Numerical wave propagation for the triangular P1DGP1_{DG}-P2P2 finite element pair

Inertia-gravity mode and Rossby mode dispersion properties are examined for discretisations of the linearized rotating shallow-water equations using the $P1_{DG}$-$P2$ finite element pair on arbitrary triangulations in planar geometry. A discrete Helmholtz decomposition of the functions in the velocity space based on potentials taken from the pressure space is used to provide a complete description of the numerical wave propagation for the discretised equations. In the $f$-plane case, this decomposition is used to obtain decoupled equations for the geostrophic modes, the inertia-gravity modes, and the inertial oscillations. As has been noticed previously, the geostrophic modes are steady. The Helmholtz decomposition is used to show that the resulting inertia-gravity wave equation is third-order accurate in space. In general the \pdgp finite element pair is second-order accurate, so this leads to very accurate wave propagation. It is further shown that the only spurious modes supported by this discretisation are spurious inertial oscillations which have frequency $f$, and which do not propagate. The Helmholtz decomposition also allows a simple derivation of the quasi-geostrophic limit of the discretised $P1_{DG}$-$P2$ equations in the $\beta$-plane case, resulting in a Rossby wave equation which is also third-order accurate.Comment: Revised version prior to final journal submissio

Numerical Description of Dilute Particle-Laden FLows by a Quadrature-Based Moment Method

The numerical simulation of gas-particle flows is divided into two families of methods. In Euler-Lagrange methods individual particle trajectories are computed, whereas in Euler-Euler methods particles are characterized by statistical descriptors. Lagrangian methods are very precise but their computational cost increases with instationarity and particle volume fraction. In Eulerian methods (also called moment methods) the particle-phase computational cost is comparable to that of the fluid phase but requires strong simplificaions. Existing Eulerian models consider unimodal or close-to-equilibrium particle velocity distributions and then fail when the actual distribution is far from equilibrium. Quadrature-based Eulerian methods introduce a new reconstruction of the velocity distribution, written as a sum of delta functions in phase space constrained to give the right values for selected low-order moments. Two of the quadrature-based Eulerian methods, differing by the reconstruction algorithm, are the focus of this work. Computational results for two academic cases (crossing jets, Taylor-Green flow) are compared to those of a Lagrangian method (considered as the reference solution) and of an existing second-order moment method. With the quadrature-based Eulerian methods, significant qualitative improvement is noticed compared to the second-order moment method in the two test cases

Fractional Generalization of Kac Integral

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.Comment: 16 pages, LaTe

You are what you eat? Vegetarianism, health and identity

This paper examines the views of ‘health vegetarians’ through a qualitative study of an online vegetarian message board. The researcher participated in discussions on the board, gathered responses to questions from 33 participants, and conducted follow-up e-mail interviews with 18 of these participants. Respondents were predominantly from the United States, Canada and the UK. Seventy per cent were female, and ages ranged from 14 to 53 years, with a median of 26 years. These data are interrogated within a theoretical framework that asks, ‘what can a vegetarian body do?’ and explores the physical, psychic, social and conceptual relations of participants. This provides insights into the identities of participants, and how diet and identity interact. It is concluded that vegetarianism is both a diet and a bodily practice with consequences for identity formation and stabilisation

An Upper Mass Limit on a Red Supergiant Progenitor for the Type II-Plateau Supernova SN 2006my

We analyze two pre-supernova (SN) and three post-SN high-resolution images of the site of the Type II-Plateau supernova SN 2006my in an effort to either detect the progenitor star or to constrain its properties. Following image registration, we find that an isolated stellar object is not detected at the location of SN 2006my in either of the two pre-SN images. In the first, an I-band image obtained with the Wide-Field and Planetary Camera 2 on board the Hubble Space Telescope, the offset between the SN 2006my location and a detected source ("Source 1") is too large: > 0.08", which corresponds to a confidence level of non-association of 96% from our most liberal estimates of the transformation and measurement uncertainties. In the second, a similarly obtained V-band image, a source is detected ("Source 2") that has overlap with the SN 2006my location but is definitively an extended object. Through artificial star tests carried out on the precise location of SN 2006my in the images, we derive a 3-sigma upper bound on the luminosity of a red supergiant that could have remained undetected in our pre-SN images of log L/L_Sun = 5.10, which translates to an upper bound on such a star's initial mass of 15 M_Sun from the STARS stellar evolutionary models. Although considered unlikely, we can not rule out the possibility that part of the light comprising Source 1, which exhibits a slight extension relative to other point sources in the image, or part of the light contributing to the extended Source 2, may be due to the progenitor of SN 2006my. Only additional, high-resolution observations of the site taken after SN 2006my has faded beyond detection can confirm or reject these possibilities.Comment: Minor text changes from Version 1. Appendix added detailing the determination of confidence level of non-association of point sources in two registered astronomical image

