Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Decomposing total IR spectra of aqueous systems into solute and solvent contributions: a computational approach using maximally localized Wannier orbitals

The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.     

Isomerization of a peptidic fragment studied theoretically in vacuum and in explicit water solvent at finite temperature

The cis-trans isomerization of N-methylacetamide, a molecular model of the polypeptide chain, is examined via umbrella sampling Car-Parrinello MD and classical MD, in both gas and solution phases at 300 K. A new analysis of the C(O)-N bond interconversion and a full examination of the solvent shell structure are presented.     

Two-dimensional incompressible viscous flow around a small obstacle

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω₀ and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier–Stokes system, with initial vorticity ω₀ + γδ, where δ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in Iftimie et al. (Comm. Part. Differ. Eqn. 28, 349–379 (2003)), where the effect of the small obstacle appears in the coefficients of the PDE and not only in the initial data. The main ingredients of the proof are L ^p − L ^q estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato’s fixed point method, energy estimates, renormalization and interpolation.     

Opérateurs différentiels magnétiques : stabilité des trous dans le spectre,invariance du spectre essentiel et applications

We study here the problem of geometry optimization for a crystal in the Thomas–Fermi–Von Weizsäcker (TFW) solid-state setting, i.e., the problem of minimizing the TFW energy with respect to the periodic lattice defining the positions of the nuclei. We show the existence of such a minimum, and use for that purpose the TFW models of polymers and thin films defined in a previous work (X. Blanc and C. Le Bris, Adv. Differential Equations, 5, 977–1032, 2000).     

TiO2 thin films as sensing gas materials

TiO₂ thin films were prepared by DC reactive magnetron sputtering on heated Si, quartz and glass substrates using O₂ and water vapor as reactive gases. The percentage of anatase and rutile as well as the grain size strongly depend on the deposition conditions, as revealed by X-ray diffraction patterns. The films deposited on Si substrates are pure rutile, while a mixed anatase/rutile structure occurs in the films deposited on glass and quartz substrates. Smaller grain rutile and anatase films were prepared in a water vapor atmosphere, in contrast to the films grown in oxygen. The former choice considerably increases the sensing properties of titanium dioxide films. The gas sensitivity was investigated for some reducing gases (methane, acetone, ethanol and liquefied petroleum gas) and the optimum operating temperatures were found.     

Spectral signatures and molecular origin of acid dissociation intermediates

The existence of a broad, mid-infrared absorption ranging from 1000 to 3000 cm(-1) is usually interpreted as a signature for the existence of protonated water networks. Herein, we use cryogenic mixtures of water and hydrogen fluoride (HF) and show experimental and computational evidence that similarly wide absorptions can be generated by a broad distribution of proton-shared and ion pair complexes. In the present case, we demonstrate that the broadening is mainly inhomogeneous, reflecting the fact that the topology of the first solvation shell determines the local degree of ionization and the shared-proton asymmetric stretching frequency within H2O x HF complexes. The extreme sensitivity of the proton transfer potential energy hypersurface to local hydrogen bonding topologies modulates its vibrational frequency from 2800 down to approximately 1300 cm(-1), the latter value being characteristic of solvation geometries that yield similar condensed-phase proton affinities for H2O and fluoride. By linking the local degree of ionization to the solvation pattern, we are able to propose a mechanism of ionization for HF in aqueous solutions and to explain some of their unusual properties at large concentrations. However, an important conclusion of broad scientific interest is our prediction that spectral signatures that are normally attributed to protonated water networks could also reveal the presence of strong hydrogen bonds between un-ionized acids and water molecules, with important consequences to spectroscopic investigations of biologically relevant proton channels and pumps.     

Thermo-oxidative degradation of some elastomers with a high content of 3,4 isoprene units

New elastomers with high content of 3,4 isoprene units have been developed during the last decades in an attempt to ensure superior performances of the final products and the present study is devoted to the investigation of some peculiarities of their ageing behaviour. On thermo-oxidative degradation, 3,4 isoprene units are less affected in comparison to cis-1, 4 and trans-1, 4 isoprene units. The degradation process consists mainly in splitting of the main chains at temperatures of 80–100 °C while at higher temperatures (120–130 °C) branching becomes a significant modification and this reaction is enhanced for the polymers containing preponderantly 3,4 units. Such behaviour leads to the fact that the processability of polymers containing high amounts of 1,2 and 1,3 isoprene units is less affected by thermo-oxidative degradation in comparison with cis-1, 4-polyisoprene, which could be explained by the fact that large amounts of double bonds are not present in the backbone of macromolecules but in the pendent groups.