Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data

In this paper we study the semiclassical limit of the Schrodinger equation. Under mild regularity assumptions on the potential U, which include Born‐Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic validity of classical dynamics globally in space and time for “almost all” initial data, with respect to an appropriate reference measure on the space of initial data. In order to achieve this goal we prove existence, uniqueness, and stability results for the flow in the space of measures induced by the continuity equation. © 2011 Wiley Periodicals, Inc.     

The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticityLa théorie Föppl–von Kármán des plaques comme Γ-limite de l'élasticité non linéaire

We show that the Föppl–von Kármán theory arises as a low energy Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [5] that for maps $\text{v:(0,1)}{}^3\text{→}\text{R}{}^3$, the L² distance of ?v from a single rotation is bounded by a multiple of the L² distance from the set SO(3) of all rotations. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 201–206.     

A Bifunctional Electrocatalyst for Oxygen Evolution and Oxygen Reduction Reactions in Water

Oxygen reduction and water oxidation are two key processes in fuel cell applications. The oxidation of water to dioxygen is a 4 H⁺/4 e^? process, while oxygen can be fully reduced to water by a 4 e^?/4 H⁺ process or partially reduced by fewer electrons to reactive oxygen species such as H₂O₂ and O₂^?. We demonstrate that a novel manganese corrole complex behaves as a bifunctional catalyst for both the electrocatalytic generation of dioxygen as well as the reduction of dioxygen in aqueous media. Furthermore, our combined kinetic, spectroscopic, and electrochemical study of manganese corroles adsorbed on different electrode materials (down to a submolecular level) reveals mechanistic details of the oxygen evolution and reduction processes.     

A Mild Efficient Procedure for the Conversion of Carboxylic Acid Esters to Primary Amides Using Formamide/Methanolic Sodium Methoxide

An improved method for the preparation of primary carboxylic acid amides from the corresponding esters is described. This reaction was easily followed by GLC and was usually complete in less than one hour.     

pH-dependent structure and energetics of H2O/MgO(100)

The structure and energetics of water on MgO(100) surfaces are studied by atomic force microscopy (AFM) and density-functional theory (DFT). Computationally, the adsorption of water monomers, small water clusters and water monolayers on MgO(100) surfaces is considered. The calculations predict the non-dissociative adsorption for water monomers. The potential energy surface for single monomers is characterized by very low diffusion barriers. Increasing water coverage leads to the formation of structures containing alternatively dissociated and molecularly adsorbed water molecules. The magnitude of the calculated adsorption energy per water molecule increases from 0.57 eV for the water monomer to 0.79 eV for the water monolayer. The present experimental and theoretical results show furthermore that the stability of MgO(100) surfaces in the presence of water depends on its pH value. The etching of MgO(100) surfaces in aqueous medium is studied with the AFM in situ with pH value changing from basic to acidic. While the atomically flat MgO(100) surface remains stable in basic and neutral pH ranges, it is easily etched when the pH turns below a value of 6. This agrees qualitatively with the present DFT calculations showing that square pits resulting from the etching reduce the MgO(100) surface energy in acidic environments.