Stress-based upper-bound method and convex optimization: case of the Gurson materialMéthode cinématique par les contraintes et optimisation convexe : cas du matériau de Gurson

A nonlinear interior point method associated with the kinematic theorem of limit analysis is proposed. Associating these two tools enables one to determine an upper bound of the limit loading of a Gurson material structure from the knowledge of the sole yield criterion. We present the main features of the interior point algorithm and an original method providing a rigorous kinematic bound from a stress formulation of the problem. This method is tested by solving in plane strain the problem of a Gurson infinite bar compressed between rough rigid plates. To cite this article: F. Pastor et al., C. R. Mecanique 334 (2006).     

Experimental and computational visualization of the flow field in a thermoacoustic stackVisualisation expérimentale et numérique du champ de vitesse dans un réfrigérateur thermoacoustique

The oscillating flow field in a thermoacoustic stack is visualized experimentally using PIV measurements, and computationally using results of low-Mach-number simulations. The experiments and computations are performed under similar conditions. Results are obtained for two distinct configurations, involving thin and thick stack plates. In the first case, the flow field around the edge of the stack exhibits elongated vorticity layers, while in the latter it is dominated by the shedding and impingement of concentrated vortices. A close agreement between experimental and computational results is found, thus providing strong support for both approaches and further predictions. To cite this article: P. Blanc-Benon et al., C. R. Mecanique 331 (2003).     

A Bioinspired Molybdenum Complex as a Catalyst for the Photo‐ and Electroreduction of Protons

A molybdenum–dithiolene–oxo complex was prepared as a model of some active sites of Mo/W‐dependent enzymes. The ligand, a quinoxaline–pyran‐fused dithiolene, mimics molybdopterin present in these active sites. For the first time, this type of complex was shown to be active as a catalyst for the photoreduction of protons with excellent turnover numbers (500) and good stability in aqueous/organic media and for the electroreduction of protons in acetonitrile with remarkable rate constants (1030 s^?1 at ?1.3 V versus Ag/AgCl). DFT calculations provided insight into the catalytic cycle of the reaction, suggesting that the oxo ligand plays a key role in proton exchange. These results provide a basis to optimize this new class of H₂‐evolving catalysts.     

A Highly Effective Ruthenium System for the Catalyzed Dehydrogenative Cyclization of Amine–Boranes to Cyclic Boranes under Mild Conditions

We recently disclosed a new ruthenium‐catalyzed dehydrogenative cyclization process (CDC) of diamine–monoboranes leading to cyclic diaminoboranes. In the present study, the CDC reaction has been successfully extended to a larger number of diamine–monoboranes ( 4 – 7 ) and to one amine–borane alcohol precursor ( 8 ). The corresponding NB(H)N‐ and NB(H)O‐containing cyclic diaminoboranes ( 12 – 15 ) and oxazaborolidine ( 16 ) were obtained in good to high yields. Multiple substitution patterns on the starting amine–borane substrates were evaluated and the reaction was also performed with chiral substrates. Efforts have been spent to understand the mechanism of the ruthenium CDC process. In addition to a computational approach, a strategy enabling the kinetic discrimination on successive events of the catalytic process leading to the formation of the NB(H)N linkage was performed on the six‐carbon chain diamine–monoborane 21 and completed with a ¹⁵N NMR study. The long‐life bis‐σ‐borane ruthenium intermediate 23 possessing a reactive NHMe ending was characterized in situ and proved to catalyze the dehydrogenative cyclization of 1 , ascertaining that bis σ‐borane ruthenium complexes are key intermediates in the CDC process.     

From Lignin‐derived Aromatic Compounds to Novel Biobased Polymers

Nowadays, the synthesis of (semi)aromatic polymers from lignin derivatives is of major interest, as aromatic compounds are key intermediates in the manufacture of polymers and lignin is the main source of aromatic biobased substrates. Phenols with a variety of chemical structures can be obtained from lignin deconstruction; among them, vanillin and ferulic acid are the main ones. Depending on the phenol substrates, different chemical modifications and polymerization pathways are developed, leading to (semi)aromatic polymers covering a wide range of thermomechanical properties. This review discusses the synthesis and properties of thermosets (vinyl ester resins, cyanate ester, epoxy, and benzoxazine resins) and thermoplastic polymers (polyesters, polyanhydrides, Schiff base polymers, polyacetals, polyoxalates, polycarbonates, acrylate polymers) prepared from vanillin, ferulic acid, guaiacol, syringaldehyde, or 4‐hydroxybenzoic acid.

     

Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set \({\mathbf {K}}\). We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on \({\mathbf {K}}\) which is a sum of squares of polynomials, so that the expectation \(\int _{{\mathbf {K}}} f(x)h(x)dx\) is minimized. We show that the rate of convergence is no worse than \(O(1/\sqrt{r})\), where 2r is the degree bound on the density function. This analysis applies to the case when f is Lipschitz continuous and \({\mathbf {K}}\) is a full-dimensional compact set satisfying some boundary condition (which is satisfied, e.g., for convex bodies). The rth upper bound in the hierarchy may be computed using semidefinite programming if f is a polynomial of degree d, and if all moments of order up to \(2r+d\) of the Lebesgue measure on \({\mathbf {K}}\) are known, which holds, for example, if \({\mathbf {K}}\) is a simplex, hypercube, or a Euclidean ball.