Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Synthesis and biological evaluation of 6-oxa-nor-tropane glycomimetics as glycosidase inhibitors

The preparation of polyhydroxylated 6-oxa-nor-tropane glycomimetics structurally related to the glycosidase inhibitor family of the calystegines is reported. The synthetic strategy involves the furanose→piperidine rearrangement of 5-deoxy-5-ureido-l-idose precursors, followed by intramolecular glycosylation involving the primary hydroxyl group. Inversion of the configuration at C-3 in the resulting 6-oxa-(+)-calystegine B₂ analogue allows accessing the elusive 3-epi-6-oxa-(+)-calystegine B₂ skeleton. Acid-catalyzed opening of the nor-tropane bicycle was observed, however, which could be avoided by careful neutralization of the reaction mixture. The inhibition results suggest that (+)-calystegine B₂ derivatives and the corresponding C-3 epimers can be seen as glucomimetics and galactomimetics, respectively, pointing to a 1-azasugar mode of action for this family of alkaloids.     

Willmore submanifolds of the Möbius space and a Bernstein-type theorem

We study Willmore immersed submanifoldsf: M ^m →S ⁿ into then-Möbius space, withm≥2, as critical points of a conformally invariant functionalW. We compute the Euler-Lagrange equation and relate this functional with another one applied to the conformal Gauss map of immersions intoS ⁿ . We solve a Bernestein-type problem for compact Willmore hypersurfaces ofS ⁿ , namely, if ?a ∈? ⁿ⁺² such that <γf, a > ≠ 0 onM, whereγ _f is the hyperbolic conformal Gauss map and <, > is the Lorentz inner product of? ⁿ⁺², and iff satisfies an additional condition, thenf(M) is an (n?1)-sphere.     

Molybdenum(VI) and molybdenum(V) mononuclear and dinuclear complexes with 1,3-diphenyl-1,3-propanedione

Summary The synthesis and the dinuclear or mononuclear nature of several molybdenum(VI) and molybdenum(V) oxocomplexes derived from 1,3-diphenyl-1,3-propanedione (HLL) are described. These complexes were identified by i.r. and electronic spectra, magnetic susceptibility and analytical data, and are assigned the following formulae: [MoO₂(LL)₂], [Mo₂O₅(LL)₂], [Mo₂O₄(LL)₂], [MoOCl(LL)₂], [MoCl₂(LL)] and [MoO(OH)(LL)₂)]. The low magnetic moments of the dinuclear complexes are due, in part, to intramolecular interactions. The i.r. data show that the dionate is bound by two oxygen atoms forming a chelate six-membered ring.     

Potentiometric studies on the complexation of copper(II) by phenolic acids as discrete ligand models of humic substances

Studies on the complexation of copper(II) by phenolic acids, as ligand models of humic substances were done by potentiometry. The acids under study were: 3,4-dihydroxyhydrocinnamic acid or hydrocaffeic acid (1), 3,4-dihydroxyphenylacetic acid (2) and 3,4-dihydroxybenzoic acid or protocatechuic acid (3). Acidity constants of the ligands and the formation constants of metal-ligand complexes were evaluated by computer programs. The carboxylic group of the phenolic acids has different pK_a1 values, being the dissociation constants intrinsically related with the distance between the function and the aromatic nucleus. The results obtained allow concluding that acidity constants of the catechol moiety of the compounds are similar with pK_a2 and pK_a3 values between 9.47-9.41 and 11.55-11.70. The complexation properties of the three ligands towards copper(II) ion are quite similar, being the species found not different either in nature or stability. Although the model ligands have some structural differences no significant differences were found in their complexation properties towards copper(II). So, it can be postulated that complexation process is intrinsically related with the presence of a catechol group.     

Vascular endothelial and smooth muscle cell culture on NaOH-treated poly(epsilon-caprolactone) films: a preliminary study for vascular graft development

Tissue engineering offers the potential of providing vessels that can be used to replace diseased and damaged native blood vessels. The endothelization of a synthetic vascular graft minimizes the failures associated with blood clotting and platelet activation. The aim of this study was to culture vascular-derived endothelial and smooth muscle cells on both untreated and NaOH-treated poly(epsilon-caprolactone) (PCL) films, a biocompatible and bio-resorbable polymer, and to evaluate the behavior of both cell types as a preliminary study for vascular graft development. PCL films were prepared by hot pressing; characterized by DSC, IR, SEM, and scanning force microscopy; and treated with NaOH to increase the surface hydrophilicity before cell culture. Endothelial and smooth muscle cells, isolated from pig cava vein, were characterized by immunofluorescence and confocal microscopy studies of endothelial nitric oxide synthase and alpha-smooth muscle actin. Good adhesion, growth, viability and morphology of both the endothelial and smooth muscle cells on PCL films were obtained, but a light stimulation of mitochondrial activity was observed during short culture times. NaOH treatment improved the adhesion and enhanced the proliferation in both cell types. This verified the possible use of this modified polymer as a support in the preparation of a synthetic vascular graft. [Diagram: see text] SEM micrograph of smooth muscle cells cultured on NaOH-treated PCL film. (Original magnification: 1000x).