A new proof of partial regularity of solutions to Navier-Stokes equations

In this paper we give a new proof of the partial regularity of solutions to the incompressible Navier-Stokes equation in dimension 3 first proved by Caffarelli, Kohn and Nirenberg. The proof relies on a method introduced by De Giorgi for elliptic equations. This work was supported in part by NSF Grant DMS-0607953.     

Iterated Stochastic Processes: Simulation and Relationship with High Order Partial Differential Equations

In this paper, we consider the composition of two independent processes: one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler scheme to simulate the trajectories of the corresponding iterated processes on a fixed time interval. This algorithm is natural and can be implemented easily. We show that it converges almost surely, uniformly in time, with a rate of convergence of order 1/4 and propose an estimation of the error. We then extend the well known Feynman-Kac formula which gives a probabilistic representation of partial differential equations (PDEs), to its higher order version using iterated processes. In particular we consider general position processes which are not necessarily Markovian or are indexed by the real line but real valued. We also weaken some assumptions from previous works. We show that intertwining diffusions are related to transformations of high order PDEs. Combining our numerical scheme with the Feynman-Kac formula, we simulate functionals of the trajectories and solutions to fourth order PDEs that are naturally associated to a general class of iterated processes.     

Instabilités de l'écoulement produisant le bruit de fenteFlow instabilities producing the slot-tone

The nature of the instability governing the self-sustained tones produced by a low Mach number plane jet impinging on a slotted plate, known as slot-tone, is identified experimentally. For a given Reynolds number, the natural shear-layer and the jet column mode frequencies of the free jet delimit the values of the measured slot-tone operating frequencies. The oscillations at lower frequencies are the result of the amplification of the jet column mode, and those at higher frequencies correspond to the shear layer instabilities. To cite this article: A. Billon et al., C. R. Mecanique 332 (2004).     

Three-dimensional effects on line-of-sight visualization measurements of supersonic and hypersonic flow over cylinders

Flow visualization experiments were performed for supersonic and hypersonic nitrogen test gas flows over a cylinder. The results were used to quantify the influence of three-dimensional effects on optical line-of-sight visualization measurements. Images of cylindrical models of varying aspect ratios (length to diameter) were taken. Shock stand-off distance measurements for the models were compared with a two-dimensional approximation and numerical simulations. For aspect ratios of two and above, the two-dimensional approximation was acceptable within experimental uncertainty. The measured shock stand-off decreased by less than 5% from an asymptotic value for an infinite length cylinder. For smaller aspect ratios, a correction factor for the shock stand-off needs to be applied if comparisons between the two-dimensional approximation and experimental measurements are to be drawn. An estimate of this correction factor has been derived from an empirical fit to the available data.      

Host-Guest Interactions between Calixarenes and Cp(2)NbCl(2)

The possible inclusion complexes of Cp₂NbCl₂ into calixarenes hosts have been investigated. The existence of a true inclusion complex in the solid state was confirmed by a combination of NMR, ab-initio calculations, thermogravimetric analysis, FTIR, Raman and PXRD. Ab-initio calculations, ¹H NMR solution and solid state ¹³C CP-MAS NMR results demonstrated that p-sulfonic calix[6]arene does form an inclusion complex with Cp₂NbCl₂. Raman spectroscopy showed, for the inclusion compound of p-sulfonic calix[6]arene-Cp₂NbCl₂, a band between 500 and 850 cm⁻¹ characteristic of Nb-O vibration. This result suggests that Nb(V) may engage in coordination with the oxygen of the sulfonate group, as part of the host-guest interaction. However, it is important to mention that the niobocene dichloride (Cp₂NbCl₂) dissolves in water and undergoes oxidation and hydrolysis processes to yield Cp₂NbCl₂(OH) species. For that reason this band does not exclude that the Nb-O band belongs to Cp₂NbCl₂(OH). Solid State ¹³C CP-MAS NMR and solution ¹H NMR spectroscopies together with ab-initio results showed that Cp₂NbCl₂ is included in the p-sulfonic calix[6]arene cavity, with both Cp rings inside the cavity. In contrast, the solution ¹H NMR results demonstrated that calix[6]arene does not form inclusion complex with Cp₂NbCl₂ in CDCl₃ solution. Cp₂NbCl₂ is not included in the calix[6]arene cavity, possibly due to the lack of sulfonate heads which promote Nb-O interactions and assist the inclusion of Cp₂NbCl₂ into the cavity.     

