Galerkin and Runge–Kutta methods: unified formulation,a posteriori error estimates and nodal superconvergence

We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods.     

Scope and limitations of the photooxidations of 2-(α-hydroxyalkyl)furans: synthesis of 2-hydroxy-exo-brevicomin

Photooxygenation of 2-(α-hydroxyalkyl)furans at 5 °C in MeOH followed by in situ reduction affords, in one synthetic operation, 6-hydroxy-3(2H)-pyranones and/or 5-hydroxy-2(5H)-furanones. The relative ratio of the final products is highly dependent on the substitution of the starting furan substrate. Photooxygenation of 2-(α,β-dihydroxyalkyl)furans followed by in situ reduction and ketalization with acid rapidly provides the 6,8-dioxabicyclo[3.2.1]oct-3-en-2-one framework. This new methodology was successfully applied to the synthesis of 2-hydroxy-exo-brevicomin.     

The influence of temperature on rheological properties of blood mixtures with different volume expanders—implications in numerical arterial hemodynamics simulations

During the complicated cardiac surgery on a non-beating heart with cardiopulmonary bypass, protection of the heart is accomplished by injecting cold cardioplegic solutions. In most forms of circulatory shock, it is necessary to immediately restore the circulating volume. Intravenous solutions of volume expanders, such as hydroxyethyl starch and dextrans, are used to increase the volume of fluid in the circulating blood. In this work, blood samples of six donors were obtained and used to prepare mixtures with different volume expanders in concentrations ranging from 10 to 50 vol./vol.%. The flow curves of all mixtures in the temperature range from 4°C to 37°C were constructed and fitted to the Herschel–Bulkley model, in order to extract the shear thinning and yield stress parameters. To assess the influence of the observed changes in the rheological properties of blood on the hemodynamics in arterial vasculature, a realistic three-dimensional rigid-wall computational model was constructed from MRI images of the right carotid bifurcation obtained in vivo from a healthy male volunteer. The time-varying flow field was numerically computed using the Newtonian model as well as the Herschel–Bulkley model with the Papanastasiou regularization. The numerical simulations indicate only moderate changes in the time-averaged flow field that become accentuated when the instantaneous flow field is considered. We also found that although the influence of temperature, hematocrit, and volume expanders on hemodynamics is significant, this can primarily be attributed to the changes in the nominal viscosity of the flow medium.     

On the mapping class group of a genus 2 handlebody

A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handlebodies, the group of automorphisms of this complex is used to characterize the mapping class group of the handlebody. In particular, it is shown that all automorphisms of the complex of incompressible surfaces are geometric, that is, induced by a homeomorphism of the handlebody.     

Promising fast energy transfer system via an easy synthesis: Bodipy-porphyrin dyads connected via a cyanuric chloride bridge, their synthesis, and electrochemical and photophysical investigations

The boron dipyrrin (Bodipy) chromophore was combined with either a free-base or a Zn porphyrin moiety (H(2)P and ZnP respectively), via an easy synthesis involving a cyanuric chloride bridging unit, yielding dyads Bodipy-H(2)P (4) and Bodipy-ZnP (5). The photophysical properties of Bodipy-H(2)P (4) and Bodipy-ZnP (5) were investigated by UV-Vis absorption and emission spectroscopy, cyclic voltammetry, and femtosecond transient absorption spectroscopy. The comparison of the absorption spectra and cyclic voltammograms of dyads Bodipy-H(2)P (4) and Bodipy-ZnP (5) with those of their model compounds Bodipy, H(2)P, and ZnP shows that the spectroscopic and electrochemical properties of the constituent chromophores are essentially retained in the dyads indicating negligible interaction between them in the ground state. In addition, luminescence and transient absorption experiments show that excitation of the Bodipy unit in Bodipy-H(2)P (4) and Bodipy-ZnP (5) into its first singlet excited state results in rapid Bodipy to porphyrin energy transfer-k(4) = 2.9 × 10(10) s(-1) and k(5) = 2.2 × 10(10) s(-1) for Bodipy-H(2)P (4) and Bodipy-ZnP (5), respectively-generating the first porphyrin-based singlet excited state. The porphyrin-based singlet excited states give rise to fluorescence or undergo intersystem crossing to the corresponding triplet excited states. The title complexes could also be used as precursors for further substitution on the third chlorine atom on the cyanuric acid moiety.     

