On the non existence of monotone linear schema for some linear parabolic equations

In this Note, we present a result concerning the non existence of linear monotone schema with fixed stencil on regular meshes for some linear parabolic equation in two dimensions. The parabolic equations of interest arise from non isotropic diffusion modelling. A corollary is that no linear monotone 9 points-schemes can be designed for the one-dimensional heat equation emerged in the plane with an arbitrary direction of diffusion. Some applications of this result are provided: for the Fokker–Planck–Lorentz model for electrons in the context of plasma physics; all linear monotone scheme for the one-dimensional hyperbolic heat equation treated as a two-dimensional problem are not consistent in the diffusion limit for an arbitrary direction of propagation. We also examine the case of the Landau equation. To cite this article: C. Buet, S. Cordier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

A rigid subspace of the real line whose square is a homogeneous subspace of the plane

Working in ZFC, we give an example as indicated in the title.

     

Equisingular Deformations of Sandwiched Singularities

We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.     

Amine‐cured epoxy/clay nanocomposites. II. The effect of the nanoclay aspect ratio

The thermophysical and mechanical properties of a nanocomposite material composed of amine‐cured diglycidyl ether of bisphenol A (DGEBA) reinforced with organomontmorillonite clay are reported. The storage modulus at 100 °C, which was above the glass‐transition temperature (T_g), increased approximately 350% with the addition of 10 wt % (6.0 vol %) of clay. Below the T_g, the storage modulus at 30 °C increased 50% relative to the value of unfilled epoxy. It was determined that the T_g linearly increased as a function of clay volume percent. The tensile modulus of epoxy at room temperature increased approximately 50% with the addition of 10 wt % of clay. The reinforcing effect of the organoclay nanoplatelets is discussed with respect to the Tandon–Weng and Halpin–Tsai models. A pseudoinclusion model is proposed to describe the behavior of randomly oriented, uniformly dispersed platelets in nanocomposite materials. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4391–4400, 2004     

Influence of surfactant and lipid chain length on the solubilisation of phosphatidylcholine vesicles by micelles comprised of polyoxyethylene sorbitan monoesters

Photon correlation spectroscopy and freeze-fracture electron microscopy have been used to determine the ability of a range of micelle-forming, polyoxyethylene (20) sorbitan monoesters (Tweens) to solubilise vesicles prepared from phosphatidylcholines of different acyl chain lengths and degrees of saturation with a view to rationalising (in terms of their membrane toxicity) which of the micelle-forming surfactants to use as drug delivery vehicles. The phosphatidylcholines used were dimyristoyl-, dipalmitoyl-, distearoyl- and dioleoylphosphatidylcholine (DMPC, DPPC, DSPC and DOPC, respectively) while the nonionic polyoxyethylene sorbitan monoesters studied were polyoxyethylene (20) sorbitan monolaurate (Tween 20), a 9:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 40), a 1:1 weight ratio mixture of polyoxyethylene (20) sorbitan monopalmitate and monostearate (Tween 60), and polyoxyethylene (20) sorbitan monooleate (Tween 80). The ability of the Tween micelles to solubilise phospholipid vesicles was found to depend both upon the length of the surfactant acyl chain and the length of the acyl chains of the phospholipid comprising the vesicle. Vesicles composed of long saturated diacyl chain phospholipids, namely DSPC and DPPC, were the most resistant to solubilisation, while those prepared from the shorter acyl chained DMPC were more readily solubilised. In terms of their solubilisation behaviour, vesicles made from phospholipids containing long, unsaturated acyl chains, namely DOPC behaved more akin to those vesicles prepared from DMPC. None of the Tween surfactants were effective at solubilising vesicles prepared from DPPC or DSPC. In contrast, there were clear differences in the ability of the various surfactants to solubilise vesicles prepared from DMPC and DOPC, in that micelles formed from Tween 20 were the most effective solubilising agent while those formed by Tween 60 were the least effective. As a consequence of these observations it was considered that Tween 60 was the surfactant least likely to cause membrane damage in vivo and, therefore, is the most suitable surfactant for use as a micellar drug delivery vehicle.     

Reform Teaching Strategies Used by Student Teachers

The purposes of this study were to observe the teaching practices occurring in student teachers' science and mathematics K‐12 classrooms, compare the student teachers' perceptions of their teaching with what was actually occurring in their classrooms, and determine which college faculty members and courses these student teachers felt contributed to the teaching methods they used. Data on each student teacher were gathered via field notes of three classes, an observation protocol completed after each lesson, and an interview. Composites were written for each of the students. The total data set of all composites was examined to see if any patterns generalizable to the whole were evident. Differences between and among grade levels and content areas surfaced and are discussed.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Champ de vitesse dans un échangeur à vortex en régime turbulentHeat exchanger velocity field with turbulent inlet condition

We consider the isothermal flow through a cylindrical flat chamber, a model of some particular heat exchanger, for which LDV measurements and a numerical simulation have been performed. Experimental results show the establishment of an important vortex zone, the secondary flow extending all along the chamber radius. This observation leads to an expected significant increase of the fluid mixing. Results issued from the numerical simulation appear to be in close agreement with experimental data. Nevertheless, the k–ε model used here must be improved to obtain a better approach near the vortex centre. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 593–599.