Application of SSA thermal fractionation and X‐ray diffraction to elucidate comonomer inclusion or exclusion from the crystalline phases in poly(butylene succinate‐ran‐butylene azelate) random copolymers

Poly(butylene succinate‐ran‐butylene azelate) random copolyesters were thermally fractionated by successive self‐nucleation and annealing (SSA). The samples before and after SSA were analyzed by differential scanning calorimetry (DSC) and X‐ray diffraction (WAXS and SAXS). WAXS results indicate that a small degree of comonomer inclusion is present in the crystalline phases that are formed in the copolymers depending on composition: a PBS‐like unit cell or/and a PBAz‐like unit cell, thus confirming the isodimorphic behavior of the samples. SSA on the other hand demonstrated that the degree of comonomer exclusion during crystallization is far larger than comonomer inclusion, as judged by the increase in fractionation degree with compositions leading to the pseudo‐eutectic point. Furthermore, WAXS, SAXS, and SSA results show that the isodimorphic behavior is not highly dependent on kinetic factors, as the degree of comonomer inclusion or exclusion in the samples was not significantly altered by SSA thermal fractionation, a thermal treatment that promotes annealing and molecular segregation of defects to the amorphous regions of the material. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2346–2358     

Mechanical properties of anion exchange membranes by combination of tensile stress–strain tests and dynamic mechanical analysis

The thermomechanical properties of anion exchange polymers based on polysulfone (PSU) quaternized with trimethylamine (TMA) or 1,4‐diazabicyclo[2.2.2]octane (DABCO) and containing hydroxide or chloride anions by tensile stress–strain tests and dynamic mechanical analysis (DMA) have been determined. The reported mechanical properties included the Young's modulus, tensile strength, and elongation at break from tensile tests and the storage and loss modulus and glass transition temperature from DMA. The anion exchange membranes behaved as stiff polymers with Young's modulus in the order of 1 GPa, relatively with high strength (about 30 MPa) and low elongation at break (around 10%) was observed. Tensile tests were also made with membranes exchanged with hydrogen‐carbonate and carbonate anions to control the absence of important carbonation of the OH form. The glass transition temperatures were of the order of 150 °C (PSU‐TMA) or 200 °C (PSU‐DABCO) for the hydroxide form, confirmed by differential scanning calorimetry; they increase further by about 50 K, when hydroxide ions are replaced by chloride. This result and the increase of the storage modulus could be interpreted by the higher hydration of hydroxide ions and the plasticizing effect of water, which reduced the Van der Waals interactions between the macromolecular chains. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1180–1187     

An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

Numerically stable,scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.     

The concept of proof in the light of mathematical work

ZDM – Mathematics Education - Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and...     

A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches

In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.