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.     

Reactions of collman complex with tin(IV) and germanium(IV) porphyris,formation of [tin(II) and germanium(II) porphyrins] tetracarbonyliron and crystal structure of [2,3,7,8,12,13,17,18-octaethylporphinato tin(II)] tetracarbonyliron

The action of Na₂Fe(CO)₄ with tin(IV) and germanium(IV) porphyrins affords metal(II) porphyrin complexes [(por)M(II)Fe(CO)₄] (por = porphyrinate, M - Sn(II) or Ge(II)). The molecular structure of [(oep)Sn(II)Fe(CO)₄] was solved by X-ray diffraction techniques. The molecular structure of [(oep)Sn(II)Fe(CO)₄] was solved by X-ray diffraction techniques : the Sn coordination is square pyramidal with the iron in axial position (Sn-Fe = 2.492(1)Å) whereas the Fe coordination is trigonal bipyramidal. Mössbauer parameters provide convincing evidence for the formal zero oxidation state of the iron atom.     

Synthesis of vinyl ethers by homologation of aldehydes via radical reductive elimination

Methoxyphenylthiomethyllithium 1 reacts with aldehydes to give adducts which are then transformed into xanthates. These compounds, by reaction with tri-n-butylstannane, afford vinyl ethers in good yields.     

Experimental study of viscoelastic effectives in a cylinder-plane lubricated contact

This experimental study is related to the flow between a stationary small diameter needle and a moving drum of much larger diameter, seen as a moving plane. Our visualisation experimental set-up adds new results regarding the flow behaviour of a polymer solution. This flow is compared to that of a Newtonian fluid used under the same kinematic conditions. Important differences between Newtonian and polymeric flows concern mainly streamlines, stagnation point positions, and reverse flow. A second experimental set-up enabled us to obtain normal stress profiles along the needle wall and the flow rate through the gap. Reslts related to Newtonian flows are compared to the well-known analytical solutions for a bidimensional laminar flow.     

Low loss negative index metamaterials with one type of meta-atom

Metamaterial building blocks from microwave to optical range are mainly based on metal-dielectric composites. In almost all structures with true negative index (not coming from losses), two kinds of meta-atoms (electric and magnetic) are mixed to drive simultaneously the effective permittivity and permeability to negative values leading in turn to a negative index of refraction. In this paper, we show that two coupled structures with localized plasmons modes (e.g. cut-wires or split ring resonators) can exhibit negative refractive index by their own, by appropriately controlling the hybridization scheme of the plasmons modes. Because of small metal filling factor and reduced optical losses, the resulting structures may pave the way to realistic applications of metamaterials at optical frequencies.     

Nonlinear behaviour of the instability of steady natural convection in a vertical air layer

In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method.