Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Preparation of stationary phases for open-tubular capillary electrochromatography using the sol-gel method

Capillary electrochromatography requires the deposition of a stationary phase inside the capillary. In this paper the sol-gel method is proposed for this purpose. The gels were prepared externally and injected into a fused-silica capillary, where anchorage to the capillary wall was possible through condensation reactions between the silanol groups of the capillary wall and the residual silanol groups the gel. Contrary to a commonly used practice, alkaline pretreatment of the inner capillary wall prior to the introduction and anchoring of the gel was found to be only marginally effective in improving the mechanical stability of the column. The influence of various parameters, such as the pH, the water content, the presence of alcohol (ethanol) on the formation of tetraethoxysilane (TEOS)-n-octyltriethoxysilane (C8-TEOS) hybrid gels of varied composition is discussed. The pH and the amount of water present were found to be the determining factors in the preparation of a stable gel with the desired mechanical and chromatographic properties. By carrying out the gel formation at 80 degrees C, capillary columns could be produced in 2.5 h. While an acidic pH was required during (external) gel formation, subsequent treatment of the gel inside the capillary with an alkaline solution ('aging') was found to improve separation and stationary phase capacity significantly. The capillary columns were subsequently used to separate a mixture of polycyclic aromatic hydrocarbons in less than 3 min.     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.     

One-Step Synthesis of Monolithic Silica Nanocomposites in Fused Silica Capillaries

The ideal way to prepare efficient, yet robust stationary phases for microanalytical high-resolution methods such as capillary chromatography and electrochromatography remains to be defined. In this contribution a one step sol-gel process is proposed for the production of monolithic, macroporous nanocomposite phases in fused silica capillaries, which require no additional derivatization, since they already bear the interactive (C8) moieties. The effect of the catalyst, the water content, the pH, as well as that of certain additives on monolith formation and porosity is investigated. Volume shrinkage and a tendency to crack were the major obstacles to overcome. Homogeneous stationary phases could be produced by applying a pH gradient during sol formation, thereby changing the catalytic principle from acidic (0.1 M HCl) to basic (gradual formation of OH^– as a consequence of the hydrolysis of N-methylformamide). Gelation/coacervation of suchgels could be induced by the addition of N,N-diethylamine. The water content during sol formation was determined as decisive for pore formation, with 250% of the amount theoretically needed for complete hydrolysis of all precursors giving optimal results. The volume shrinkage problem during xerogel formation was resolved by integrating dialkyldialkoxysilane units (dimethyldiethoxysilane 35 mol%) into the silica network.     

Nanocrystals grown in amorphous Cr and CrNi thin films

The structure of vacuum annealed amorphous sputtered Cr and CrNi (55:45) thin films has been studied by transmission electron microscopy (TEM) and electron diffraction (TED). The thin films with thicknesses ranging from 150 to 600 Å were annealed while still on their alkali halide substrates under high vacuum at temperatures ranging from 200 to 370°C. The TEM and TED data permitted to establish the annealing conditions (temperature, duration), which lead to the nucleation and growth of nanosized crystals in the Cr and CrNi icosahedral glasses.     

Preparation and characterisation of thermoresponsive poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethyl acrylate)] microspheres as a matrix for the pulsed release of drugs

Despite the large number of publications and patents concerning pH/thermoresponsive polymers, few data are available concerning the preparation of thermoresponsive cross-linked microspheres from preformed polymers. Therefore, N-isopropylacrylamide-co-acrylamide-co-(2-hydroxyethyl acrylate) copolymers were obtained as a new thermoresponsive material with a lower critical solution temperature (LCST) around 36 degrees C, in phosphate buffer at pH 7.4, and with a cross-linkable OH group in their structure. The LCST value was determined both by UV spectroscopy and microcalorimetric analysis. These copolymers were solubilised in acidified aqueous solution below their LCST, dispersed in mineral oil, and transformed into stable microspheres by cross-linking with glutaraldehyde. The thermoresponsive microspheres were characterised by optical and scanning electron microscopy, degree of swelling, and water retention. The pore dimensions of the microspheres and the retention volumes of some drugs and typical compounds were evaluated at different temperatures by liquid chromatography. Indomethacin, as a model drug, was included in the microspheres by the solvent evaporation method. Finally, the influence of temperature and of temperature cycling on drug release was investigated.     

Sur les fibrés instables de rang 2 sur ℙ3 (ℂ)

Sans résumé