The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.Comment: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chao

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

TRAITE A LA MACHINE DES BREBIS PRÉALPES DU SUD. IMPORTANCE DES DIFFÉRENTES OPÉRATIONS DE LA TRAITE

International audienc

A unified framework for the orbital structure of bars and triaxial ellipsoids

We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (~4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (~7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediate axis owing to the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (~2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform some x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies

Cross-cultural adaptation, reliability, internal consistency and validation of the Trinity Amputation and Prosthetic Experience Scales-Revised (TAPES-R) for French speaking patients with lower limb amputation

AimThe aim of this study was the French cross-cultural adaptation and validation of The Trinity Amputation and Prosthetic Experience Scales-Revised (TAPES-R-F), in a lower limb amputation population. This self-reported multidimensional amputee-specific questionnaire [1] evaluates with 33 items psychosocial adjustment (3 subscales), activity restriction (1 subscale) and satisfaction with prosthesis (2 subscales).Patients and methodsOne hundred and twenty-nine patients with a mean age of 62 years and with lower limb amputations for at least 1 year were recruited in 5 clinical centers. Translation and cross-cultural adaptation were made according to international guidelines. Internal consistency of each subscale was measured with Cronbach's alpha. Test-retest reliability was assessed by intraclass correlation in a sub- group of 24 subjects who completed the TAPES-R twice with an interval of 7 days. Construct validity was estimated through correlations with 2 main components of SF-36 (MCS, PCS). Correlations were also calculated with 3 scales of the Brief Pain Inventory (BPI).ResultsCronbach's alpha was high, ranging from 0.85 to 0.95. Reliability was acceptable to high (ICC=0.72 to 0.91) for all subscales with the exception of the Social adjustment (ICC=0.67) and Adjustment to limitation (ICC=0.42) subscales. The 2 component of SF-36 was significantly correlated with all subscales (PCS: r=0.24 to 0.66); MCS: r=0.30 to 0.58), except with aesthetic satisfaction and adjustment to limitation. Regarding the BPI, significant correlations were found for all subscales (r=–0.20 to –0.68) with the exception of adjustment to limitation. Ceiling or floor effects (>15%) were found for all but Activity Restriction and Functional Satisfaction Scales.DiscussionThe TAPES-R-F has acceptable psychometric properties for most of its subscales. Our results may suggest that the French version is more useful in a population research perspective than in an individual perspective. Other studies are necessary to clarify the role and the psychometric properties of this measurement

Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298

How can existing ground-based profiling instruments improve European weather forecasts?

Observations of profiles of winds, aerosol, clouds, winds, temperature and humidity in the lowest few km of the atmosphere from networks of ceilometers, Doppler wind lidars and microwave radiometers are starting to flow in real time to forecasting centers in Europe. To realise the promise of improved predictions of hazardous weather such as flash floods, wind storms, fog and poor air quality from high-resolution mesoscale models, the forecast models must be initialized with an accurate representation of the current state of the atmosphere, but the lowest few km are hardly accessible by satellite, especially in dynamically-active conditions. We report on recent European developments in the exploitation of existing ground-based profiling instruments so that they are networked and able to send data in real-time to forecast centers. The three classes of instruments are: (i) Automatic lidars and ceilometers providing backscatter profiles of clouds, aerosols, dust, fog and volcanic ash, the last two being especially important for air traffic control; (ii) Doppler wind lidars deriving profiles of wind, turbulence, wind shear, wind-gusts and low-level jets; and (iii) Microwave radiometers estimating profiles of temperature and humidity in nearly all weather conditions. Twenty-two European countries and fifteen European National Weather Services are collaborating in the project, that involves the implementation of common operating procedures, instrument calibrations, data formats and retrieval algorithms. Currently, data from 220 ceilometers in 17 countries are being distributed in near real-time to national weather forecast centers; this should soon rise to many hundreds. The wind lidars should start delivering real time data in late 2018, and the plan is to incorporate the microwave radiometers in 2019. Initial data assimilation tests indicate a positive impact of the new data

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig