A finite element finite-strain formulation for modeling colliding blocks of Gent materials

The present paper is devoted to the analysis of the contact/impact problems with Coulomb friction and large deformation between two hyperelastic bodies of Gent model. The total Lagrangian formulation is adopted to describe the geometrically non-linear behavior. For the finite element implementation, the explicit expression of the incremental law of Gent model is derived. A first order algorithm is applied for the numerical integration of the time-discretized equation of motion. Efficiency and accuracy of the resulting method is illustrated on a two-dimensional static contact problem and a three-dimensional dynamic contact problem as compared with ANSYS simulations.     

A regularized stiffened-gas equation of state

An alternative to the stiffened-gas equation of state is proposed that corrects for unphysical behavior, namely the returning of negative pressure values for densities lower than the reference density. The question of generalizing a given isentropic equation of state is first addressed. Then, a regularized stiffened-gas equation of state is derived, which is the main goal of this work. Finally, the use of the new equation of state is briefly illustrated for a classical computational fluid dynamics benchmark concerning the evaluation of liquid impact on a wall.     

Synthesis of 3-Adenyl- and 3-Thyminylcyclobutane-1,1-dimethanols and Their Homo-octameric Phosphodiesters

Starting from 3-(benzyloxy)cyclobutane-1,1-dimethanol, 3-thyminyl- and 3-adenylcyclobutane-1,1-dimethanol were synthesized by direct introduction of the heterocycles (Scheme 1). The mono-O-substituted methoxytrityl derivatives were separately converted to octameric phosphodiesters on an aminomethyl-polystyrene carrier by the phosphotriester method. These oligomers of carba-nucleosides were prepared in order to study their annealing behaviour towards ribo- and deoxyribo-nucleic acids as well as their potential for homologous hybridization.     

Pyridine as proton acceptor in the concerted proton electron transfer oxidation of phenol

Taking pyridine as a prototypal example of biologically important nitrogen bases involved in proton-coupled electron transfers, it is shown with the example of the photochemically triggered oxidation of phenol by Ru(III)(bpy)(3) that this proton acceptor partakes in a concerted pathway whose kinetic characteristics can be extracted from the overall kinetic response. The treatment of these data, implemented by the results of a parallel study carried out in heavy water, allowed the determination of the intrinsic kinetic characteristics of this proton acceptor. Comparison of the reorganization energies and of the pre-exponential factors previously derived for hydrogen phosphate and water (in water) as proton acceptors suggests that, in the case of pyridine, the proton charge is delocalized over a primary shell of water molecules firmly bound to the pyridinium cation.     

Electrochemistry and spectroelectrochemistry of bismanganese porphyrin-corrole dyads

A series of homobimetallic manganese cofacial porphyrin-corrole dyads were synthesized and investigated as to their electrochemistry, spectroelectrochemistry, and ligand binding properties in nonaqueous media. Four dyads were investigated, each of which contained a Mn(III) corrole linked in a face-to-face arrangement with a Mn(III) porphyrin. The main difference between compounds in the series is the type of spacer, 9,9-dimethylxanthene, anthracene, dibenzofuran, or diphenylether, which determines the distance and interaction between the metallomacrocycles. Each redox process of the porphyrin-corrole dyads was assigned on the basis of spectroscopic and electrochemical data and by comparison with reactions and properties of the monocorrole and the monoporphyrin which were examined under the same solution conditions. The Mn(III) porphyrin part of the dyad undergoes two major one-electron reductions in pyridine and benzonitrile, the first of which involves a Mn(III)/Mn(II) process and the second the addition of an electron to the conjugated π-ring system of the macrocycle. The Mn(III) corrole part of the dyads also exhibits two major redox processes, one involving Mn(III)/Mn(II) and the other Mn(III) to Mn(IV) under the same solution conditions. The potentials and reversibility of each electron transfer reaction were shown to depend upon the solvent, type of spacer separating the two macrocycles, and the presence or absence of axial ligation, the latter of which was investigated in detail for the case of acetate ion which was found to bind within the cavity of the dyad to both manganese centers, both before and after the stepwise electroreduction to the Mn(II) forms of the two macrocycles. An intramolecular chloride ion exchange between the porphyrin part of the dyads which contain Mn(III)Cl and the singly oxidized corrole in the dyad is observed after the Mn(III)/Mn(IV) reaction of the corrole, suggesting that chloride is coordinated inside the cavity in the neutral compound.     

Diffusion of Myelin Oligodendrocyte Glycoprotein in Living OLN-93 Cells Investigated by Raster-Scanning Image Correlation Spectroscopy (RICS)

Many membrane proteins and lipids are partially confined in substructures ranging from tens of nanometers to micrometers in size. Evidence for heterogeneities in the membrane of oligodendrocytes, i.e. the myelin-producing cells of the central nervous system, is almost exclusively based on detergent methods. However, as application of detergents can alter the membrane phase behaviour, it is important to investigate membrane heterogeneities in living cells. Here, we report on the first investigations of the diffusion behavior of the myelin-specific protein MOG (myelin oligodendrocyte glycoprotein) in OLN-93 as studied by the recently developed RICS (raster-scanning image correlation spectroscopy) technique. We implemented RICS on a standard confocal laser-scanning microscope with one-photon excitation and analog detection. Measurements on FITC-dextran were used to evaluate the performance of the system and the data analysis procedure. Ellen Gielen and Nick Smisdom contributed equally to this work.     

Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flamesJustification mathématique d'une équation intégro-différentielle non linéaire pour un modèle de flamme sphérique

This Note is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [7]. The paper [7] derives, by means of a three-scale matched asymptotic expansion, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis number – i.e., the ratio between thermal and molecular diffusion – to be strictly less than unity. In this Note, we give the main ideas of a rigorous proof of the validity of this model, under the additional restriction that the Lewis number is close to 1. To cite this article: C. Lederman et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 569–574.     

Les formes de torsion holomorphes du complexe de de RhamThe holomorphic torsion forms of the de Rham complex

In this Note, we announce the vanishing of the holomorphic torsion forms of the relative de Rham complex of an equivariant fibration. To cite this article: J.-M. Bismut, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 243–247.     

NMR (195Pt and 13C) contribution to the study of some Pt(II), Pt(IV) and mixed-valence thioamido complexes

The ¹⁹⁵Pt and ¹³C chemical shifts (δ_Pt and δ_c) are reported for platinum(II), platinum(IV) and class II mixed-valence complexes, with general formula [PtL₄]X₂, cis- and trans-PtL₂X₂, PtL₂X₄ and Pt₂L₄X₆ (where L may be thiourea, 2-imidazolidine-thione, tetrahydro 2-pyrimidinethione, thiocaprolactam, pyridine-2-thione and tetramethylthiourea, and X may be Cl or Br). The ¹⁹⁵Pt chemical shifts can be understood in view of ¹³C data in terms of variations of electronegativities and σ-donor abilities of ligands attached to platinum.