Lp resolvent estimates for magnetic Schrödinger operators with unbounded background fields

We prove L^p and smoothing estimates for the resolvent of magnetic Schrödinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we prove an estimate on the location of eigenvalues of magnetic Schrödinger and Pauli operators with complex electromagnetic potentials.     

Review: Lanthanide coordination chemistry: from old concepts to coordination polymers

Because of their remarkable and unmatched optical and magnetic properties, the lanthanides are under the limelight when it comes to high technology. These elements are used in strategic applications such as optical glasses and lasers, telecommunications, lighting and displays, magnetic materials, hard-disk drives, security inks and counterfeiting tags, catalysis, biosciences, and medicine, to name but a few. Long considered as minor actors in transition metal chemistry, they have now gained respect from coordination chemists who insert them into sophisticated functional and polyfunctional molecules and materials. This mini review focuses on trivalent lanthanide ions and first summarizes their basic properties. Then some classical aspects of their coordination chemistry are discussed, followed by macrocyclic chemistry, supramolecular chemistry, and self-assembly processes. The last part of this contribution deals with coordination polymers and hybrid materials including potential applications.     

Dépose dynamique d'un micro-objet saisi par adhésionManipulation of micro-objects using adhesion forces and dynamical effects

This paper describes a dynamical strategy for releasing micro objects picked-up by means of adhesion forces. While sticking effects are used in order to capture an object by adequately choosing a high surface energy constitutive material for the end-effector, these same effects handicap considerably the release. We propose to take advantage of the inertial effects of both the end-effector and the manipulated object to overbalance adhesion forces and to achieve the release. Simulations show that for this purpose, accelerations as high as 10⁵ m/s² are needed. Successful manipulation of a 40 μm radius glass sphere is demonstrated. To cite this article: S. Haliyo et al., C. R. Mecanique 331 (2003).     

Treatment of interface problems with Godunov-type schemes

A correction is proposed of Godunov-type schemes, yielding a perfect capture of contact discontinuities in hydrodynamic flows. The correction method is based upon the following simple idea: If an Euler scheme is employed starting from a non-degraded solution at a certain instant of time, the presence of a discontinuity will entail, at the next instant, the degradation of the solution at the two points adjacent to the discontinuity only. On the other hand, an exact solution of the Riemann problem yields the state variables at the nodes affected by numerical diffusion can be corrected. The method is applied to problems involving a gas-liquid interface. The liquid is supposed to be compressible, obeying an equation of state of the “Stiffened Gas” type, for which a solution to Riemann's problem is readily obtained.     

(2S,4S,SFc)-2-[2-(Diphenyl­thio­phosphinoyl)­ferrocenyl]-4-methoxy­methyl-1,3-dioxane

The title compound, [Fe(C₅H₅)(C₂₃H₂₄O₃PS)], is a very useful inter­mediate for the synthesis of enanti­omerically pure (S)-2-[(diphenyl­thio­phosphinoyl)ferrocenyl]methanol or (S)-2-(diphenyl­thio­phosphinoyl)ferrocene­carboxaldehyde. The dioxane ring has a chair conformation and is twisted with respect to the cyclo­penta­dienyl ring to which it is attached. There is an inter­molecular C—H⋯O hydrogen-bonding inter­action which links the mol­ecules into C(8) chains developing parallel to the a axis. Owing to this weak inter­action, the two cyclo­penta­dienyl rings are twisted with respect to each other by 16.0 (3)°, and so have a conformation which might be regarded as inter­mediate between eclipsed and staggered. The absolute configuration deduced from the X-ray analysis fully confirms the sterochemistry expected from the chemical pathway.     

Study of the electrochemical properties in substituted Li2Ti3O7 ramsdellite

Substituting the ramsdellite compound Li₂Ti₃O₇ has been considered in order to improve the structure stability and performances for its use as electrode material for Li-ion accumulators. Two substitutions have been carried out, Ti/Fe and (Ti, Li)/(Fe,Ni). The presence of ⁵⁷Fe as a local Mössbauer probe is interesting for studying its local environment and the electrochemical mechanisms induced by lithium insertion.     

Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure.     

Regioselective electrophilic trifluoromethylation of substituted anilines and derivatives in superacid

In a one pot procedure, treatment of chloro or methyl substituted acetanilides in HF/SbF₅/CCl₄ followed by addition of HF/pyridine yields trifluoromethyl derivatives with high regioselectivity.