Two novel classes of solvable many-body problems of goldfish type with constraints

Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints): i. e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited: i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.Comment: 30 pages, 2 figure

Accurate and automatic NOAA-AVHRR image navigation using a global contour matching approach

The problem of precise and automatic AVHRR image navigation is tractable in theory, but has proved to be somewhat difficult in practice. The authors' work has been motivated by the need for a fully automatic and operational navigation system capable of geo-referencing NOAA-AVHRR images with high accuracy and without operator supervision. The proposed method is based on the simultaneous use of an orbital model and a contour matching approach. This last process, relying on an affine transformation model, is used to correct the errors caused by inaccuracies in orbit modeling, nonzero value for the spacecraft's roll, pitch and yaw, errors due to inaccuracies in the satellite positioning and failures in the satellite internal clock. The automatic global contour matching process is summarized as follows: i) Estimation of the gradient energy map (edges) in the sensed image and detection of the cloudless (reliable) areas in this map. ii) Initialization of the affine model parameters by minimizing the Euclidean distance between the reference and sensed images objects. iii) Simultaneous optimization of all reference image contours on the sensed image by energy minimization in the domain of the global transformation parameters. The process is iterated in a hierarchical way, reducing the parameter searching space at each iteration. The proposed image navigation algorithm has proved to be capable of geo-referencing a satellite image within 1 pixel.Peer ReviewedPostprint (published version

Analytic estimates and topological properties of the weak stability boundary

The weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3 body problem (PCR3BP), 1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; 2) a precise description of the topology of the WSB; 3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB

Understanding the spiral structure of the Milky Way using the local kinematic groups

We study the spiral arm influence on the solar neighbourhood stellar kinematics. As the nature of the Milky Way (MW) spiral arms is not completely determined, we study two models: the Tight-Winding Approximation (TWA) model, which represents a local approximation, and a model with self-consistent material arms named PERLAS. This is a mass distribution with more abrupt gravitational forces. We perform test particle simulations after tuning the two models to the observational range for the MW spiral arm properties. We explore the effects of the arm properties and find that a significant region of the allowed parameter space favours the appearance of kinematic groups. The velocity distribution is mostly sensitive to the relative spiral arm phase and pattern speed. In all cases the arms induce strong kinematic imprints for pattern speeds around 17 km/s/kpc (close to the 4:1 inner resonance) but no substructure is induced close to corotation. The groups change significantly if one moves only ~0.6 kpc in galactocentric radius, but ~2 kpc in azimuth. The appearance time of each group is different, ranging from 0 to more than 1 Gyr. Recent spiral arms can produce strong kinematic structures. The stellar response to the two potential models is significantly different near the Sun, both in density and kinematics. The PERLAS model triggers more substructure for a larger range of pattern speed values. The kinematic groups can be used to reduce the current uncertainty about the MW spiral structure and to test whether this follows the TWA. However, groups such as the observed ones in the solar vicinity can be reproduced by different parameter combinations. Data from velocity distributions at larger distances are needed for a definitive constraint.Comment: 18 pages, 21 figures, 4 tables; acccepted for publication in MNRA

The formation of planetary disks and winds: an ultraviolet view

Planetary systems are angular momentum reservoirs generated during star formation. This accretion process produces very powerful engines able to drive the optical jets and the molecular outflows. A fraction of the engine energy is released into heating thus the temperature of the engine ranges from the 3000K of the inner disk material to the 10MK in the areas where magnetic reconnection occurs. There are important unsolved problems concerning the nature of the engine, its evolution and the impact of the engine in the chemical evolution of the inner disk. Of special relevance is the understanding of the shear layer between the stellar photosphere and the disk; this layer controls a significant fraction of the magnetic field building up and the subsequent dissipative processes ougth to be studied in the UV. This contribution focus on describing the connections between 1 Myr old suns and the Sun and the requirements for new UV instrumentation to address their evolution during this period. Two types of observations are shown to be needed: monitoring programmes and high resolution imaging down to, at least, milliarsecond scales.Comment: Accepted for publication in Astrophysics and Space Science 9 figure