Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

The dimension of C1C^1 splines of arbitrary degree on a tetrahedral partition

We consider the linear space of piecewise polynomials in three variables which are globally smooth, i.e., trivariate $C^1$ splines. The splines are defined on a uniform tetrahedral partition $\Delta$, which is a natural generalization of the four-directional mesh. By using Bernstein-B{\´e}zier techniques, we establish formulae for the dimension of the $C^1$ splines of arbitrary degree

Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume delta-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.Comment: 17 pages, 15 figures, full paper following arXiv:1205.5354 and Phys. Rev. C 86 (2012) 021301(R

Microstructural characterization and simulation of damage for geared sheet components

The evolution of damage in geared components manufactured from steel sheets was investigated, to analyse the influence of damage caused by the sheet-bulk-metal forming. Due to the inhomogeneous and multi-axial deformation in the investigated parts, different aspects such as the location-dependent shape and size of voids are analysed by means of various microscopic methods. In particular, a method to characterize the state of damage evolution, i. e. void nucleation, growth and coalescence using scanning electron microscopy (SEM) is applied. The investigations reveal a strong dependence of the void area fraction, shape of voids and thus damage evolution on the loading mode. The microstructural analysis is complemented with FEM simulations using material models which consider the characteristics of the void evolution. © Published under licence by IOP Publishing Ltd

Star Formation in the Starburst Cluster in NGC 3603

We have used new, deep, visible and near infrared observations of the compact starburst cluster in the giant HII region NGC 3603 and its surroundings with the WFC3 on HST and HAWK-I on the VLT to study in detail the physical properties of its intermediate mass (~ 1 - 3 M_sun) stellar population. We show that after correction for differential extinction and actively accreting stars, and the study of field star contamination, strong evidence remains for a continuous spread in the ages of pre-main sequence stars in the range ~ 2 to ~ 30 Myr within the temporal resolution available. Existing differences among presently available theoretical models account for the largest possible variation in shape of the measured age histograms within these limits. We also find that this isochronal age spread in the near infrared and visible Colour-Magnitude Diagrams cannot be reproduced by any other presently known source of astrophysical or instrumental scatter that could mimic the luminosity spread seen in our observations except, possibly, episodic accretion. The measured age spread and the stellar spatial distribution in the cluster are consistent with the hypothesis that star formation started at least 20-30 Myrs ago progressing slowly but continuously up to at least a few million years ago. All the stars in the considered mass range are distributed in a flattened oblate spheroidal pattern with the major axis oriented in an approximate South-East - North-West direction, and with the length of the equatorial axis decreasing with increasing age. This asymmetry is most likely due to the fact that star formation occurred along a filament of gas and dust in the natal molecular cloud oriented locally in this direction.Comment: 21 pages, 19 figures, accepted for publication in Astrophysics & Space Scienc

The photometric evolution of dissolving star clusters I: First predictions

We calculated the broad-band photometric evolution of unresolved star clusters, including the preferential loss of low-mass stars due to mass segregation. The stellar mass function of a cluster evolves due to three effects: (a) the evolution of massive stars; (b) early tidal effects reduce the mass function independently of the stellar mass; (c) after mass segregation has completed, tidal effects preferentially remove the lowest-mass stars from the cluster. Results: (1) During the first ~40% of the lifetime of a cluster the cluster simply gets fainter due to the loss of stars by tidal effects. (2) Between ~40 and ~80% of its lifetime the cluster gets bluer due to the loss of low-mass stars. This will result in an underestimate of the age of clusters if standard cluster evolution models are used (0.15 -- 0.5 dex). (3) After ~80% of the total lifetime of a cluster it will rapidly get redder. This is because stars at the low-mass end of the main sequence, which are preferentially lost, are bluer than the AGB stars that dominate the light at long wavelengths, resulting in an age overestimate. (4) Clusters with mass segregation and the preferential loss of low-mass stars evolve along almost the same tracks in colour-colour diagrams as clusters without mass segregation. Therefore it will be difficult to distinguish this effect from that due to the cluster age for unresolved clusters, unless the total lifetime of the clusters can be estimated. (5) The changes in the colour evolution of unresolved clusters due to the preferential loss of low-mass stars will affect the determination of the SFHs. (6) The preferential loss of low-mass stars might explain the presence of old (~13 Gyr) clusters in NGC 4365 which are photometrically disguised as intermediate-age clusters (2 - 5 Gyr). [Abridged]Comment: accepted for publication in A&

Common Proper Motion Search for Faint Companions Around Early-Type Field Stars - Progress Report

The multiplicity of early-type stars is still not well established. The derived binary fraction is different for individual star forming regions, suggesting a connection with the age and the environment conditions. The few studies that have investigated this connection do not provide conclusive results. To fill in this gap, we started the first detailed adaptive-optic-assisted imaging survey of early-type field stars to derive their multiplicity in a homogeneous way. The sample has been extracted from the Hipparcos Catalog and consists of 341 BA-type stars within ~300 pc from the Sun. We report the current status of the survey and describe a Monte-Carlo simulation that estimates the completeness of our companion detection.Comment: 4 pages, 1 figure, conference proc. Syros 200

Variability in the stellar initial mass function at low and high mass: 3-component IMF models

Three component models of the IMF are made to consider possible origins for the observed relative variations in the numbers of brown dwarfs, solar-to-intermediate mass stars, and high mass stars. Three distinct physical processes are noted. The characteristic mass for most star formation is identified with the thermal Jeans mass in the molecular cloud core, and this presumably leads to the middle mass range by the usual collapse and accretion processes. Pre-stellar condensations (PSCs) observed in mm-wave continuum studies presumably form at this mass. Significantly smaller self-gravitating masses require much larger pressures and may arise following dynamical processes inside these PSCs, including disk formation, tight-cluster ejection, and photoevaporation as studied elsewhere, but also gravitational collapse of shocked gas in colliding PSCs. Significantly larger stellar masses form in relatively low abundance by normal cloud processes, possibly leading to steep IMFs in low-pressure field regions, but this mass range can be significantly extended in high pressure cloud cores by gravitationally-focussed gas accretion onto PSCs and by the coalescence of PSCs. These models suggest that the observed variations in brown dwarf, solar-to-intermediate mass, and high mass populations are the result of dynamical effects that depend on environmental density and velocity dispersion. They accommodate observations ranging from shallow IMFs in cluster cores to Salpeter IMFs in average clusters and whole galaxies to steep and even steeper IMFs in field and remote field regions. They also suggest how the top-heavy IMFs in some starburst clusters may originate and they explain bottom-heavy IMFs in low surface brightness galaxies.Comment: 10 pages, 2 figures, accepted by Monthly Notices of the Royal Astronomical Societ