Homogenization of a Ginzburg–Landau functional

We consider a nonlinear homogenization problem for a Ginzburg–Landau functional with a (positive or negative) surface energy term describing a nematic liquid crystal with inclusions. Assuming that sizes and distances between inclusions are of the same order ?, we obtain a limiting functional as $?\to 0$. We generalize the method of mesocharacteristics to show that a corresponding homogenized problem for arbitrary, periodic or non-periodic geometries is described by an anisotropic Ginzburg–Landau functional. We give computational formulas for material characteristics of an effective medium. To cite this article: L. Berlyand et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Efficient access to bisphenol A metabolites: Synthesis of monocatechol,mono-o-quinone,dicatechol, and di-o-quinone of bisphenol A

2-Iodoxybenzoic acid (IBX) oxidation of bisphenol A (BPA) is described. The selective production of either the mono-o-quinone or the di-o-quinone can be controlled by IBX stoichiometry. Isolated yields of quinone were greater than 80%. Previous synthesis of BPA-di-o-quinone using a large excess of Fremy’s salt produced only trace amounts of product. In addition to o-quinone products, both mono- and dicatechols of BPA can synthesize in high yield and isolated without chromatography. The more stable catechols can be quantitatively converted back to o-quinones using silver oxide oxidation in either acetone or DMF. These one-pot reactions provide access to four different BPA metabolites in high yield and significant scale.     

Kinetics and mechanisms of the tropospheric reactions of menthol, borneol, fenchol, camphor, and fenchone with hydroxyl radicals (OH) and chlorine atoms (Cl)

Relative kinetic techniques have been used to measure the rate coefficients for the reactions of oxygenated terpenes (menthol, borneol, fenchol, camphor, and fenchone) and cyclohexanol with hydroxyl radicals (OH) and chlorine atoms (Cl) at 298 ± 2 K and atmospheric pressure. The rate coefficients obtained for the reactions of the title compounds with OH are the following (in units of 10(-11) cm(3) molecule(-1) s(-1)): (1.48 ± 0.31), (2.65 ± 0.32), (2.49 ± 0.30), (0.38 ± 0.08), (0.39 ± 0.09) for menthol, borneol, fenchol, camphor, and fenchone, respectively. For the corresponding reactions with Cl atoms the rate coefficients are as follows (in units of 10(-10) cm(3) molecule(-1) s(-1)): (3.21 ± 0.26), (3.40 ± 0.28), (2.72 ± 0.13), (2.93 ± 0.17), (1.59 ± 0.10), and (1.86 ± 0.29) for cyclohexanol, menthol, borneol, fenchol, camphor, and fenchone, respectively. The reported error is twice the standard deviation. Product studies of the reactions were performed using multipass in situ FTIR (Fourier transform infrared spectroscopy) and solid-phase microextraction (SPME) with analysis by GC-MS (gas chromatography-mass spectrometry). A detailed mechanism is proposed to justify the observed reaction products.     

Periodic unfolding and homogenizationÉclatement périodique et homogénéisation

A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures). To cite this article: D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104.     

Kähler manifolds of quasi-constant holomorphic sectional curvature

In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context, we introduce in the K?hlerian framework the geometric notion of quasi-constant holomorphic sectional curvature. Some characterizations and properties are given. We obtain necessary and sufficient conditions for these manifolds to be locally symmetric, Ricci or Bochner flat, K?hler η-Einstein or K?hler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.      

Thermal behaviour and electro-optical properties of a series of liquid crystals based on palladium complexes with mixed ligands

A series of ortho-metallated palladium(II) complexes with two dimeric liquid crystals Schiff base (methoxy and decyloxy as terminal groups) as cyclometallated ligands and N-aryl-N′-benzoyl thiourea derivatives as co-ligands were prepared and investigated for their liquid crystalline properties. Their structures were assigned based on elemental analysis, FT-IR and ¹H NMR spectroscopy while the thermal behaviour was investigated by differential scanning calorimetry and polarising optical microscopy. The complexes with Schiff base ligand bearing methoxy group as terminal group show extensive decomposition during melting while the complexes with Schiff base having decyloxy group as terminal group show monotropic nematic phases, with the mesophase stability strongly related to the type of N-aryl-N′-benzoyl thiourea derivative used. Their liquid crystalline properties are compared with their analogues having N,N-dialkyl-N′-benzoyl thiourea as co-ligands which were reported previously. One of the latter complexes was also investigated by thermally stimulated depolarisation currents method while the optical transmission was recorded simultaneously. The thermally stimulated depolarisation currents and optical transmission spectra confirmed the previous observation regarding the phase transition temperatures. The current intensity–applied voltage dependencies of this complex were investigated by specific electrical measurements.     

Palladium and nickel complexes of (P,N)-ligands based on quinolines: Catalytic activity for polymerization and oligomerization

Four (P,N)-ligands (1-4) with different steric and electronic properties were synthesized. They were used to prepare the monocationic palladium complexes [Pd(P,N)(CH₃)(NCCH₃)](PF₆) (9-12). The structures of the newly prepared ligand 3 and the neutral palladium complex [Pd(P,N)(CH₃)Cl] (10) were analysed by X-ray. The catalytic activity of the palladium complexes toward the copolymerization of styrene and ethylene with CO was low or non-existent. The nickel complexes [Ni(P,N)(1-naphthyl)Cl] (13-16), modified with the ligands 1-4, were prepared and their catalytic activity toward ethylene oligomerization was studied. They showed high activity at ambient temperature and low ethylene pressure (1-12 bar) in the presence of MAO.