at v_LSR = 7 km/s in agreement with CO observations. A new reduction process reveals a complex extended structure in the northwest direction, of estimated size ~18 arcmin, with a PA (~310 degrees) opposite to the direction of the stellar proper motion (~140 degrees). We derive an HI mass of ~3 10^-2 M_sun for this structure. Based on a non-spherical simulation, we find that this structure is consistent with arising from the interaction of the star undergoing mass loss at an average rate of ~10^-7 M_sun.yr^-1 over ~2-3 10^5 years with the interstellar medium. This work illustrates the powerful complementarity of CO and HI observations with regard to a more complete description of circumstellar environments around AGB stars.Comment: accepted for publication in A&

Assessment of the cervical range of motion over time, differences between results of the Flock of Birds and the EDI-320:A comparison between an electromagnetic tracking system and an electronic inclinometer

The objective of this study was to analyse cervical range of motion, assessed over time by means of a digital inclinometer (EDI-320) and a three-dimensional electromagnetic tracking device (Flock of Birds). The maximum active cervical range of motion was assessed with two measurement devices in three sessions over time, with 6-week intervals. In total, 26 women and 24 men (mean age: 44.4, SD: 9.9) without known pathology of the cervical spine participated. Four movements were measured axial rotation with the cervical spine in a flexed and in an extended position, flexion-extension, and lateral bending. The results showed that the factor time was significant for rotation in extension and rotation in flexion. The factor device was significant for all movements measured. and the interaction term between time and device was significant for all movements except rotation in extension. The Flock of Birds measured significantly higher ranges of motion on all motions except for lateral bending. A substantial variation in cervical range of motion was observed over time (ranging from -5.6 to 8.1) as well as between devices (ranging from - 13.1 to 29.9). Substantial and significant differences in cervical range of motion were found over time as well as differences between the Flock of Birds and the EDI-320. (C) 2007 Elsevier Ltd. All rights reserved

Copious Amounts of Dust and Gas in a z=7.5 Quasar Host Galaxy

We present IRAM/NOEMA and JVLA observations of the quasar J1342+0928 at z=7.54 and report detections of copious amounts of dust and [CII] emission in the interstellar medium (ISM) of its host galaxy. At this redshift, the age of the universe is 690 Myr, about 10% younger than the redshift of the previous quasar record holder. Yet, the ISM of this new quasar host galaxy is significantly enriched by metals, as evidenced by the detection of the [CII] 158micron cooling line and the underlying far-infrared (FIR) dust continuum emission. To the first order, the FIR properties of this quasar host are similar to those found at a slightly lower redshift (z~6), making this source by far the FIR-brightest galaxy known at z>7.5. The [CII] emission is spatially unresolved, with an upper limit on the diameter of 7 kpc. Together with the measured FWHM of the [CII] line, this yields a dynamical mass of the host of <1.5x10^11 M_sun. Using standard assumptions about the dust temperature and emissivity, the NOEMA measurements give a dust mass of (0.6-4.3)x10^8 M_sun. The brightness of the [CII] luminosity, together with the high dust mass, imply active ongoing star formation in the quasar host. Using [CII]-SFR scaling relations, we derive star formation rates of 85-545 M_sun/yr in the host, consistent with the values derived from the dust continuum. Indeed, an episode of such past high star formation is needed to explain the presence of ~10^8 M_sun of dust implied by the observations.Comment: 8 pages, 4 figures. Published in ApJ Letter

Corticosteroid injection for de Quervain's tenosynovitis

Back ground De Quervain's tenosynovitis is a disorder characterised by pain on the radial (thumb) side of the wrist and functional disability of the hand. It can be treated by corticosteroid injection, splinting and surgery. Objectives To summarise evidence on the efficacy and safety of corticosteroid injections for de Quervain's tenosynovitis. Search strategy We searched the following databases: the Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2009, Issue 2), MEDLINE (1966 to April 2009), EMBASE (1956 to April 2009), CINAHL (1982 to April 2009), AMED (1985 to April 2009), DARE, Dissertation Abstracts and PEDro (physiotherapy evidence database). Selection criteria Randomised and controlled clinical trials evaluating the efficacy and safety of corticosteroid injections for de Quervain's tenosynovitis. Data collection and analysis After screening abstracts of studies identified by the search we obtained full text articles of studies which fulfilled the selection criteria. We extracted data using a predefined electronic form. We assessed the methodological quality of included trials by using the checklist developed by Jadad and the Delphi list. We extracted data on the primary outcome measures: treatment success; severity of pain or tenderness at the radial styloid; functional impairment of the wrist or hand; and outcome of Finkelstein's test, and the secondary outcome measures: proportion of patients with side effects; type of side effects and patient satisfaction with injection treatment. Main results We found one controlled clinical trial of 18 participants (all pregnant or lactating women) that compared one steroid injection with methylprednisolone and bupivacaine to splinting with a thumb spica. All patients in the steroid injection group (9/9) achieved complete relief of pain whereas none of the patients in the thumb spica group (0/9) had complete relief of pain, one to six days after intervention (number needed to treat to benefit (NNTB) = 1, 95% confidence interval (CI) 0.8 to 1.2). No side effects or local complications of steroid injection were noted. Authors' conclusions The efficacy of corticosteroid injections for de Quervain's tenosynovitis has been studied in only one small controlled clinical trial, which found steroid injections to be superior to thumb spica splinting. However, the applicability of our findings to daily clinical practice is limited, as they are based on only one trial with a small number of included participants, the methodological quality was poor and only pregnant and lactating women participated in the study. No adverse effects were observed