Comparing the behavior of orbits in different 3D dynamical models for elliptical galaxies

We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion together with extended chaotic regions. A detailed investigation of the properties of motion is made for the 2D and 3D Hamiltonian systems, using a number of different dynamical parameters, such as the Poincare surface of section, the maximal Lyapunov Characteristic Exponent, the S(c) spectrum, the S(w) spectrum and the P(f) indicator. The numerical calculations suggest that the properties of motion in both potentials are very similar. Our results show that one may use different kinds of gravitational potentials in order to describe the motion in triaxial galaxies while obtaining quantitatively similar results.Comment: Published in Research in Astronomy and Astrophysics journa

Design of a Magnetic Vibration Absorber with Tunable Stiffnesses

International audienceThe design and characterisation of a magnetic vibration absorber (MVA), completely relying on magnetic forces, is addressed. A distinctive feature of the absorber is the ability of tuning the linear stiffness together with the nonlinear cubic and quintic stiffnesses by means of repulsive magnets located in the axis of the main vibrating magnetic mass, together with a set of corrective magnets located off the main axis. The tuning methodology is passive and relies only on three geometrical parameters. Consequently the MVA can be adjusted to design either a nonlinear tuned vibration absorber (NLTVA), a nonlinear energy sink (NES), or a bi-stable absorber with negative linear stiffness. The expressions of the stiffnesses are given from a multipole expansion of the magnetic fields of repulsive and corrective magnets. A complete static and dynamic characterisation is performed, showing the robustness of the modelling together with the ability of the MVA to work properly in different vibratory regimes, thus making it a suitable candidate for passive vibration mitigation in a wide variety of contexts

DYNAMIC BEHAVIOR OF A TUNABLE MAGNETIC VIBRATION ABSORBER

International audienceA magnetic vibration absorber (MVA), completely relying on magnetic forces, is used to reduce the displacement of a vibrating structure. The distinctive feature of this absorber is the ability of tuning its linear stiffness together with its nonlinear cubic and quintic stiffnesses. Repulsive and corrective magnets are used to finely tune the values of these stiffness coefficients. A modelisation, relying on a multipolar expansion of the magnetic fields of each magnets, is used to predict the values of the stiffnesses from the geometry. Using only three geometrical parameters the MVA can be passively designed either as a nonlinear tuned vibration absorber (NLTVA), a nonlinear energy sink (NES), or a bi-stable absorber with negative linear stiffness

Intrinsic Axis Ratio Distribution of Early-type Galaxies From Sloan Digital Sky Survey

Using Sloan Digital Sky Survey Data Release 5, we have investigated the intrinsic axis ratio distribution (ARD) for early-type galaxies. We have constructed a volume-limited sample of 3,922 visually-inspected early-type galaxies at $0.05 \leq z \leq 0.06$ carefully considering sampling biases caused by the galaxy isophotal size and luminosity. We attempt to de-project the observed ARD into three-dimensional types (oblate, prolate, and triaxial), which are classified in terms of triaxiality. We confirm that no linear combination of $randomly$-distributed axis ratios of the three types can reproduce the observed ARD. However, using Gaussian intrinsic distributions, we have found reasonable fits to the data with preferred mean axis ratios for oblate, prolate, and triaxial (triaxials in two axis ratios), $\mu_o=0.44, \mu_p=0.72, \mu_{t,\beta}=0.92, \mu_{t,\gamma}=0.78$ where the fractions of oblate, prolate and triaxial types are \textrm{O:P:T}=0.29^{\pm0.09}:0.26^{\pm0.11}:0.45^{\pm0.13}$. We have also found that the luminous sample ($-23.3 < M_r \leq -21.2$) tends to have more triaxials than the less luminous ($-21.2 < M_r <-19.3$) sample does. Oblate is relatively more abundant among the less luminous galaxies. Interestingly, the preferences of axis ratios for triaxial types in the two luminosity classes are remarkably similar. We have not found any significant influence of the local galaxy number density on ARD. We show that the results can be seriously affected by the details in the data selection and type classification scheme. Caveats and implications on galaxy formation are discussed.Comment: 9 pages, 11 figures, Accepted for publication in Ap

The Dependence of Galaxy Shape on Luminosity and Surface Brightness Profile

For a sample of 96,951 galaxies from the Sloan Digital Sky Survey Data Release 3, we study the distribution of apparent axis ratios as a function of r-band absolute magnitude and surface brightness profile type. We use the parameter fracDeV to quantify the profile type (fracDeV = 1 for a de Vaucouleurs profile; fracDeV = 0 for an exponential profile). When the apparent axis ratio q_{am} is estimated from the moments of the light distribution, the roundest galaxies are very bright (M_r \sim -23) de Vaucouleurs galaxies and the flattest are modestly bright (M_r \sim -18) exponential galaxies. When the apparent axis ratio q_{25} is estimated from the axis ratio of the 25 mag/arcsec^2 isophote, we find that de Vaucouleurs galaxies are flatter than exponential galaxies of the same absolute magnitude. For a given surface brightness profile type, very bright galaxies are rounder, on average, than fainter galaxies. We deconvolve the distributions of apparent axis ratios to find the distribution of the intrinsic short-to-long axis ratio gamma, assuming constant triaxiality T. For all profile types and luminosities, the distribution of apparent axis ratios is inconsistent with a population of oblate spheroids, but is usually consistent with a population of prolate spheroids. Bright galaxies with a de Vaucouleurs profile (M_r < -21.84, fracDeV > 0.9) have a distribution of q_{am} that is consistent with triaxiality in the range 0.4 < T < 0.8, with mean intrinsic axis ratio 0.66 < gamma < 0.69. The fainter de Vaucouleurs galaxies are best fit with prolate spheroids (T = 1) with mean axis ratio gamma = 0.51.Comment: 32 pages, 12 figures, to appear in Ap

Consolidation in the air transport sector and antitrust enforcement in Europe

The paper aims at analysing the role for Antitrust intervention in the light of the consolidation trend of the airline industry in Europe. The almost full liberalization in the aviation sector (at least for intra-community routes) leaded to a situation where, at the same time, (i) new players have been entering the market with an increase in competition (actual and potential) on EU routes, and (ii) deep forms of co-operation (alliances and code sharing) and integration (mergers) have been exploited to better perform at national and international level. The paper highlights the economic analysis behind Antitrust assessment in the evaluation of mergers and cooperation agreements in the air transport sector. Consolidated standards for market definition, competitive assessment and feasible remedies are presented and discussed in the light of the relevant EU case law. Moreover, according to the radical changes occurring in the industry – i.e. the emergence of peculiar market forces such as low cost carriers and their interaction with traditional full service carriers – some preliminary considerations are introduced on the likely need for adjusting the assessment criteria for an effective Antitrust intervention

A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver

Efficient hyperbolic-parabolic models on multi-dimensional unbounded domains using an extended DG approach

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and non-linear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi-infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single-domain discontinuous finite element techniques.Comment: 28 pages, 13 figure