Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Effect of surface restoring on subsurface variability in a climate model during 1949-2005

Initializing the ocean for decadal predictability studies is a challenge, as it requires reconstructing the little observed subsurface trajectory of ocean variability. In this study we explore to what extent surface nudging using well-observed sea surface temperature (SST) can reconstruct the deeper ocean variations for the 1949–2005 period. An ensemble made with a nudged version of the IPSLCM5A model and compared to ocean reanalyses and reconstructed datasets. The SST is restored to observations using a physically-based relaxation coefficient, in contrast to earlier studies, which use a much larger value. The assessment is restricted to the regions where the ocean reanalyses agree, i.e. in the upper 500 m of the ocean, although this can be latitude and basin dependent. Significant reconstruction of the subsurface is achieved in specific regions, namely region of subduction in the subtropical Atlantic, below the thermocline in the equatorial Pacific and, in some cases, in the North Atlantic deep convection regions. Beyond the mean correlations, ocean integrals are used to explore the time evolution of the correlation over 20-year windows. Classical fixed depth heat content diagnostics do not exhibit any significant reconstruction between the different existing observation-based references and can therefore not be used to assess global average time-varying correlations in the nudged simulations. Using the physically based average temperature above an isotherm (14 °C) alleviates this issue in the tropics and subtropics and shows significant reconstruction of these quantities in the nudged simulations for several decades. This skill is attributed to the wind stress reconstruction in the tropics, as already demonstrated in a perfect model study using the same model. Thus, we also show here the robustness of this result in an historical and observational context.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

GALAXY EVOLUTION IN A COMPLEX ENVIRONMENT: A MULTI-WAVELENGTH STUDY OF HCG 7

The environment where galaxies are found heavily influences their evolution. Close groupings, like the ones in the cores of galaxy clusters or compact groups, evolve in ways far more dramatic than their isolated counterparts. We have conducted a multi-wavelength study of Hickson Compact Group 7 (HCG 7), consisting of four giant galaxies: three spirals and one lenticular. We use Hubble Space Telescope (HST) imaging to identify and characterize the young and old star cluster populations. We find young massive clusters (YMCs) mostly in the three spirals, while the lenticular features a large, unimodal population of globular clusters (GCs) but no detectable clusters with ages less than a few Gyr. The spatial and approximate age distributions of the similar to 300 YMCs and similar to 150 GCs thus hint at a regular star formation history in the group over a Hubble time. While at first glance the HST data show the galaxies as undisturbed, our deep ground-based, wide-field imaging that extends the HST coverage reveals faint signatures of stellar material in the intragroup medium (IGM). We do not, however, detect the IGM in H I or Chandra X-ray observations, signatures that would be expected to arise from major mergers. Despite this fact, we find that the H I gas content of the individual galaxies and the group as a whole are a third of the expected abundance. The appearance of quiescence is challenged by spectroscopy that reveals an intense ionization continuum in one galaxy nucleus, and post-burst characteristics in another. Our spectroscopic survey of dwarf galaxy members yields a single dwarf elliptical galaxy in an apparent stellar tidal feature. Based on all this information, we suggest an evolutionary scenario for HCG 7, whereby the galaxies convert most of their available gas into stars without the influence of major mergers and ultimately result in a dry merger. As the conditions governing compact groups are reminiscent of galaxies at intermediate redshift, we propose that HCGs are appropriate for studying galaxy evolution at z similar to 1-2.

Hydrodynamical simulations of Galactic fountains - II. Evolution of multiple fountains

The ejection of gas out of the disc in late-type galaxies is related to star formation and is mainly due to the explosion of Type II supernovae (SN II). In a previous paper, we considered the evolution of a single Galactic fountain, that is, a fountain powered by a single SN cluster. Using three-dimensional hydrodynamical simulations, we studied in detail the fountain flow and its dependence with several factors, such as the Galactic rotation, the distance to the Galactic centre and the presence of a hot gaseous halo. As a natural followup, this paper investigates the dynamical evolution of multiple generations of fountains generated by similar to 100 OB associations. We have considered the observed size-frequency distribution of young stellar clusters within the Galaxy in order to appropriately fuel the multiple fountains in our simulations. Most of the results of the previous paper have been confirmed, like for example the formation of intermediate velocity clouds above the disc by the multiple fountains. Also, this work confirms the localized nature of the fountain flows: the freshly ejected metals tend to fall back close to the same Galactocentric region where they are delivered. Therefore, the fountains do not change significantly the radial profile of the disc chemical abundance. The multiple fountain simulations also allowed us to consistently calculate the feedback of the star formation on the halo gas. We found that the hot gas gains about 10 per cent of all the SN II energy produced in the disc. Thus, the SN feedback more than compensate for the halo radiative losses and allow for a quasi steady-state disc-halo circulation to exist. Finally, we have also considered the possibility of mass infall from the intergalactic medium and its interaction with the clouds that are formed by the fountains. Though our simulations are not suitable to reproduce the slow rotational pattern that is typically observed in the haloes around the disc galaxies, they indicate that the presence of an external gas infall may help to slow down the rotation of the gas in the clouds and thus the amount of angular momentum that they transfer to the coronal gas, as previously suggested in the literature.

