On the time continuity of entropy solutions

We show that any entropy solution $u$ of a convection diffusion equation $\partial_t u + \div F(u)-\Delta\phi(u) =b$ in \OT belongs to C([0,T),L^1_{Loc}(\o\O)). The proof does not use the uniqueness of the solution

Error estimates for a numerical approximation to the compressible barotropic Navier-Stokes equations

We present here a general method based on the investigation of the relative energy of the system, that provides an unconditional error estimate for the approximate solution of the barotropic Navier Stokes equations obtained by time and space discretization. We use this methodology to derive an error estimate for a specific DG/finite element scheme for which the convergence was proved in [27]. This is an extended version of the paper submitted to IMAJNA

Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations

We prove in this paper the convergence of the Marker and Cell (MAC) scheme for the discretization of the steady state compressible and isentropic Navier-Stokes equations on two or three-dimensional Cartesian grids. Existence of a solution to the scheme is proven, followed by estimates on approximate solutions, which yield the convergence of the approximate solutions, up to a subsequence, and in an appropriate sense. We then prove that the limit of the approximate solutions satisfies the mass and momentum balance equations, as well as the equation of state, which is the main difficulty of this study

Results for a turbulent system with unbounded viscosities: weak formulations, existence of solutions, boundedness, smoothness'

We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solutions are considered and compared. We establish existence and regularity results. In particular we study the boundedness of weak solutions. We also establish an existence result for a classical solutio

Entropy estimates for a class of schemes for the euler equations

In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (eventually with a positive corrective term at the righ-hand-side so as to ensure consistency) and the possible upwinding is performed with respect to the material velocity only. The implicit-in-time first-order upwind scheme satisfies a local entropy inequality. A generalization of the convection term is then introduced, which allows to limit the scheme diffusion while ensuring a weaker property: the entropy inequality is satisfied up to a remainder term which is shown to tend to zero with the space and time steps, if the discrete solution is controlled in L $\infty$ and BV norms. The explicit upwind variant also satisfies such a weaker property, at the price of an estimate for the velocity which could be derived from the introduction of a new stabilization term in the momentum balance. Still for the explicit scheme, with the above-mentioned generalization of the convection operator, the same result only holds if the ratio of the time to the space step tends to zero

Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I

We explore how well crowded field point-source photometry can be accomplished with SDSS data: We present a photometric pipeline based on DoPhot, and tuned for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations we show that the completeness of source extraction is above 80% to i < 21 (AB) and a stellar surface density of about 200 sq.amin. Hence, a specialized data pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS images, where the standard SDSS photometric package Photo, when applied in normal survey mode, gives poor results. We apply our pipeline to an area of about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and construct a high S/N star-count map of Leo I via an optimized filter in color-magnitude space (g,r,i). Although the radial surface-density profile of the dwarf deviates from the best fit empirical King model towards outer radii, we find no evidence for tidal debris out to a stellar surface-density of 4*10^(-3) of the central value. We determine the total luminosity of Leo I, and model its mass using the spherical and isotropic Jeans equation. Assuming that 'mass follows light' we constrain a lower limit of the total mass of the dSph to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a constant density dark-matter (DM) halo, then the mass within the central 12' is (2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and possibly >75 if the DM halo dominates the mass and extends further out than 12'. In summary, our results show that Leo I is a symmetric, relaxed and bound system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A

Nonlinear Eigenvalues and Bifurcation Problems for Pucci's Operator

In this paper we extend existing results concerning generalized eigenvalues of Pucci's extremal operators. In the radial case, we also give a complete description of their spectrum, together with an equivalent of Rabinowitz's Global Bifurcation Theorem. This allows us to solve equations involving Pucci's operators

The Resolved Structure and Dynamics of an Isolated Dwarf Galaxy: A VLT and Keck Spectroscopic Survey of WLM

We present spectroscopic data for 180 red giant branch stars in the isolated dwarf irregular galaxy WLM. Observations of the Calcium II triplet lines in spectra of RGB stars covering the entire galaxy were obtained with FORS2 at the VLT and DEIMOS on Keck II allowing us to derive velocities, metallicities, and ages for the stars. With accompanying photometric and radio data we have measured the structural parameters of the stellar and gaseous populations over the full galaxy. The stellar populations show an intrinsically thick configuration with $0.39 \leq q_{0} \leq 0.57$. The stellar rotation in WLM is measured to be $17 \pm 1$ km s$^{-1}$, however the ratio of rotation to pressure support for the stars is $V/\sigma \sim 1$, in contrast to the gas whose ratio is seven times larger. This, along with the structural data and alignment of the kinematic and photometric axes, suggests we are viewing WLM as a highly inclined oblate spheroid. Stellar rotation curves, corrected for asymmetric drift, are used to compute a dynamical mass of $4.3\pm 0.3\times10^{8}$M$_{\odot}$ at the half light radius ($r_{h} = 1656 \pm 49$ pc). The stellar velocity dispersion increases with stellar age in a manner consistent with giant molecular cloud and substructure interactions producing the heating in WLM. Coupled with WLM's isolation, this suggests that the extended vertical structure of its stellar and gaseous components and increase in stellar velocity dispersion with age are due to internal feedback, rather than tidally driven evolution. These represent some of the first observational results from an isolated Local Group dwarf galaxy which can offer important constraints on how strongly internal feedback and secular processes modulate SF and dynamical evolution in low mass isolated objects.Comment: 14 Pages, 17 figures, 3 tables. Accepted for publication in Ap

Dynamical modelling of the elliptical galaxy NGC 2974

In this paper we analyse the relations between a previously described oblate Jaffe model for an ellipsoidal galaxy and the observed quantities for NGC 2974, and obtain the length and velocity scales for a relevant elliptical galaxy model. We then derive the finite total mass of the model from these scales, and finally find a good fit of an isotropic oblate Jaffe model by using the Gauss-Hermite fit parameters and the observed ellipticity of the galaxy NGC 2974. The model is also used to predict the total luminous mass of NGC 2974, assuming that the influence of dark matter in this galaxy on the image, ellipticity and Gauss-Hermite fit parameters of this galaxy is negligible within the central region, of radius $0.5R_{\rm e}.$Comment: 7 figure

TRIM33 switches off Ifnb1 gene transcription during the late phase of macrophage activation

Despite its importance during viral or bacterial infections, transcriptional regulation of the interferon-β gene (Ifnb1) in activated macrophages is only partially understood. Here we report that TRIM33 deficiency results in high, sustained expression of Ifnb1 at late stages of toll-like receptor-mediated activation in macrophages but not in fibroblasts. In macrophages, TRIM33 is recruited by PU.1 to a conserved region, the Ifnb1 Control Element (ICE), located 15 kb upstream of the Ifnb1 transcription start site. ICE constitutively interacts with Ifnb1 through a TRIM33-independent chromatin loop. At late phases of lipopolysaccharide activation of macrophages, TRIM33 is bound to ICE, regulates Ifnb1 enhanceosome loading, controls Ifnb1 chromatin structure and represses Ifnb1 gene transcription by preventing recruitment of CBP/p300. These results characterize a previously unknown mechanism of macrophage-specific regulation of Ifnb1 transcription whereby TRIM33 is critical for Ifnb1 gene transcription shutdown