On the turbulent couette flow of an incompressible fluid with temperature-dependent viscosity

Summary Starting from energy and Navier-Stokes equations with temperature-dependent viscosity, we have obtained the Reynolds equations for the mean values of velocity, temperature and pressure. We have then applied these equations to the Couette flow; on the well-known hypothesis of mixing-length and Prandtl turbulent number, the above mentioned relations have been written in a more amenable form.Some general considerations concerning the reciprocal dependence between temperature and velocity gradients at wall have been deduced.Finally some solutions numerically obtained for several values of Reynolds number are given and discussed in some detail to point out the influence of the temperature-dependent viscosity.

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Sommario Introducendo nelle equazioni dell'energia e di Navier-Stokes le parti medie e fluttuanti della velocità, temperatura, pressione e viscosità, vengono ricavate le cosiddette equazioni di Reynolds, ossia le equazioni che descrivono i campi di velocità e temperatura medi. Dal confronto di quest'ultime, in cui la viscosità è considerata dipendente dalla temperatura, con quelle originarie di Reynolds si deduce la forma che nel caso in esame assumono gli sforzi apparenti.Successivamente le equazioni ottenute vengono applicate al moto a Couette e discusse, dopo aver introdotto in esse le ipotesi della lunghezza di miscelamento e del numero di Prandtl turbolento; da questa analisi vengono tratte alcune conclusioni di carattere generale riguardanti i legami tra il campo dinamico e quello termico. Infine vengono date alcune soluzioni ottenute per via numerica, le quali illustrano l'influenza che sulle distribuzioni di temperatura e velocità viene esercitata dalla dipendenza della viscosità dalla temperatura.

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Synthesis and aggregation behaviour of a new sultaine surfactant

The aggregation properties of a new sultaine surfactant have been studied in buffered aqueous solution at pH 7.4 under controlled condition of osmolarity. Spontaneously formed sultaine vesicles with a mean diameter of about 1 μm can be observed by optical microscopy. The phase behaviour of the surfactant has been investigated by differential scanning calorimetry (DSC) and Nile Red fluorescence. Two critical vesicular concentrations (CVC(1) and CVC(2)) have been fluorimetrically measured, by using pyrene and Nile Red as the fluorescent probes. The two populations of vesicles behave differently as a consequence of their size. The stability of extruded large unilamellar vesicles (LUV) formed slightly above the CVC(1) has been evaluated in the temperature range 25-75°C by following the rate of spontaneous release of entrapped 5(6)-carboxyfluorescein (CF). The stability of the same vesicles at 70°C has also been investigated under osmotic stress obtained by adding NaCl or sucrose to the bulk solution. At a sultaine concentration above the CVC(2) LUV tend to associate and form stable larger closely packed aggregates as suggested by Dynamic Laser Light Scattering and rheological measurements.     

Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance

In this paper, we describe nuclear magnetic resonance measurements of water diffusion in highly confined and heterogeneous colloidal systems using an anomalous diffusion model. For the first time, temporal and spatial fractional exponents, α and μ, introduced within the framework of continuous time random walk, are simultaneously measured by pulsed gradient spin-echo NMR technique in samples of micro-beads dispersed in aqueous solution. In order to mimic media with low and high level of disorder, mono-dispersed and poly-dispersed samples are used. We find that the exponent α depends on the disorder degree of the system. Conversely, the exponent μ depends on both bead sizes and magnetic susceptibility differences within samples. The new procedure proposed here may be a useful tool to probe porous materials and microstructural features of biological tissue.     

In vitro anti-HMPV activity of meroditerpenoids from marine alga Stypopodium zonale (Dictyotales)

In this paper, we evaluated the antiviral activity against HMPV replication of crude extract of the marine algae Stypopodium zonale and of two meroditerpenoids obtained from it, atomaric acid and epitaondiol, and a methyl ester derivative of atomaric acid. Their selectivity indexes were 20.78, >56.81, 49.26 and 12.82, respectively. Compared to ribavirin, the substances showed a relatively low cytotoxicity on LLC-MK2 cells, with a significant antiviral activity, inhibiting at least 90% of viral replication in vitro, which demonstrates the potential of these marine natural products to combat infections caused by HMPV in vitro.     