An analysis of the composite stellar population in M32

We obtained long-slit spectra of high signal-to-noise ratio of the galaxy M32 with the Gemini Multi-Object Spectrograph at the Gemini-North telescope. We analysed the integrated spectra by means of full spectral fitting in order to extract the mixture of stellar populations that best represents its composite nature. Three different galactic radii were analysed, from the nuclear region out to 2 arcmin from the centre. This allows us to compare, for the first time, the results of integrated light spectroscopy with those of resolved colour-magnitude diagrams from the literature. As a main result we propose that an ancient and an intermediate-age population co-exist in M32, and that the balance between these two populations change between the nucleus and outside one effective radius (1r(eff)) in the sense that the contribution from the intermediate population is larger at the nuclear region. We retrieve a smaller signal of a young population at all radii whose origin is unclear and may be a contamination from horizontal branch stars, such as the ones identified by Brown et al. in the nuclear region. We compare our metallicity distribution function for a region 1 to 2 arcmin from the centre to the one obtained with photometric data by Grillmair et al. Both distributions are broad, but our spectroscopically derived distribution has a significant component with [Z/Z(circle dot)] <= -1, which is not found by Grillmair et al.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Global properties of `ordinary` early-type galaxies: photometry and spectroscopy of stars and globular clusters in NGC 4494

We present a comprehensive analysis of the spatial, kinematic and chemical properties of stars and globular clusters (GCs) in the `ordinary` elliptical galaxy NGC 4494 using data from the Keck and Subaru telescopes. We derive galaxy surface brightness and colour profiles out to large galactocentric radii. We compare the latter to metallicities derived using the near-infrared Calcium Triplet. We obtain stellar kinematics out to similar to 3.5 effective radii. The latter appear flattened or elongated beyond similar to 1.8 effective radii in contrast to the relatively round photometric isophotes. In fact, NGC 4494 may be a flattened galaxy, possibly even an S0, seen at an inclination of similar to 45 degrees. We publish a catalogue of 431 GC candidates brighter than i(0) = 24 based on the photometry, of which 109 are confirmed spectroscopically and 54 have measured spectroscopic metallicities. We also report the discovery of three spectroscopically confirmed ultra-compact dwarfs around NGC 4494 with measured metallicities of -0.4 less than or similar to [Fe/H] less than or similar to -0.3. Based on their properties, we conclude that they are simply bright GCs. The metal-poor GCs are found to be rotating with similar amplitude as the galaxy stars, while the metal-rich GCs show marginal rotation. We supplement our analysis with available literature data and results. Using model predictions of galaxy formation, and a suite of merger simulations, we find that many of the observational properties of NGC 4494 may be explained by formation in a relatively recent gas-rich major merger. Complete studies of individual galaxies incorporating a range of observational avenues and methods such as the one presented here will be an invaluable tool for constraining the fine details of galaxy formation models, especially at large galactocentric radii.

Metallicity gradients at large galactocentric radii using the near-infrared Calcium triplet

We describe a new spectroscopic technique for measuring radial metallicity gradients out to large galactocentric radii. We use the DEep Imaging Multi-Object Spectrograph (DEIMOS) on the Keck telescope and the galaxy spectrum extraction technique of Proctor et al. We also make use of the metallicity sensitive near-infrared Calcium ii triplet (CaT) features together with single stellar population models to obtain metallicities. Our technique is applied as a pilot study to a sample of three relatively nearby (< 30 Mpc) intermediate-mass to massive early-type galaxies. Results are compared with previous literature inner region values and generally show good agreement. We also include a comparison with profiles from dissipational disc-disc major merger simulations. Based on our new extended metallicity gradients combined with other observational evidence and theoretical predictions, we discuss possible formation scenarios for the galaxies in our sample. The limitations of our new technique are also discussed.

Probing the 2D kinematic structure of early-type galaxies out to three effective radii

We detail an innovative new technique for measuring the two-dimensional (2D) velocity moments (rotation velocity, velocity dispersion and Gauss-Hermite coefficients h(3) and h(4)) of the stellar populations of galaxy haloes using spectra from Keck DEIMOS (Deep Imaging Multi-Object Spectrograph) multi-object spectroscopic observations. The data are used to reconstruct 2D rotation velocity maps. Here we present data for five nearby early-type galaxies to similar to three effective radii. We provide significant insights into the global kinematic structure of these galaxies, and challenge the accepted morphological classification in several cases. We show that between one and three effective radii the velocity dispersion declines very slowly, if at all, in all five galaxies. For the two galaxies with velocity dispersion profiles available from planetary nebulae data we find very good agreement with our stellar profiles. We find a variety of rotation profiles beyond one effective radius, i.e. rotation speed remaining constant, decreasing and increasing with radius. These results are of particular importance to studies which attempt to classify galaxies by their kinematic structure within one effective radius, such as the recent definition of fast- and slow-rotator classes by the Spectrographic Areal Unit for Research on Optical Nebulae project. Our data suggest that the rotator class may change when larger galactocentric radii are probed. This has important implications for dynamical modelling of early-type galaxies. The data from this study are available on-line.

Thermal photon production in Au plus Au collisions: Viscous corrections in two different hydrodynamic formalisms

We calculate the spectra of produced thermal photons in Au + Au collisions taking into account the nonequilibrium contribution to photon production due to finite shear viscosity. The evolution of the fireball is modeled by second-order as well as by divergence-type 2 + 1 dissipative hydrodynamics, both with an ideal equation of state and with one based on Lattice QCD that includes an analytical crossover. The spectrum calculated in the divergence-type theory is considerably enhanced with respect to the one calculated in the second-order theory, the difference being entirely due to differences in the viscous corrections to photon production. Our results show that the differences in hydrodynamic formalisms are an important source of uncertainty in the extraction of the value of eta/s from measured photon spectra. The uncertainty in the value of eta/s associated with different hydrodynamic models used to compute thermal photon spectra is larger than the one occurring in matching hadron elliptic flow to RHIC data. (C) 2010 Elsevier B.V. All rights reserved.

Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

Soliton solutions for quasilinear Schrodinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.