Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

Star Formation History of Early-Type Galaxies in Low Density Environments V. Blue line-strength indices for the nuclear region

We analyze the star formation properties of a sample of 21 shell galaxies and 30 early-type galaxies members of interacting pairs, located in low density environments (Longhetti et al 1998a, 1998b). The study is based on new models developed to interpret the information coming from `blue' H$\delta$/FeI, H+K(CaII) and \D4000 line-strength indices proposed by Rose (1984; 1985) and Hamilton (1985). We find that the last star forming event that occurred in the nuclear region of shell galaxies is statistically old (from 0.1 up to several Gyr) with respect to the corresponding one in the sub-sample of pair galaxies (<0.1 Gyr or even ongoing star formation). If the stellar activity is somehow related to the formation of shells, as predicted by several dynamical models of galaxy interaction, shells have to be considered long lasting structures. Since pair members show evidence of very recent star formation, we suggest that either large reservoirs of gas have to be present to maintain active star formation, if these galaxies are on periodic orbits, or most of the pair members in the present sample are experiencing unbound encounters.Comment: 12 pages, including 7 figures - Accepted for publication in A&

Catching Spiral - S0 transition in groups. Insights from SPH simulations with chemo-photometric implementation

We are investigating the co-evolution of galaxies within groups combining multi-wavelength photometric and 2D kinematical observations. Here we focus on S0s showing star formation in ring/arm-like structures. We use smooth particle hydrodynamical simulations (SPH) with chemo-photometric implementation which provide dynamical and morphological information together with the spectral energy distribution (SED) at each evolutionary stage. As test cases, we simulate the evolution of two such S0s: NGC 1533 and NGC 3626. The merging of two halos with mass ratio 2:1, initially just composed of dark matter (DM) and gas, well match their observed SEDs, their surface brightness profiles and their overall kinematics. The residual star formation today "rejuvenating" the ring/arm like structures in these S0s is then a mere consequence of a major merger, i.e. this is a phase during the merger episode. The peculiar kinematical features, e.g. gas-stars counter rotation in NGC 3626, depends on the halos initial impact parameters. Furthermore, our simulations allow to follow, in a fully consistent way, the transition of these S0s through the green valley in the NUV-r vs. Mr colour magnitude diagram, which they cross in about 3-5 Gyr, before reaching their current position in the red sequence. We conclude that a viable mechanism driving the evolution of S0s in groups is of gravitational origin.Comment: 30 pages, 6 figures; accepted for publication in Advances in Space Research, Special Issue: Ultraviolet Astrophysic

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Galaxy evolution in groups. USGC U268 and USGC U376 in the Leo cloud

With the aim of investigating galaxy evolution in nearby galaxy groups, we analysed the spectral energy distribution of 24 galaxies, members of two groups in the Leo cloud, USGC U268 and USGC U376. We estimated the ages and stellar masses of the galaxies by fitting their total apparent magnitudes from far-ultraviolet to near-infrared with population synthesis models. The comparison of the results for a subsample of galaxies with smooth particle hydrodynamic (SPH) simulations with chemo-photometric implementation, shows that in most cases the estimated stellar masses obtained with the two different approaches are in good agreement. The kinematical and dynamical analysis indicates that USGC U268 is in a pre-virial collapse phase while USGC U376 is likely in a more evolved phase towards virialization.Comment: 16 pages, 6 figures; accepted for publication in Advances in Space Research, Special Issue: Ultraviolet Astrophysic

Galaxy Evolution in Local Group Analogs. I. A GALEX study of nearby groups

Understanding the astrophysical processes acting within galaxy groups and their effects on the evolution of the galaxy population is one of the crucial topic of modern cosmology, as almost 60% of galaxies in the Local Universe are found in groups. We imaged in the far (FUV 1539 A) and near ultraviolet (NUV 2316 A) with GALEX three nearby groups, namely LGG93, LGG127 and LGG225. We obtained the UV galaxy surface photometry and, for LGG225, the only group covered by the SDSS, the photometry in u, g, r, i, z bands. We discuss galaxy morphologies looking for interaction signatures and we analyze the SED of galaxies to infer their luminosity-weighted ages. The UV and optical photometry was also used to perform a kinematical and dynamical analysis of each group and to evaluate the stellar mass. A few member galaxies in LGG225 show a distorted UV morphology due to ongoing interactions. (FUV-NUV) colors suggest that spirals in LGG93 and LGG225 host stellar populations in their outskirts younger than that of M31 and M33 in the LG or with less extinction. The irregular interacting galaxy NGC3447A has a significantly younger stellar population (few Myr old) than the average of the other irregular galaxies in LGG225 suggesting that the encounter triggered star formation. The early-type members of LGG225, NGC3457 and NGC3522, have masses of the order of a few 10^9 Mo, comparable to the Local Group ellipticals. For the most massive spiral in LGG225, we estimate a stellar mass of ~4x10$^{10}$ Mo, comparable to M33 in the LG. Ages of stellar populations range from a few to ~7 Gyr for the galaxies in LGG225. The kinematical and dynamical analysis indicates that LGG127 and LGG225 are in a pre-virial collapse phase, i.e. still undergoing dynamical relaxation, while LGG93 is likely virialized. (Abridged)Comment: 20 pages, 13 figures, accepted for publication in Astronomy and Astrophysic

Observing System Simulation Experiments for the assessment of temperature sampling strategies in the Mediterranean Sea

International audienceFor the first time in the Mediterranean Sea various temperature sampling strategies are studied and compared to each other by means of the Observing System Simulation Experiment technique. Their usefulness in the framework of the Mediterranean Forecasting System (MFS) is assessed by quantifying their impact in a Mediterranean General Circulation Model in numerical twin experiments via univariate data assimilation of temperature profiles in summer and winter conditions. Data assimilation is performed by means of the optimal interpolation algorithm implemented in the SOFA (System for Ocean Forecasting and Analysis) code. The sampling strategies studied here include various combinations of eXpendable BathyThermograph (XBT) profiles collected along Volunteer Observing Ship (VOS) tracks, Airborne XBTs (AXBTs) and sea surface temperatures. The actual sampling strategy adopted in the MFS Pilot Project during the Targeted Operational Period (TOP, winter-spring 2000) is also studied. The data impact is quantified by the error reduction relative to the free run. The most effective sampling strategies determine 25?40% error reduction, depending on the season, the geographic area and the depth range. A qualitative relationship can be recognized in terms of the spread of information from the data positions, between basin circulation features and spatial patterns of the error reduction fields, as a function of different spatial and seasonal characteristics of the dynamics. The largest error reductions are observed when samplings are characterized by extensive spatial coverages, as in the cases of AXBTs and the combination of XBTs and surface temperatures. The sampling strategy adopted during the TOP is characterized by little impact, as a consequence of a sampling frequency that is too low. Key words. Oceanography: general (marginal and semi-enclosed seas; numerical modelling