Rôle de l'espace de Besov B∞−1,∞ dans le contrôle de l'explosion éventuelle en temps fini des solutions régulières des équations de Navier–Stokes

Let $\text{u∈C([0,T}{}^1\text{[;L}{}^{\mathrm{n}}\text{(}\text{R}{}^{\mathrm{n}}\text{)}{}^{\mathrm{n}}\text{)}$ be a maximal solution of the Navier–Stokes equations. We prove that u is C^∞ on $\text{]0,T}{}^1\text{[×}\text{R}{}^{\mathrm{n}}$ and there exists a constant $\text{ε}{}_1\text{>0}$, which depends only on n, such that if $\text{T}{}^1$ is finite then, for all $\text{ω∈S(}\text{R}{}^{\mathrm{n}}\text{)}{}^{\mathrm{n}}\text{,}$ we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Thermal stability and UV–Vis-NIR spectroscopy of a new erbium-doped fluorotellurite glass

A new transparent bulk glass from the system 76TeO₂?·?10ZnO?·?9.0PbO?·?1.0PbF₂?·?3.0Na₂O doped with Er³⁺ (TZPPN doped with Er³⁺) has been prepared using the conventional melt-quenching method. Results of differential thermal analysis (DTA) measurements indicate good thermal stability of this glass. The refractive indices at different wavelengths, the optical energy gap, the Sellmeier gap energy and the dispersion energy have been estimated. The Judd–Ofelt parameters, Ω _t (t?=?2,?4,?6) of Er³⁺ were evaluated from optical absorption spectra. Electric dipole, magnetic dipole type transition probabilities, spectroscopic quality factors, branching ratio and radiative lifetimes of several excited states of Er³⁺ have been predicted using intensity Judd–Ofelt parameters. The spectroscopic properties indicate that TZPPN glass doped with Er³⁺ is a promising candidate for laser applications and may be suitable for upconversion fibre optical devices.     

Ternary complexes in gels from agarose and from chemically‐modified agarose

Thermodynamic data and mechanical measurements are shown for gels prepared in aqueous binary solvents (water/DMSO, water/DMF, water/methyl formamide and water/formamide). When electrostatic interactions, as opposed to hydrogen bonding, can be established with the cosolvent (DMSO, DMF, methyl formamide) we come to the conclusion that ternary complexes are formed (agarose/water/cosolvent). In the case of chemically‐modified agarose (OH groups replaced by OCH₃ groups) we suggest that these cosolvents are directly involved in the formation of the gel.     

Global Behavior of Positive Solutions of a Generalized Lane–Emden System of Nonlinear Differential Equations

In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations:

$$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$

where \(r,\,s\in {\mathbb {R}}\), \(\alpha ,\,\beta <1\) such that \(\gamma :=(1-\alpha )(1-\beta )-rs>0\) and the nonnegative functions \(a,\,b\) satisfy some conditions related to the Karamata regular variation theory.

     

Multigrid solvers in reconfigurable hardware

The problem of finding the solution of partial differential equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high convergence rate which is independent of the problem size. For this reason, many attempts for exploiting the inherent parallelism of Multigrid have been made to achieve the desired efficiency and scalability of the method. Yet, most efforts fail in this respect due to many factors (time, resources) governed by software implementations. In this paper, we present a hardware implementation of the V-cycle Multigrid method for finding the solution of a 2D-Poisson equation. We use Handel-C to implement our hardware design, which we map onto available field programmable gate arrays (FPGAs). We analyze the implementation performance using the FPGA vendor's tools. We demonstrate the robustness of Multigrid over other similar iterative solvers, such as Jacobi and successive over relaxation (SOR  ), in both hardware and software. We compare our findings with a C++$\mathrm{C}++$ version of each algorithm. The obtained results show better performance when compared to existing software versions.     

Combined perturbation effects for a class of nonlinear fourth-order Navier problems

We study a class of nonlinear elliptic problems with Navier boundary condition and involving the Laplace and the biharmonic operators. The main result of this paper establishes a sufficient condition for the existence of nontrivial weak solutions, in relationship with the values of a certain real parameter with respect to the principal eigenvalue of the Laplace operator.     