On partial tilting modules and right bounded complexes

We construct rather short partial tilting complexes [(T)\dot]{\dot T} such that quite different indecomposable right bounded complexes [(C)\dot]{\dot C} have the property that any morphism from [(T)\dot]{\dot T} to a shift of [(C)\dot]{\dot C} is homotopic to zero. We also show that, for some [(T)\dot]{\dot T} , the strategy to obtain a bounded complex [(C)\dot]{\dot C} as a mutation of [(T)\dot]{\dot T} is not unique.     

Synthesis of polysiloxane xerogels with fluorine-containing groups in the surface layer and their sorption properties

Hydrolysis and polycondensation reactions of tetraethoxysilane (TEOS) with 3,3,3-trifluoropropyl-trimethoxysilane (TFMS) or 1H,1H,2H,2H-perfluorooctyltriethoxysilane (PFES) were used to synthesize xerogels functionalized with fluorine-containing groups. According to transmission electron microscopy, the skeletons of synthesized polysiloxane xerogels have globular structures and consist of agglomerates of particles with fluorinated groups on their surfaces. FTIR spectroscopy showed that primary xerogel particles possess spatial polysiloxane networks, with fluorinated groups along with silanol groups and water in the surface layer. According to thermal analyses, the water content was 3–8 wt.%, and it decreased with increasing length of the fluorinated chain. Thermal destruction of the surface layer starts above 300 °C. The sorbents that were obtained were predominantly mesoporous materials with well-developed porous structures (S_BET = 400–960 m² g⁻¹, V_s = 0.66–0.93 cm³ g⁻¹). The influence of the TEOS/functional silane ratio and the natures of the functional groups on the structural and adsorptive properties were shown. The samples synthesized are organophilic. The affinity for n-hexane increases with increasing length of the fluorine-containing chain (PFES) and the content of fluorinated groups in the surface layer. The hybrid organic–inorganic materials that were obtained can be used for adsorption of hydrocarbons, including oil, from water.     

Alkoxyamine-cyanoborane adducts: efficient cyanoborane transfer agents

We report the synthesis of the hitherto unknown zwitterionic alkoxyamino cyanoboranes by reduction of O-alkyloximes with sodium cyanoborohydride; unprecedented cyanoboronated N-alkoxyformamidines were also isolated as by-products. Boronated alkoxyamines were found to be efficient cyanoborane transfer agents towards more basic amines, including aminosugars; they were also successfully transformed into neoglycoconjugates by the neoglycorandomization reaction with reducing sugars.     

Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon

Motivated by the study of gauge field vortices, we consider a mean field equation on the standard sphere 𝕊² involving a Dirac distribution supported at a point P ∈ 𝕊². Consistently with the physical applications, we show that solutions “concentrate” precisely around the point P for some limiting value of a given parameter. We use this fact to obtain symmetry (about the axis ) and uniqueness property for the solution. The presence of the Dirac measure makes such a task particularly delicate to handle from the analytical point of view. In fact, the bubbling phenomenon about the singularity allows the existence of solution sequences with a double‐peak profile near P. The new and more delicate part of this paper is to exclude this possibility by using the method of moving planes together with the Alexandrov‐Bol inequality. © 2011 Wiley Periodicals, Inc.     

A coassociativeC *-quantum group with nonintegral dimensions

By weakening the counit and antipode axioms of aC ^*-Hopf algebra and allowing for the coassociative coproduct to be nonunital, we obtain a quantum group, that we call aweak C ^*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every finite-dimensional weakC ^*-Hopf algebra has a dual which is again a weakC ^*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.Supported by the Hungarian Scientific Research Fund, OTKA T 016 233.Supported by the Hungarian Scientific Research Fund, OTKA-1815.