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

Influences on the formability and mechanical properties of 7000-aluminum alloys in hot and warm forming

Aluminum alloys of the 7000 series possess high lightweight potential due to their high specific tensile strength combined with a good ultimate elongation. For this reason, hot-formed boron-manganese-steel parts can be substituted by these alloys. Therefore, the application of these aluminum alloys for structural car body components is desired to decrease the weight of the body in white and consequently CO2 emissions during vehicle operation. These days, the limited formability at room temperature limits an application in the automobile industry. By increasing the deformation temperature, formability can be improved. In this study, two different approaches to increase the formability of these alloys by means of higher temperatures were investigated. The first approach is a warm forming route to form sheets in T6 temper state with high tensile strength at temperatures between 150 °C and 300 °C. The second approach is a hot forming route. Here, the material is annealed at solution heat treatment temperature and formed directly after the annealing step. Additionally, a quench step is included in the forming stage. After the forming and quenching step, the sheets have to be artificially aged to achieve the high specific tensile strength. In this study, several parameters in the presented process routes, which influence the formability and the mechanical properties, have been investigated for the aluminum alloys EN AW7022 and EN AW7075. © Published under licence by IOP Publishing Ltd

Metabolic and haemodynamic effects of oral glucose loading in young healthy men carrying the 825T-allele of the G protein β3 subunit

BACKGROUND: A C825T polymorphism was recently identified in the gene encoding the β3 subunit of heterotrimeric G-proteins (GNB3). The T-allele is significantly associated with essential hypertension and obesity. In order to further explore a possible pathogenetic link between the T-allele and impaired glucose tolerance we studied metabolic and haemodynamic responses to oral glucose loading in young, healthy subjects with and without the 825T-allele. METHODS: Twelve subjects with and 10 without the 825T-allele were investigated at rest and following glucose ingestion (75 g). Blood glucose, serum insulin and haemodynamics were determined prior to and over 2 hours following glucose ingestion. We non-invasively measured stroke volume (SV, by impedance-cardiography), blood pressure (BP), heart rate (HR), and systolic-time-intervals. Cardiac output (CO) was calculated from HR and SV. Total peripheral resistance was calculated from CO and BP. Metabolic and haemodynamic changes were quantified by maximal responses and by calculation of areas under the concentration time profile (AUC). Significances of differences between subjects with and without the T-allele were determined by unpaired two-tailed t-tests. A p < 0.05 was considered statistically significant. RESULTS: Metabolic and haemodynamic parameters at baseline were very similar between both groups. The presence of the T-allele did not alter the response of any metabolic or haemodynamic parameter to glucose loading. CONCLUSIONS: In conclusion, this study does not support the hypothesis that the C825T polymorphism may serve as a genetic marker of early impaired glucose tolerance

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

Mechanical properties and formability of en AW-7075 in cold forming processes

Due to a low density and high tensile strength, the aluminum alloy EN AW 7075 T6 offers a high lightweight potential for structural components. Since its formability is limited at room temperature in the T6 temper state, the potential of this alloy for automotive bodies is only utilizable by adapted deep drawing processes. In recent years, process chains suited for warm and hot forming have been researched and developed. However, warm and hot forming solutions require additional process steps and a complex tooling system in comparison to cold forming processes. Alternatively, the forming of such blanks at room temperature in the W temper state is favorable since conventional tools can be used. The W temper state is a heat treatment condition achieved after solution heat treatment and subsequent quenching, which is characterized by an increased ductility. However, this condition is unstable, due to the onset of natural ageing. With increasing time after the quenching step, the strength of the material increases, which leads to a reduction of formability. Another phenomenon that occurs after quenching is the Portevin Le-Chatelier effect. This effect causes the formation of flow lines during cold forming and results in a decrease of ductility. Hence, the objective of the investigations was to determine the formability of EN AW 7075 as a function of the natural ageing time after solution heat treatment and quenching. Therefore, tensile tests of various aged samples were carried out. The results show a relation of the formability to the natural ageing time and a dependency on the quenching rate. Furthermore, a heat treatment strategy for EN AW-7075 was developed, that considers manufacturing processes like the cathodic dip coating. The influence of the quenching rate, ageing time and temperature as well as the influence of temperature of the paint baking process after the cathodic dip coating were considered. Therefore, a design of experiments and tensile tests were carried out. Thus, the deep drawing of EN AW-7075 at room temperature is particularly promoted. © 2020 Published under licence by IOP Publishing Ltd

The cool atmospheres of the binary brown dwarf eps Indi B

We have imaged $\epsilon$ Indi B, the closest brown dwarf binary known, with VISIR at the VLT in three narrow-band mid-infrared bandpasses located around 8.6$\mu$m, 10.5$\mu$m and 11.3$\mu$m. We are able to spatially resolve both components, and determine accurate mid-infrared photometry for both components independently. In particular, our VISIR observations probe the NH$_3$ feature in the atmospheres of the cooler and warmer brown dwarfs. For the first time, we can disentangle the contributions of the two components, and find that % our photometry of $\epsilon$ IndiBb is in good agreement with recent ``cloud-free'' atmosphere models having an effective temperature of $T_\mathrm{eff}=800$ K. With an assumed age of 1 Gyr for the $\epsilon$ Indi system, component Ba agrees more with $T_\mathrm{eff} \approx 1100$ K rather than with $T_\mathrm{eff}=1200$ K, as suggested by SPITZER spectroscopic observations of the combined $\epsilon$ Indi B system (Roellig et al., 2004). Even higher effective temperatures appear inconsistent with our absolute photometry, as they would imply an unphysical small size of the brown dwarf $\epsilon$ IndiBa.Comment: 4 pages, 2 figure

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