Grids of stellar models with rotation II. WR populations and supernovae/GRB progenitors at Z = 0.014

We used a recent grid of stellar models computed with and without rotation to make predictions concerning the WR populations and the frequency of different types of core-collapse SNe. Current rotating models were checked to provide good fits to the following features: solar luminosity and radius at the solar age, main-sequence width, red-giant and red-supergiant (RSG) positions in the HRD, surface abundances, and rotational velocities. Rotating stellar models predict that about half of the observed WR stars and at least half of the type Ibc SNe may be produced through the single-star evolution channel. Rotation increases the duration of the WNL and WNC phases, while reducing those of the WNE and WC phases, as was already shown in previous works. Rotation increases the frequency of type Ic SNe. The upper mass limit for type II-P SNe is \sim 19.0 MSun for the non rotating models and \sim 16.8 MSun for the rotating ones. Both values agree with observations. Moreover, present rotating models provide a very good fit to the progenitor of SN 2008ax. We discuss future directions of research for further improving the agreement between the models and the observations. We conclude that the mass-loss rates in the WNL and RSG phases are probably underestimated at present. We show that up to an initial mass of 40 M\odot, a surface magnetic field inferior to about 200 G may be sufficient to produce some braking. Much lower values are needed at the red supergiant stage. We suggest that the presence/absence of any magnetic braking effect may play a key role in questions regarding rotation rates of young pulsars and the evolution leading to LGRBs.Comment: 19 pages, 12 figures, accepted for publication in A&

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453

Star clusters near and far; tracing star formation across cosmic time

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00690-x.Star clusters are fundamental units of stellar feedback and unique tracers of their host galactic properties. In this review, we will first focus on their constituents, i.e.\ detailed insight into their stellar populations and their surrounding ionised, warm, neutral, and molecular gas. We, then, move beyond the Local Group to review star cluster populations at various evolutionary stages, and in diverse galactic environmental conditions accessible in the local Universe. At high redshift, where conditions for cluster formation and evolution are more extreme, we are only able to observe the integrated light of a handful of objects that we believe will become globular clusters. We therefore discuss how numerical and analytical methods, informed by the observed properties of cluster populations in the local Universe, are used to develop sophisticated simulations potentially capable of disentangling the genetic map of galaxy formation and assembly that is carried by globular cluster populations.Peer reviewedFinal Accepted Versio

Chemical abundance analysis of the Open Clusters Berkeley 32, NGC 752, Hyades and Praesepe

Context. Open clusters are ideal test particles to study the chemical evolution of the Galactic disc. However the existing high-resolution abundance determinations, not only of [Fe/H], but also of other key elements, is largely insufficient at the moment. Aims. To increase the number of Galactic open clusters with high quality abundance determinations, and to gather all the literature determinations published so far. Methods. Using high-resolution (R~30000), high-quality (S/N$>60 per pixel), we obtained spectra for twelve stars in four open clusters with the fiber spectrograph FOCES, at the 2.2 Calar Alto Telescope in Spain. We use the classical equivalent widths analysis to obtain accurate abundances of sixteen elements: Al, Ba, Ca, Co, Cr, Fe, La, Mg, Na, Nd, Ni, Sc, Si, Ti, V, Y. Oxygen abundances have been derived through spectral synthesis of the 6300 A forbidden line. Results. We provide the first determination of abundance ratios other than Fe for NGC 752 giants, and ratios in agreement with the literature for the Hyades, Praesepe and Be 32. We use a compilation of literature data to study Galactic trends of [Fe/H] and [alpha/Fe] with Galactocentric radius, age, and height above the Galactic plane. We find no significant trends, but some indication for a flattening of [Fe/H] at large Rgc, and for younger ages in the inner disc. We also found a possible decrease of [Fe/H] with |z| in the outer disc, and a weak increase of [alpha/Fe] with Rgc.Comment: 21 pages, Accepted for publication in A&A, Updated Table 1

Stellated Icosahedra

An excerpt of an article published in Mathematica in Education. There are 59 stellations of the icosahedron; these pages contain various images of them, ordered by increasing circumradius, and some background information. The metric properties and graphics data were computed with a Mathematica program. Included are a guided tour, a visual index (clickable map), and floor plans (clickable map) of all 59 stellations

Programming in Mathematica

X, 279 tr.; 24 cm

The Mathematica programmer

The Mathematica Programmer covers the fundamental programming paradigms and applications of programming languages. This book is organized into two parts encompassing 10 chapters. Part 1 begins with an overview of the programming paradigms. This part also treats abstract data types, polymorphism and message passing, object-oriented programming, and relational databases. Part 2 looks into the practical aspects of programming languages, including in lists and power series, fractal curves, and minimal surfaces.This book will prove useful to mathematicians and computer scientists