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.     

Micro- and nano-mechanical characterization of polyamide 11 and its composites containing cellulose nanofibers

Nanocomposites from polyamide 11 and dried cellulose nanofibers (CNs), 16–30 nm in thickness and 50–400 nm in length, were prepared via direct melt mixing and their micro- and nano-mechanical properties were studied. (PF) QNM (Quantitative Nanomechanical Mapping) method was used to map nanomechanical properties at the surface of polyamide 11 and nanocomposites. This new AFM method emphasized both the increased modulus in nanocomposites as compared to the matrix and the microstructure on different levels in polyamide 11 and its nanocomposites. PF QNM showed that their crystalline structure consists of bundles of lamellar stacks, 200–350 nm in width and 20–40 nm wide lamellar stacks. Moreover, PF QNM study emphasized higher structural order in nanocomposites with 3 and 5 wt.% CNs and lower in the nanocomposite with 8 wt.% CNs as compared to the reference. These observations were verified and are consistent with both crystallinity values determined by DSC and micro-mechanical test results. The oriented bundles of lamellar stacks, observed by PF QNM, could be considered as the main blocks determining high mechanical properties for the studied nanomaterials.     

Investigation of thermal stability, spectral, magnetic, and antimicrobial behavior for new complexes of Ni(II), Cu(II), and Zn(II) with a bismacrocyclic ligand

Novel complexes of type M₂LCl₄·nH₂O (M: Ni, n = 4; M: Cu, n = 2.5 and M: Zn, n = 1.5; L: ligand resulted from 1,3-phenylenediamine, 3,6-diazaoctane-1,8-diamine, and formaldehyde one-pot condensation) were synthesized and characterized. The ligand was also isolated and characterized. The complexes features have been assigned from microanalytical, electrospray ionization tandem mass spectrometry, IR, UV–vis, ¹H NMR, and EPR spectra as well as magnetic data at room temperature. Simultaneous thermogravimetric/dynamic scanning calorimetry/evolved gas analysis measurements were performed to evidence the nature of the gaseous products formed in each step. Processes as water elimination, fragmentation, and oxidative degradation of the organic ligand as well as chloride elimination were observed during the thermal decomposition. The final product of decomposition was metal(II) oxide except for copper complex where CuCl remained also in the oxide network. The complexes exhibited an improved antibacterial activity in comparison with the ligand concerning both planktonic as well as biofilm-embedded cells.     

“Surface water” and “strong-bonded water” in cyclodextrins: a Karl Fischer titration approach

Cyclodextrins are some of the most used carriers for bioactive compounds (as host–guest complex) and many factors influence the association–dissociation of this complex, some of them being related to hydrophobicity. In the solid state, cyclodextrins contain two types of water molecules: “surface” water molecules (especially close to the crystal surface) and “strong-bonded” water molecules (especially from the cyclodextrin cavity), but the classification is hard to do, and the concentration of these water molecules are relatively difficult to estimate by simple methods. In the present study we used the volumetric Karl Fischer titration to estimate these types of water molecules in cyclodextrins by means of the rate of water reaction (related to diffusion from cyclodextrin crystals). “Surface” water molecules are titrated with rates between 1.8–2.8 mM/s for α-cyclodextrin, while for β-cyclodextrin these rates are little bit higher (2.9–3.4 mM/s). The rates corresponding to “strong-bonded” water molecules are approximately tens fold lower (0.05–0.3 mM/s for α-cyclodextrin and 0.15–0.33 mM/s for β-cyclodextrin). The approximate ratio between “surface” and “strong-bonded” water molecules could also be estimated by this simple and rapid method.     

Polyol-modified layered double hydroxides with attenuated basicity for a truly reversible capture of CO2

