1,077 research outputs found
Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems
We consider an exit-time minimum problem with a running cost, and
unbounded controls. The occurrence of points where 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 -minimum
restraint function provides not only global asymptotic controllability (despite
non-transversality) but also a state-dependent upper bound for the value
function (provided ). 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/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 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
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