Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation

Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified entropy functional. The existence of a weak semi-discrete solution and, in a particular case, its temporal second-order convergence to the continuous solution is proved. The proofs employ an algebraic relation which implies the G-stability of the two-step BDF. Second, an implicit Euler and $q$ -step BDF discrete variational derivative method are considered. This scheme, which exploits the variational structure of the equation, dissipates the discrete Fisher information (or energy). Numerical experiments show that the discrete (relative) entropies and Fisher information decay even exponentially fast to zero.     

Synthesis of thermosensitive guar‐based hydrogels with tunable physico‐chemical properties by click chemistry

Thermosensitive guar‐based hydrogels are obtained in water solutions by copper‐catalyzed 1,3‐dipolar cycloaddition between alkyne‐functionalized guars and α,ω‐diazido‐poly[(ethylene glycol)‐co‐(propylene glycol)]. Characterization by TGA, HR‐MAS ¹H NMR, and rheology have shown that hydrogels with tunable physico‐chemical properties, such as crosslinking density, viscoelasticity, swelling ratio, and so forth, could be obtained by varying the guar molar mass, the degree of alkyne functionality, the guar/crosslinker weight ratio, and the reaction temperature. Based on swelling measurements, it has been shown that the thermal sensitiveness of guar‐based hydrogels is fast, reversible, and intimately related to the weight fraction of the thermosensitive crosslinker in the network. Finally, the monitoring of doxorubicin hydrochloride release has demonstrated the potential of these hydrogels as temperature‐dependent drug release devices. The robust, efficient, and orthogonal approach described herein represents a general approach towards the development of well‐controlled guar‐based hydrogels using α,ω‐diazido crosslinkers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2733–2742, 2010     

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.