Self-assembly into spheres of a hybrid diphenylalanine-porphyrin: increased fluorescence lifetime and conserved electronic properties

A series of protected phenylalanine and diphenylalanine derivatives have been coupled through a peptide bond to a monoaminoporphyrin to form new materials. A comparative study in solution and in the solid state has been performed and confirmed new and interesting properties for the self-assembled hybrid materials while conserving the electronic properties of the chromophore. Thus, they are powerful candidates for use in dye-sensitized solar cells.     

Application of association models to mixtures containing alkanolamines

Two association models, the CPA and sPC-SAFT equations of state, are applied to binary mixtures containing alkanolamines and hydrocarbons or water. CPA is applied to mixtures of MEA and DEA, while sPC-SAFT is applied to MEA-n-heptane liquid-liquid equilibria and MEA-water vapor-liquid equilibria. The role of association schemes is investigated in connection with CPA, while for sPC-SAFT emphasis is given on the role of different types of data in the determination of pure compound parameters suitable for mixture calculations. Moreover, the performance of CPA and sPC-SAFT for MEA-containing systems is compared. The investigation showed that vapor pressures and liquid densities were not sufficient for obtaining reliable parameters with either CPA or sPC-SAFT, but that at least one other type of information is needed. LLE data for a binary mixture of the associating component with an inert compound is very useful in the estimation. The simple 4-site scheme is suitable for both CPA and sPC-SAFT and little is gained by using more complex association schemes. Finally, the results of CPA and sPC-SAFT are overall similar and whatever differences are seen appear to be more related to details in the parametrization rather than the different functional forms of the two equations of state.     

Linking photo- and redoxactive phthalocyanines covalently to graphene

"Green" graphene: For the first time, the covalent attachment of a light-harvesting and electron-donating phthalocyanine to the basal plane of few-layer graphene is reported. Physicochemical characterizations reveal an ultrafast charge separation from the photoexcited phthalocyanine to few-layer graphene followed by a slower charge recombination.     

Rediscovering cobalt's surface chemistry

Cobalt is an active metal for a variety of commercially and environmentally significant heterogeneously catalysed processes. Despite its importance, Co's surface chemistry is less studied compared to other key industrial catalyst metals. This stems in part from the difficulties associated with single crystal preparation and stability. Recent advances in scanning probe microscopy have enabled the atomic scale study of the structural, electronic, and magnetic properties of well-defined Co nanoparticles on metal substrates. Such systems offer an excellent platform to investigate the adsorption, diffusion, dissociation, and reaction of catalytically relevant molecules. Here we discuss the current understanding of metal-supported Co nanoparticles, review the limited literature on molecular adsorption, and suggest ways that they can be used to explore Co's rich surface chemistry. Our discussion is accompanied by new high resolution scanning tunnelling microscopy data from our group, which illustrate some of the interesting properties of these complex systems.     

Raman spectroscopy and support vector machines for quick toxicological evaluation of titania nanoparticles

With the rapid development of nanotechnology products, there is a significant concern on the adverse effects that might be associated with them. Traditional biological assays are typically used to asses the toxicity in vitro. There are, however, questions regarding the suitability of these assays for this purpose, mainly due to the potential interaction of the particles with the utilized dyes. In addition, this process can be costly and time consuming, as a large number of different assays have to be used. To address some of these issues, Raman spectroscopy is used in this study to investigate the particle‐cell interactions. The spectrum of a living cell is a very complex and rich collection of data directly related to its chemical composition. To enhance the data resolution and make the detection of toxicity more robust, data‐mining techniques have been deployed. Furthermore, data‐mining techniques enable full automation of the entire process, minimizing user input. The Raman spectroscopy successfully evaluated the toxicity of TiO₂ nanoparticles by both the peak‐by‐peak analysis and with the implementation of support vector machines. The particles were found to display cytotoxicity after 36 h of exposure. The results were confirmed by MTT (3‐(4,5‐Dimethylthiazol‐2‐Yl)‐2,5‐Diphenyltetrazolium Bromide) assay and are in agreement with the existing literature on the subject. Overall, Raman spectroscopy appears to be among the very few techniques that exhibit low levels of interferences (obscuration, fluorescence, emission, etc.) from the particle addition. Since it does not rely on biomarkers, it can be used in situ for an extended period with minimal effects on the cellular biochemistry. Copyright © 2011 John Wiley & Sons, Ltd.