Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chao

High-speed mobile robot control in off-road conditions: a multi-model based adaptive approach

International audienceThis paper is focused on the design of a control strategy for the path tracking of off-road mobile robots acting at high speed. In order to achieve high accuracy in such a context, uncertain and fast dynamics have to be explicitly taken into account. Since these phenomena (grip conditions, delays due to inertial and low-level control properties) are hardly measurable directly, the proposed approach relies on predictive and observer-based adaptive control techniques. In particular, the adaptive part is based on an observer loop, taking advantage of both kinematic and dynamic vehicle models. This multi-model based adaptive approach permits to adapt on-line the grip conditions (represented by cornering stiffnesses), enabling highly reactive sideslip angles observation and then accurate path tracking. The relevance of this approach is investigated through full scale experiments

Off-road mobile robot control: An adaptive approach for accuracy and integrity

International audienceThis paper proposes an algorithm dedicated to the control of off-road mobile robots at high speed. Based on adaptive and predictive principles, it first proposes a control law to preserve a high level of accuracy in the path tracking problem. Next, the dynamic model used for grip condition estimation is considered to address also robot integrity preservation thanks to the velocity limitation

Comparison of bar strengths in active and non-active galaxies

Bar strengths are compared between active and non-active galaxies for a sample of 43 barred galaxies. The relative bar torques are determined using a new technique (Buta and Block 2001), where maximum tangential forces are calculated in the bar region, normalized to the axisymmetric radial force field. We use JHK images of the 2 Micron All Sky Survey. We show a first clear empirical indication that the ellipticies of bars are correlated with the non-axisymmetric forces in the bar regions. We found that nuclear activity appears preferentially in those early type galaxies in which the maximum bar torques are weak and appear at quite large distances from the galactic center. Most suprisingly the galaxies with the strongest bars are non-active. Our results imply that the bulges may be important for the onset of nuclear activity, but that the correlation between the nuclear activity and the early type galaxies is not straightforward.Comment: MNRAS macro in tex format, 9 pages, 10 figure

Very Massive Star Models: I. Impact of Rotation and Metallicity and Comparisons with Observations

In addition to being spectacular objects, Very Massive Stars (VMS) are suspected to have a tremendous impact on their environment and on the whole cosmic evolution. The nucleosynthesis both during their advanced stages and their final explosion may contribute greatly to the overall enrichment of the Universe. Their resulting supernovae are candidates for the most superluminous events and their extreme conditions also lead to very important radiative and mechanical feedback effects, from local to cosmic scale. We explore the impact of rotation and metallicity on the evolution of very massive stars across cosmic times. With the recent implementation of an equation of state in the GENEC stellar evolution code, appropriate for describing the conditions in the central regions of very massive stars in the advanced phases, we present new results on VMS evolution from Population III to solar metallicity. Low metallicity VMS models are highly sensitive to rotation, while the evolution of higher metallicity models is dominated by mass loss effects. The mass loss affects strongly their surface velocity evolution, breaking quickly at high metallicity while reaching the critical velocity for low metallicity models. The comparison to observed VMS in the LMC shows that the mass loss prescriptions used for these models are compatible with observed mass loss rates. In our framework for modelling rotation, our models of VMS need a high initial velocity to reproduce the observed surface velocities. The surface enrichment of these VMS is difficult to explain with only one initial composition, and could suggest multiple populations in the R136 cluster. At a metallicity typical of R136, only our non- or slowly rotating VMS models may produce Pair Instability supernovae. The most massive black holes that can be formed are less massive than about 60 M$_\odot$.Comment: 13 pages, 11 figure

A Connection between Star Formation in Nuclear Rings and their Host Galaxies

We present results from a photometric H-alpha survey of 22 nuclear rings, aiming to provide insight into their star formation properties, including age distribution, dynamical timescales, star formation rates, and galactic bar influence. We find a clear relationship between the position angles and ellipticities of the rings and those of their host galaxies, which indicates the rings are in the same plane as the disk and circular. We use population synthesis models to estimate ages of each H-alpha emitting HII region, which range from 1 Myr to 10 Myrs throughout the rings. We find that approximately half of the rings contain azimuthal age gradients that encompass at least 25% of the ring, although there is no apparent relationship between the presence or absence of age gradients and the morphology of the rings or their host galaxies. NGC1343, NGC1530, and NGC4321 show clear bipolar age gradients, where the youngest HII regions are located near the two contact points of the bar and ring. We speculate in these cases that the gradients are related to an increased mass inflow rate and/or an overall higher gas density in the ring, which would allow for massive star formation to occur on short timescales, after which the galactic rotation would transport the HII regions around the ring as they age. Two-thirds of the barred galaxies show correlation between the locations of the youngest HII region(s) in the ring and the location of the contact points, which is consistent with predictions from numerical modeling.Comment: 23 pages, 10 figures (7 color), 23 tables, accepted for publication in ApJS (Feb 08); NASA-GSFC, IAC, University of Maryland, STSc

Extension of formal conjugations between diffeomorphisms

We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of ${\mathbb C}^{n}$. More precisely, we are interested on the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms $\phi, \eta$ such that every formal conjugation $\hat{\sigma}$ (i.e. $\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi$) does not extend to the fixed points set $Fix (\phi)$ of $\phi$, meaning that it is not transversally formal (or semi-convergent) along $Fix (\phi)$. We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page