Dendrimers bearing hydroxyl groups supported by layered double hydroxides (CO₃–LDH) with Mg/Al ratio ranging from 1:1 to 5:1 showed improved properties for the reversible capture of carbon dioxide (CO₂). The adsorption capacity of the starting LDH was due to the intrinsic base-like behavior, and was found to depend on the Mg/Al ratio. When contacted with polyol dendrimers in aqueous media, no intercalation took place. This was explained in terms of low exfoliation grade of LDH and hydrophobic character of the dendrimer molecules. The latter rather adsorb on the external surface of the LDH stacks for low dendrimer loadings, or aggregate into organic clusters for higher contents. Analyses through thermal programmed desorption of CO₂ revealed that dendrimer incorporation advantageously attenuates the basicity strength of the starting LDH support, by lowering the desorption temperature. The OH groups of the organic moiety were found to display an amphoteric character, and act as the main adsorption sites. The weak interactions with CO₂ facilitate easier release of the major part of adsorbed CO₂ at temperature not exceeding 80–100 °C. On polyol organo-LDHs, the reversible CO₂ retention was discussed herein in terms of acid–base interactions. This concept allows envisaging the capture of diverse pollutants and other greenhouse gases by modifying the chemical groups on the dendritic moiety.     

Towards a receptor-free immobilization and SERS detection of urinary tract infections causative pathogens

Based on molecular-specific surface-enhanced Raman scattering (SERS) spectroscopy we were able to discriminate between rough and smooth strains of Escherichia coli and Proteus mirabilis bacteria. For this purpose, bacteria have been immobilized through electrostatic forces by inducing a positive charge on the glass slide. This way, SERS spectra on bacterial biomass and also on single bacteria could be recorded in less than 2 h, by using concentrated silver nanoparticles as SERS-active substrate. Single-bacterium SERS spectral fingerprints showed to be sensitive to the presence of the O-antigen at strain level and to the microorganisms growth phase. By using principal component analysis (PCA) on the SERS spectra recorded from E. coli and P. mirabilis, these two uropathogens could be fairly discriminated.     

Combined Experimental and Theoretical Insights into the Corrosion Inhibition Activity on Carbon Steel Iron of Phosphonic Acids

The inhibition effect of N,N′-phosphonomethylglycine (PMG) and vinyl phosphonic acid (VPA) on the 3% NaCl acidic solution corrosion of carbon steel iron was studied at different immersion times by potentiodynamic polarization, electrochemical impedance spectroscopy, attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy, and computational methods. It is found from the polarization studies that PMG and VPA behave as mixed-type inhibitors in NaCl. Values of charge transfer resistance (R_ct) and double layer capacitance (C_dl) in the absence and presence of inhibitors are determined. The PMG and VPA inhibitors were capable of inhibiting the corrosion process up to ≈91% and ≈85%, respectively. In the presence of PMG, the synergic effect of chlorine ions was observed. Density functional theory (DFT) was engaged to establish the adsorption site of PMG, VPA, and their deprotonated states. For studied compounds, the resulted values of E_LUMO, E_HOMO, energy gap (∆E), dipole moment (μ), electronic hardness (η), global softness (σ), electrophilic index (ω), and the electronic potential map are in concordance with the experimental data results regarding their corrosion inhibition behavior and adsorption on the metal surface.     

Attempts for Developing Novel Sugar-Based and Sugar-Free Sea Buckthorn Marmalades

Sea buckthorn (Hippophaė rhamnoides L.) is recognized as a valuable source of vitamin C and antioxidants, frequently used as nutraceuticals and cosmeceuticals. In the present study, attempts are made to produce and characterize a novel type of marmalade using sea buckthorn berries processed at 102 °C into marmalade in two combinations, with whole cane or stevia sugar. Changes in the phytochemical profile, antioxidant activity, color, shelf-life, texture, microbiological, and sensorial characteristics were determined. The total carotenoids content in the marmalades were significantly different, with values of 0.91 ± 0.03 mg/g dry weight (DW) in the sample with whole sugar cane (C_z) and 2.69 ± 0.14 mg/g DW in the sample with Stevia sugar (C_s). Significant values of polyphenols were found, of 59.41 ± 1.13 mg GAE/g DW in C_z and 72.44 ± 2.31 mg GAE/g DW in C_s, leading to an antioxidant activity of 45.12 ± 0.001 μMol Trolox/g DW and 118.07 ± 0.01 μMol Trolox/g DW, respectively. Accelerated storage study showed a decrease in all the phytochemicals, however no significant changes were found in antioxidant activity. Values of <100 CFU/g for yeasts and molds and <5 CFU/g for Enterobacteriaceae after 21 days of storage at the room temperature of the marmalades were determined. The sensorial and color results were more than acceptable. Overall, the results highlighted the potential of using sea buckthorn as a potential rich source of bioactive compounds to be used in the sugar-based products manufacturing.