Interfacial impregnation chemistry in the synthesis of nickel catalysts supported on titania

The interfacial chemistry of the impregnation step involved in the preparation of nickel catalysts supported on titania is presented. Several methodologies based on deposition data, pH measurements, potentiometric mass titrations, and microelectrophoresis have been used in conjunction with diffuse reflectance UV/Vis/NIR spectroscopy, simulations, and semiempirical quantum chemical calculations. Three mononuclear inner-sphere complexes were formed at the compact layer of the "titania/electrolyte solution" interface: A monosubstituted, dihydrolyzed complex above a terminal oxo group, a disubstituted, dihydrolyzed complex above two terminal adjacent oxo groups, and a disubstituted, nonhydrolyzed complex above one terminal and one bridging adjacent oxo groups. The monosubstituted, dihydrolyzed complex predominates. The contribution of the disubstituted configurations is also important at very low Ni(II) surface concentration, but it decreases as the Ni(II) surface concentration increases. In addition, bi- and trinuclear inner-sphere complexes were formed. The receptor site involves one bridging and two terminal oxo groups in the first case and two bridging and three terminal oxo groups in the second case. The relative surface concentrations of these configurations increase initially with Ni(II) surface concentration and then remain practically constant. The understanding of these interfacial processes at a molecular level is very important to shift the catalytic synthesis from an art to a science as well as to obtain strict control of the impregnation step and, to some extent, of the whole preparative sequence. This study is very relevant to the synthesis of submonolayer/monolayer nickel catalysts supported on TiO(2) following equilibrium deposition filtration (otherwise called equilibrium adsorption).     

Helichrysum gymnocephalum essential oil: chemical composition and cytotoxic, antimalarial and antioxidant activities, attribution of the activity origin by correlations

Helichrysum gymnocephalum essential oil (EO) was prepared by hydrodistillation of its leaves and characterized by GC-MS and quantified by GC-FID. Twenty three compounds were identified. 1,8-Cineole (47.4%), bicyclosesquiphellandrene (5.6%), γ-curcumene (5.6%), α-amorphene (5.1%) and bicyclogermacrene (5%) were the main components. Our results confirmed the important chemical variability of H. gymnocephalum. The essential oil was tested in vitro for cytotoxic (on human breast cancer cells MCF-7), antimalarial (Plasmodium falciparum: FcB1-Columbia strain, chloroquine-resistant) and antioxidant (ABTS and DPPH assays) activities. H. gymnocephalum EO was found to be active against MCF-7 cells, with an IC(50) of 16 ± 2 mg/L. The essential oil was active against P. falciparum (IC(50) = 25 ± 1 mg/L). However, the essential oil exhibited a poor antioxidant activity in the DPPH (IC(50) value > 1,000 mg/L) and ABTS (IC(50) value = 1,487.67 ± 47.70 mg/L) assays. We have reviewed the existing results on the anticancer activity of essential oils on MCF-7 cell line and on their antiplasmodial activity against the P. falciparum. The aim was to establish correlations between the identified compounds and their biological activities (antiplasmodial and anticancer). β-Selinene (R2 = 0.76), α-terpinolene (R2 = 0.88) and aromadendrene (R2 = 0.90) presented a higher relationship with the anti-cancer activity. However, only calamenene (R2 = 0.70) showed a significant correlation for the antiplasmodial activity.     

A Geometric Framework for Stochastic Shape Analysis

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in the large deformation diffeomorphic metric mapping framework for shape analysis and image registration. The stochasticity thereby models errors or uncertainties of the flow in following the prescribed deformation velocity. The approach is illustrated in the example of finite-dimensional landmark manifolds, whose stochastic evolution is studied both via the Fokker–Planck equation and by numerical simulations. We derive two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points. The first of the two approaches matches moments of the Fokker–Planck equation to sample moments of the data, while the second approach employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood. We derive and numerically test the ability of the two approaches to infer the spatial correlation length of the underlying noise.

     

Effect of excess methanol addition on the morphology of sonogel-derived silica

Sonochemical processing techniques may be used to create fully miscible sols without the initial addition of a solvent. However, by intentionally adding excess alcohol to a sol produced by sonication, it is possible to manipulate the porosity of the resulting sonogel. Sonogels of systematically varied methanol content were prepared using a two-step process with subsequent drying at 60°C. The as-prepared sol with no excess methanol produced a purely microporous solid. The addition of excess methanol to the sol resulted in the formation of mixed microporosity and mesoporosity as revealed by nitrogen gas adsorption and transmission electron microscopy.