The Chaotic Mixmaster and the Suppression of Chaos in Scalar–Tensor Cosmologies

We show that there is a threshold in energy for the onset of chaos in cosmology for the Universe described as a dynamical system derived from the Einstein equations of General Relativity (GR). In the case of the mixmaster model (homogeneous and anisotropic cosmology with a Bianchi IX metric), the chaos occurs precisely at the prescribed necessary value H _vac=0 of the GR for the energy of the Universe while the system is found to be regular for H<0 and chaotic for H>0 with respect to its pure vacuum part. In the case of generalized scalar tensor theories within the Bianchi IX model, we show using the ADM formalism and a conformal transformation that the energy of the dynamical system as compared to vacuum lies below the zero energy threshold. The system is thus not exhibiting chaos and the conclusion still holds in the presence of ordinary matter as well. The suppression of chaos occurs in a similar way for stiff matter alone.     

X-ray diffraction study of 'side-on fixed' homopolysiloxanes from nematic to smectic C phases

The X-ray patterns for the nematic phase in a series of side-on fixed polysiloxanes show different kinds of diffuse elements which imply complex short range ordering. A systematic structural study of the evolution of the patterns versus two molecular parameters, namely the spacer length and the length of the terminal aliphatic tails, suggests the possible occurrence of a smectic C phase for certain values of these parameters. Taking into account these tendencies, new synthesis led to a nematic-smectic C polymorphism observed for the first time in side-on fixed polysiloxanes.     

Liquid crystal side chain polysiloxanes containing various proportions of non-mesogenic units

Recent studies have established that side chain polymeric liquid crystals composed of mesogenic and non-mesogenic side groups keep their liquid-crystalline properties even for a low proportion of mesogens. We show that the detailed structures of three kinds of new diluted liquid crystal polysiloxanes depend on the nature of the co-substituent as well as on the proportion of the silicon sites occupied by the mesogenic groups. Mixtures of these systems with low molar mass liquid crystals were also investigated in terms of compatibility and/or stabilization of smectic A phases.     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

Improved synthesis of tocopherol fatty alcohols and analogs: microglial activation modulators

The synthesis of tocopherol fatty alcohols (TFAs), potent microglial activation modulators, was achieved via C-alkylation of trimethylhydroquinone. Several analogs, in particular water-soluble prodrugs, have been synthesized using a Wittig reaction and their antioxidant activities have been evaluated.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Geometric modeling of homoepitaxial CVD diamond growth: I. The {1 0 0}{1 1 1}{1 1 0}{1 1 3} system

Plasma-assisted CVD homoepitaxial diamond growth is a process that must satisfy many stringent requirements to meet industrial applications, particularly in high-power electronics. Purity control and crystalline quality of the obtained samples are of paramount importance and their optimization is a subject of active research. In the process of such studies, we have obtained high purity CVD diamond monocrystals with unusual morphologies, namely with apparent {1 1 3} stable faces. This phenomenon has led us to examine the process of CVD diamond growth and build up a 3D geometrical model, presented here, describing the film growth as a function of time. The model has been able to successfully describe the morphology of our obtained crystals and can be used as a predictive tool to predetermine the shape and size of a diamond crystal grown in a given process configuration. This renders accessible control of desirable properties such as largest usable diamond surface area and/or film thickness, before the cutting and polishing manufacture steps take place. The two latter steps are more sensitive to the geometry of the growth sectors, which will be addressed in a companion paper.Our model, applicable to the growth of any cubic lattice material, establishes a complete mapping of the final morphology state of growing diamond, as a function of the growth rates of the crystalline planes considered, namely {1 0 0}, {1 1 1}, {1 1 0}, and {1 1 3} planes, all of which have been observed experimentally in diamond films. The model makes no claim as to the stability of the obtained faces, such as the occurrence of non-epitaxial crystallites or twinning. It is also possible to deduce transient behavior of the crystal morphology as growth time is increased. The model conclusions are presented in the form of a series of diagrams, which trace the existence (and dominance) boundaries of each face type, in presence of the others, and where each boundary crossing represent a topology change in terms of number of faces, edges and vertices. We validate the model by matching it against crystals published in the literature and illustrate its predictive value by suggesting ways to increase usable surface area of the diamond film.     

Allophane: a natural gel in volcanic soils with interesting environmental properties

Volcanic (allophanic) soils are interesting in terms of the control of the greenhouse effect and the knowledge of the porous features is of importance to understand the mechanism of C and N sequestration. These soils contain a peculiar clay: allophane aggregates quite close to the synthetic mineral gels aggregates. These volcanic materials behave as gels during drying with a large irreversible shrinkage that can modify the soil physical properties. Consequently, as for silica gels, we use the CO₂ supercritical drying procedure (SD) to control the drying step and to preserve the structural and textural properties of the soils. The experimental results show that the N and C content in the soils is clearly dependent on the allophane content. We also show that the textural properties, such as specific surface area, are higher for the supercritically dried samples, compared to the classically dried samples, and SAXS results confirm the preserving effect of the SD. With these data, we propose possible effects of the specific surface area on the C and N content of the allophanic soils.     

ALTERATIONS OF PROTEOGLYCANS IN ULTRAVIOLET-IRRADIATED SKIN

Abstract— The effect of UVB exposure on the distribution and synthesis of dermal proteoglycans was measured in the skin of hairless mice. Two groups of mice were included: one was irradiated for 10 weeks; the other was kept as control. After intraperitoneal injection of sodium ³⁵S-sulfate, punch biopsies were taken for histology and proteoglycans were extracted from the remaining skin with 4 M guanidinium chloride, containing 3–[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate (0.5%, weight per volume). Following proteolytic digestion, the glycosaminoglycan constituents were isolated and analyzed by quantitative cellulose acetate electrophoresis and enzymatic digestibility.
Under the influence of UVB radiation, newly synthesized proteoglycans measured by ³⁵SO₄ uptake increased as much as 60%. In addition, the irradiated skin had a higher average content of proteoglycan than had control skin (4981 μg vs 4134 μg/g dry weight). This could be ascribed to an increase in heparin (1400 vs 533 μ g/g dry weight) and heparan sulfate (472 vs 367 μg/g dry weight), whereas no change in the concentration of hyaluronic acid (1243 vs 1372 μg/g dry weight) and dermatan sulfate (1866 vs 1863 μg/g dry weight) was observed. The irradiated animals also exhibited a marked increase in the synthesis of heparan sulfate and heparin (62% and 71%, respectively). These results demonstrate that chronic doses of UVB altered proteoglycan metabolism through both quantitative and qualitative changes.