An optimisation method for separating and rebuilding one-dimensional dispersive waves from multi-point measurements. Application to elastic or viscoelastic bars

When using a classical SHPB (split Hopkinson pressure bar) set-up, the useful measuring time is limited by the length of the bars, so that the maximum strain which can be measured in material testing applications is also limited. In this paper, a new method with no time limits is presented for measuring the force and displacement at any station on a bar from strain or velocity measurements performed at various places on the bar. The method takes the wave dispersion into account, as must inevitably be done when making long time measurements. It can be applied to one-dimensional and single-mode waves of all kinds propagating through a medium (flexural waves in beams, acoustic waves in wave guides, etc.). With bars of usual sizes, the measuring time can be up to 50 times longer than the time available with classical methods. An analysis of the sensitivity of the results to the accuracy of the experimental data and to the quality of the wave propagation modelling was also carried out. Experimental results are given which show the efficiency of the method.     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.     

Poly(ethylene glycol)--oligolactates with monodisperse hydrophobic blocks: preparation, characterization, and behavior in water

Methoxypoly(ethylene glycol)-b-oligo-L-lactate (mPEG-b-OLA) diblock oligomers with monodisperse OLA blocks were obtained by fractionation of polydisperse block oligomers using preparative HPLC. The fractionated oligomers were composed of an mPEG block with a molecular weight of 350, 550, or 750 and an OLA block with a degree of polymerization of 4, 6, 8, or 10. The diblock oligomers with a low PEG content were fully amorphous, with glass transition temperatures ranging from -60 to -20 degrees C, indicating that the blocks were miscible. Upon heating aqueous dispersions of the block oligomers, cloud points, depending on the PEG/OLA ratio of the block oligomer, were observed at temperatures above 40 degrees C. The monodispersity of the hydrophobic block enabled the amphiphilic molecules to form nanoparticles in water with a hydrodynamic radius of 130-300 nm, at concentrations above the critical aggregation concentration (0.4-1 mg/mL), whereas polydisperse mPEG-b-OLAs gave formation of large aggregates. Static light scattering measurements showed that the nanoparticles have a low density (0.6-25 mg/mL), indicating that the particles are highly hydrated. In agreement herewith, the (1)H NMR spectra of nanoparticles in D2O closely resembled spectra in a good solvent for both blocks (CDCl3). It is therefore suggested that the nanoparticles contain a hydrated core of mPEG-b-OLA block oligomers, stabilized by a thin outer PEG layer. The particles were stable for two weeks, except for the mPEG350 series and mPEG750-b-OLA4, indicating that both the PEG block size and the PEG weight fraction of the oligomers determine their stability. The evident self-emulsifying properties of mPEG-b-oligo-l-lactates with monodisperse hydrophobic blocks as demonstrated in this study, together with their expected biocompatibility and biodegradability, make these systems well suitable for pharmaceutical applications.     

Physicochemical characterization of degradable thermosensitive polymeric micelles

Amphiphilic AB block copolymers consisting of thermosensitive poly(N-(2-hydroxypropyl) methacrylamide lactate) and poly(ethylene glycol), pHPMAmDL-b-PEG, were synthesized via a macroinitiator route. Dynamic light scattering measurements showed that these block copolymers form polymeric micelles in water with a size of around 50 nm by heating of an aqueous polymer solution from below to above the critical micelle temperature (cmt). The critical micelle concentration as well as the cmt decreased with increasing pHPMAmDL block lengths, which can be attributed to the greater hydrophobicity of the thermosensitive block with increasing molecular weight. Cryogenic transmission electron microscopy analysis revealed that the micelles have a spherical shape with a narrow size distribution. 1H NMR measurements in D2O showed that the intensity of the peaks of the protons from the pHPMAmDL block significantly decreased above the cmt, indicating that the thermosensitive blocks indeed form the solidlike core of the micelles. Static light scattering measurements demonstrated that pHPMAmDL-b-PEG micelles with relatively large pHPMAmDL blocks possess a highly packed core that is stabilized by a dense layer of swollen PEG chains. FT-IR analysis indicated that dehydration of amide bonds in the pHPMAmDL block occurs when the polymer dissolved in water is heated from below to above its cmt. The micelles were stable when an aqueous solution of micelles was incubated at 37 degrees C and at pH 5.0, where the hydrolysis rate of lactate side groups is minimized. On the other hand, at pH 9.0, where hydrolysis of the lactic acid side groups occurs, the micelles started to swell after 1.5 h of incubation and complete dissolution of micelles was observed after 4 h as a result of hydrophilization of the thermosensitive block. Fluorescence spectroscopy measurements with pyrene loaded in the hydrophobic core of the micelles showed that when these micelles were incubated at pH 8.6 and at 37 degrees C the microenvironment of pyrene became increasingly hydrated in time during this swelling phase. The results demonstrate the potential applicability of pHPMAmDL-b-PEG block copolymer micelles for the controlled delivery of hydrophobic drugs.