Une démonstration simple de la fidélité de la représentation de Lawrence–Krammer–Paris

The theorem of linearity of the Artin–Tits groups of spherical type and the theorem of injectivity of any Artin–Tits monoid in its group are essentially based on the faithfulness of the Lawrence–Krammer–Paris representation restricted to the monoid. We prove this faithfulness using neither the normal forms of the elements of the monoid nor the closed subsets of the associated root system; only very elementary notions are needed.     

The Local Geometry of Gas Injection into Saturated Homogeneous Porous Media

The injection of gases into liquid saturated porous media is of theoretical and practical interest (e.g., air sparging for the removal of volatile organic compounds from contaminated aquifer sediments). The influence of the rate of gas delivery and the vertical distance from the source are developed. The concept of a “near-injection region” is presented in which the pressure gradients exceed buoyant gradients and thus exhibits largely radial flow. The near-injection size is shown to have an area required to carry the injected gas flow under unit gradient. The parabolic movement of gas outside of this area which has often been observed is explained as reflecting the sum of many realizations of gas channels following random lateral movements as they precede upward independent of flux. These concepts are confirmed through comparison with published and experimental data of air injection into slabs consisting of saturated sands of a range of textures.     

Interaction of a Wetting Front with an Impervious Wall – a New Superposition Method for the Boussinesq Equation

The interaction of the wetting front, described by the Boussinesq equation, with an impervious wall is considered using a superposition principle. A number of approximate solutions are compared with the numerical solution of the Boussinesq equation. The results show that the superposition approach provides an excellent method for obtaining an approximate solution.     

Titan Based Hybrid Organic-Inorganic Gels Comprising Carbohydrate Moiety

Abstract

A series of titanium based gels comprising carbohydrate moieties was synthesized. The sugars used include a specific hydrazide group as complex forming agent. Additionally, this group forms stable hydrates which allow further slow water release. As a result, the compounds used in this study form transparent and stable gels with titanium alkoxide without addition of external water. Interpretation of the IR-spectra reveals that some compounds form monodentate ligands and other bidentate ligands. Further Tian-Calvet calorimetric measurements confirmed our IR-based conclusions. This strategy of synthesis gives a new opportunity to obtain hybrid materials by addition of natural chelating ligands to slow down the hydrolysis/condensation reactions that occur during the sol-gel process. Therefore, carbohydrate moieties have been incorporated in the gels obtained and different type of Ti coordination was proposed based on the IR spectroscopy studies. SEM investigations show the influence of the ligand on the morphology of the xerogel.

GRAPHICAL ABSTRACT      

Stereoselective Synthesis of Versatile Intermediates for Clerodanes Total synthesis

The stereoselective synthesis of compounds 2a-d, attractive intermediates for the synthesis of clerodane diterpenes is described in 6 to 9 steps in good overall yields from commercially available racemic Wieland-Miescher ketone.     

A Simple and Efficient Procedure for the Preparation of Benzal Chlorides and Benzal Bromides

Benzal chlorides and benzal bromides were conveniently synthesized by reaction of aryl aldehydes with a Vilsmeier type reagent formed in situ by reduction of CC1₄ or CBr₄ in dimethylformamide (DMF) as solvent.     

Symmetry lowering by cage doping in spherical superatoms: Evaluation of electronic and optical properties of 18-electron W@Au12Pt n (n = 0-4) superatomic clusters from relativistic DFT calculations

Attempts to expand the versatility of well defined clusters are a relevant issue in the design of building blocks for functional nanostructures. Here, we investigate the plausible formation of related structures from the emblematic highly symmetrical 18-e [W@Au₁₂] cluster. The calculated [W@Au₁₂Pt_n] series, with n = 0, 1, 2, 3, and 4, show cohesion energies, HOMO-LUMO gap, adiabatic electron affinities (AEAs) and adiabatic ionization potentials (AIPs), indicating a relative stability to the parent cluster [W@Au₁₂] experimentally characterized, where clusters with n = 1 and n = 4 are suggested as the most stable with respect to oxidation. The resulting symmetry lowering away from the high icosahedral symmetry upon adding Pt atoms induces a sizable splitting of the frontiers shells, which in turn effectively modify the properties of the calculated clusters, as observed from calculated optical properties. The estimated absorption spectra show an interesting broadening effect of the absorption peaks, which appears as a useful approach for further design of broad black absorbers, which are able to absorb light in a wider range, with potential capabilities to enhance the efficiency of thin film solar cells and photocatalysis processes, among other applications.     

Extended three-dimensional digital image correlation (X3D-DIC)

A correlation algorithm is proposed to measure full three-dimensional displacement fields in a three-dimensional domain. The chosen kinematic basis for this measurement is based on continuous finite-element shape functions. It is furthermore proposed to account for the presence of strong discontinuities, similarly to extended finite element schemes, with a suited enrichment of the kinematics with discontinuities supported by a (crack) surface. An optimization of the surface geometry is proposed based on correlation residuals. The procedure is applied to analyze one loading cycle of a fatigue-cracked nodular graphite cast iron sample by using computed tomography pictures. Subvoxel crack openings are revealed and measured. To cite this article: J. Réthoré et al., C. R. Mecanique 336 (2008).     

Anion-π Interaction for Molecular Recognition of Anions: Focus on Cooperativity with Hydrogen Bonding

Anion recognition represents an active area of research in supramolecular chemistry. The last two decades have been marked by spectacular advances in the design of new anion receptors. Moreover, the development of approaches combining experimental and theoretical studies has proved to be particularly relevant, allowing for a better understanding and rationalization of the phenomena involved in anion complexation processes. In this context, the combination of weak interactions within the same receptor and their synergistic effects, called cooperativity, has attracted increasing interest within the scientific community. This Review focuses on the combination of anion-π and hydrogen bonds and the emerging concept of cooperativity. The most relevant anion-π donor families are presented. The concept of cooperativity is illustrated using the most recent examples present in current literature.