Extreme weights in Steinhaus triangles

Let {0=w0<w1<w2<…<wm0=w0<w1<w2<…<wm} be the set of weights of binary Steinhaus triangles of size n , and let Wibe the set of sequences in F2n that generate triangles of weight wi. In this paper we obtain the values of wi and the corresponding sets Wi for i¿{2,3,m}i¿{2,3,m}, and partial results for i=m-1i=m-1.Peer ReviewedPostprint (author's final draft

An aluminium tool for multiple stellar generations in the globular clusters 47 Tuc and M 4

We present aluminium abundances for a sample of about 100 red giant stars in each of the Galactic globular clusters 47 Tuc (NGC 104) and M 4 (NGC 6121). We have derived homogeneous abundances from intermediate-resolution FLAMES/GIRAFFE spectra. Aluminium abundances are from the strong doublet Al I at 8772-8773 A as in previous works done for giants in NGC 6752 and NGC 1851, and nitrogen abundances are extracted from a large number of features of the CN molecules, by assuming a suitable carbon abundance. We added previous homogeneous abundances of O and Na and newly derived abundances of Mg and Si for our samples of 83 stars in M 4 and 116 stars in 47 Tuc to obtain the full set of elements from proton-capture reactions produced by different stellar generations in these clusters. By simultaneously studying the Ne-Na and Mg-Al cycles of H-burning at high temperature our main aims are to understand the nature of the polluters at work in the first generation and to ascertain whether the second generation of cluster stars was formed in one or, rather, several episodes of star formation. Our data confirm that in M 4 only two stellar populations are visible. On the other hand, for 47 Tuc a cluster analysis performed on our full dataset suggests that at least three distinct groups of stars are present on the giant branch. The abundances of O, Na, Mg and Al in the intermediate group can be produced within a pollution scenario; results for N are ambiguous, depending on the C abundance we adopt for the three groups.Comment: 11 pages, 9 figures, 2 on-line tables: accepted for publication on Astronomy and Astrophysic

Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study

The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number (\mbox {Ca}), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to \mbox{Ca} \approx 3 \times 10^{-2}. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of \mbox{Ca} which is broad enough to characterize all the three characteristic mechanisms of breakup in the confined T-junction, i.e. ${\it squeezing}$, ${\it dripping}$ and ${\it jetting}$ regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time $\tau_P$ and the finite extensibility parameter $L^2$, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with ${\it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with ${\it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios $Q \approx {\cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.Comment: 16 pages, 14 figures; This Work applies the Numerical Methodology described in arXiv:1406.2686 to the Problem of Droplet Generation in Microfluidic T-Junctions. arXiv admin note: substantial text overlap with arXiv:1508.0055