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

Properties of active galactic star-forming regions probed by imaging spectroscopy with the Fourier transform spectrometer (FTS) onboard AKARI

We investigate the structure of the interstellar medium (ISM) and identify the location of possible embedded excitation sources from far-infrared (FIR) line and mid-infrared continuum emission maps. We carried out imaging spectroscopic observations of four giant Galactic star-forming regions with the Fourier Transform Spectrometer (FTS) onboard AKARI. We obtained [OIII] 88 micron and [CII] 158 micron line intensity maps of all the regions: G3.270-0.101, G333.6-0.2, NGC3603, and M17. For G3.270-0.101, we obtained high-spatial-resolution [OIII] 88 micron line-emission maps and a FIR continuum map for the first time, which imply that [OIII] 88 micron emission identifies the excitation sources more clearly than the radio continuum emission. In G333.6-0.2, we found a local [OIII] 88 micron emission peak, which is indicative of an excitation source. This is supported by the 18 micron continuum emission, which is considered to trace the hot dust distribution. For all regions, the [CII] 158 micron emission is distributed widely as suggested by previous observations of star-forming regions. We conclude that [OIII] 88 micron emission traces the excitation sources more accurately than the radio continuum emission, especially where there is a high density and/or column density gradient. The FIR spectroscopy provides a promising means of understanding the nature of star-forming regions.Comment: 14 pages with 15 figures, accepted for publication in Astronomy and Astrophysic

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

Coherent strong-field control of multiple states by a single chirped femtosecond laser pulse

We present a joint experimental and theoretical study on strong-field photo-ionization of sodium atoms using chirped femtosecond laser pulses. By tuning the chirp parameter, selectivity among the population in the highly excited states 5p, 6p, 7p and 5f, 6f is achieved. Different excitation pathways enabling control are identified by simultaneous ionization and measurement of photoelectron angular distributions employing the velocity map imaging technique. Free electron wave packets at an energy of around 1 eV are observed. These photoelectrons originate from two channels. The predominant 2+1+1 Resonance Enhanced Multi-Photon Ionization (REMPI) proceeds via the strongly driven two-photon transition $4s\leftarrow\leftarrow3s$, and subsequent ionization from the states 5p, 6p and 7p whereas the second pathway involves 3+1 REMPI via the states 5f and 6f. In addition, electron wave packets from two-photon ionization of the non-resonant transiently populated state 3p are observed close to the ionization threshold. A mainly qualitative five-state model for the predominant excitation channel is studied theoretically to provide insights into the physical mechanisms at play. Our analysis shows that by tuning the chirp parameter the dynamics is effectively controlled by dynamic Stark-shifts and level crossings. In particular, we show that under the experimental conditions the passage through an uncommon three-state "bow-tie" level crossing allows the preparation of coherent superposition states

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

Approximation of excitonic absorption in disordered systems using a compositional component weighted CPA

Employing a recently developed technique of component weighted two particle Green's functions in the CPA of a binary substitutional alloy $A_cB_{1-c}$ we extend the existing theory of excitons in such media using a contact potential model for the interaction between electrons and holes to an approximation which interpolates correctly between the limits of weak and strong disorder. With our approach we are also able to treat the case where the contact interaction between carriers varies between sites of different types, thus introducing further disorder into the system. Based on this approach we study numerically how the formation of exciton bound states changes as the strengths of the contact potentials associated with either of the two site types are varied through a large range of parameter values.Comment: 27 pages RevTeX (preprint format), 13 Postscript figure file

Photon Dominated Regions in NGC 3603

Aims: We aim at deriving the excitation conditions of the interstellar gas as well as the local FUV intensities in the molecular cloud surrounding NGC 3603 to get a coherent picture of how the gas is energized by the central stars. Methods: The NANTEN2-4m submillimeter antenna is used to map the [CI] 1-0, 2-1 and CO 4-3, 7-6 lines in a 2' x 2' region around the young OB cluster NGC 3603 YC. These data are combined with C18O 2-1 data, HIRES-processed IRAS 60 and 100 micron maps of the FIR continuum, and Spitzer/IRAC maps. Results: The NANTEN2 observations show the presence of two molecular clumps located south-east and south-west of the cluster and confirm the overall structure already found by previous CS and C18O observations. We find a slight position offset of the peak intensity of CO and [CI], and the atomic carbon appears to be further extended compared to the molecular material. We used the HIRES far-infrared dust data to derive a map of the FUV field heating the dust. We constrain the FUV field to values of \chi = 3 - 6 \times 10^3 in units of the Draine field across the clouds. Approximately 0.2 to 0.3 % of the total FUV energy is re-emitted in the [CII] 158 {\mu}m cooling line observed by ISO. Applying LTE and escape probability calculations, we derive temperatures (TMM1 = 43 K, TMM2 = 47 K), column densities (N(MM1) = 0.9 \times 10^22 cm^-2, N(MM2) = 2.5 \times 10^22 cm^-2) and densities (n(MM1) = 3 \times 10^3 cm^-3, n(MM2) = 10^3 -10^4 cm^-3) for the two observed molecular clumps MM1 and MM2. Conclusions: The cluster is strongly interacting with the ambient molecular cloud, governing its structure and physical conditions. A stability analysis shows the existence of gravitationally collapsing gas clumps which should lead to star formation. Embedded IR sources have already been observed in the outskirts of the molecular cloud and seem to support our conclusions.Comment: 13 pages, 10 figures, accepted for publication by A&

Molecular Outflows and a Mid-Infrared Census of the Massive Star Formation Region Associated with IRAS 18507+0121

We have observed the central region of the infrared-dark cloud filament associated with IRAS 18507+0121 at millimeter wavelengths in CO(J = 1-0), ^(13)CO(J = 1-0), and C^(18)O(J = 1-0) line emission and with Spitzer at mid-infrared wavelengths. Five massive outflows from two cloud cores were discovered. Three outflows are centered on or near an ultracompact (UC) H II region (G34.4+0.23), while the remaining two outflows originate from the millimeter core G34.4+0.23 MM. Modeling of the spectral energy distributions of the mid-infrared sources identified 31 young stellar objects in the filament with a combined stellar mass of ~127 ± 27 M_☉. An additional 22 sources were identified as probable cluster members based on the presence of strong 24 μm emission. The total star formation efficiency in the G34.4 cloud filament is estimated to be ~7%, while the massive and intermediate-mass star formation efficiency in the entire cloud filament is estimated to be roughly 2%. A comparison of the gravitational binding energy with the outflow kinetic energy suggests that the compact core containing G34.4+0.23 MM is being destroyed by its molecular outflows, whereas the outflows associated with the more massive core surrounding the G34.4 UC H II region are not likely to totally disrupt the cloud. In addition, a qualitative evaluation of the region appears to suggest that stars in this region may have formed in two stages: first lower mass stars formed and then, a few Myr later, the more massive stars began to form