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

X-shooter, NACO, and AMBER observations of the LBV Pistol Star \footnote{Based on ESO runs 85.D-0182A, 085.D-0625AC}

We present multi-instruments and multi-wavelengths observations of the famous LBV star Pistol Star. These observations are part of a larger program about early O stars at different metallicities. The Pistol star has been claimed as the most massive star known, with 250 solar masses. We present the preliminary results based on X-Shooter spectra, as well as the observations performed with the VLTI-AMBER and the VLT-NACO adaptive optics. The X-shooter spectrograph allows to obtain simultaneously a spectrum from the UV to the K-band with a resolving power of $\sim$15000. The preliminary results obtained indicate that Pistol Star has similar properties of Eta Car, including shells of matter, but also the binarity. Other objects of the program, here briefly presented, were selected for their particular nature: early O stars with mass discrepancies between stellar evolution models and observations, discrepancies with the wind momentum luminosity relation.Comment: Poster at the 39th LIAC, submitted version of the proceeding

Evolution of the dust mass loss with luminosity along the giant branch of the globular cluster 47 Tuc

The paper investigates the properties of the dust mass loss in stars populating the giant branch of the globular cluster 47 Tuc, by combining ISOCAM and DENIS data. Raster maps of 5 fields covering areas ranging from 4 x 4 to 15 x 15 arcmin2 at different distances from the center of the cluster have been obtained with ISOCAM at 11.5 mum (LW10 filter). The covered fields include most of the red variables known in this cluster. A detection threshold of about 0.2 mJy is achieved, allowing to detect giant stars at 11.5 mum all the way down to the horizontal branch. No dust-enshrouded asymptotic giant branch stars have been found in the observed fields, contrary to the situation encountered in LMC/SMC globular clusters with larger turnoff masses. The color index [12]-[2] (based on the ISO 11.5 mum flux and on the DENIS Ks magnitude) is used as a diagnostic of dust emission (and hence dust mass loss). Its evolution with luminosity along the giant branch reveals that dust mass loss is only present in V3 (the only cluster Mira variable observed in the present study) and in V18, a star presenting intermittent variability. This conclusion confirms the importance of stellar pulsations in the dust formation and ensuing mass loss.Comment: 16 pages, accepted in Astronomy & Astrophysic

New search strategy for high z intervening absorbers: GRB021004, a pilot study

We present near-infrared narrow- and broad-band imaging of the field of GRB021004, performed with ISAAC on the UT1 of the ESO Very Large Telescope. The narrow-band filters were chosen to match prominent emission lines at the redshift of the absorption-line systems found against the early-time afterglow of GRB021004: [OIII] at z=1.38 and Halpha at z=1.60, respectively. For the z=1.38 system we find an emission-line source at an impact parameter of 16", which is somewhat larger than the typical impact parameters of a sample of MgII absorbers at redshifts around unity. Assuming that this tentative redshift-identification is correct, the star formation rate of the galaxy is 13 +- 2 Msun/year. Our study reaches star-formation rate limits (5 sigma) of 5.7 Msun/year at z=1.38, and 7.7 Msun/year at z=1.60. These limits correspond to a depth of roughly 0.13 L*. Any galaxy counterpart of the absorbers nearer to the line of sight either has to be fainter than this limit or not be an emission-line source.Comment: 4 pages, 3 figures, accepted for publication in A&A letter

On the performance of non-conforming finite elements for the upper bound limit analysis of plates

This is a preprint version of an article accepted for publication in International Journal for Numerical Methods in Engineering Copyright © 2012 John Wiley & Sons, Ltd.International audienceIn this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming (SOCP) for the minimization problem. Three different C1-discontinuous finite elements are considered : the quadratic 6 node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble function at centroid (T6b) and the cubic Hermite triangle (H3). Through numerical examples involving Johansen and von Mises yield criteria, it is shown that cubic elements (H3) give far better results in terms of convergence rate and precision than fully conforming elements found in the literature, especially for problems involving clamped boundaries