Block triangular preconditioners for linearization schemes of the Rayleigh–Bénard convection problem

In this paper, we compare two block triangular preconditioners for different linearizations of the Rayleigh–Bénard convection problem discretized with finite element methods. The two preconditioners differ in the nested or nonnested use of a certain approximation of the Schur complement associated to the Navier–Stokes block. First, bounds on the generalized eigenvalues are obtained for the preconditioned systems linearized with both Picard and Newton methods. Then, the performance of the proposed preconditioners is studied in terms of computational time. This investigation reveals some inconsistencies in the literature that are hereby discussed. We observe that the nonnested preconditioner works best both for the Picard and for the Newton cases. Therefore, we further investigate its performance by extending its application to a mixed Picard–Newton scheme. Numerical results of two‐ and three‐dimensional cases show that the convergence is robust with respect to the mesh size. We also give a characterization of the performance of the various preconditioned linearization schemes in terms of the Rayleigh number.     

Energy and radiation transfer in a finite convex body with general boundary conditions

Summary We consider a nonlinear system of equations describing the interaction of radiation with matter through a balance of the specific intensity of radiation and the specific internal energy in a convex bounded body.The boundary conditions are not homogeneous. However, suitable additive decompositions of the unknown functions lead to systems with homogeneous boundary conditions and known source terms. We give two such decompositions: one of these, suggested by physical considerations, arises from the study of a nonhomogeneous linear integral equation in a convenient Banach space. The system is studied by using the theory of semigroups of linear operators and nonlinear perturbations in an L ₁ setting. We prove the existence and uniqueness of a positive differentiable solution, which is global in time.

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Sommario Si considera un sistema non lineare di equazioni che descrivono l'interazione della radiazione con la materia e rappresentano il bilancio dell'intensità specifica di radiazione e dell'energia specifica internu in un mezzo finito convesso. Le condizioni al contorno sono di tipo generale e non omogenee; l'introduzione di opportune scomposizioni della funzione incognita permette di ricondurci a sistemi con condizioni al contorno omogenee; ciò comporta l'introduzione di termini di sorgente noti. Si presentano due esempi di scomposizione, uno dei quali, suggerito da considerazioni fisiche, scaturisce dallo studio di un'equazione integrale lineare non omogenea in un opportuno spazio di Banach. Si riduce quindi il problema ad un'equazione di evoluzione non lineare in uno spazio di Banach di norma L ₁.Si prova l'esistenza di un'unica soluzione forte non negativa, utilizzando la teoria dei semigruppi e delle perturbazioni non lineari; tale soluzione risulta inoltre globale nel tempo.

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Work performed under the auspices of C.N.R. (Gruppo Nazionale per la Fisica Matematica) and partially supported by M.P.I.     

Ultrametricity in the Edwards-Anderson model

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 20(3) spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory.     

Mass distribution, polydispersity and focusing properties of carrier ampholytes for IEF. III: pH 2.5-4 intervals

To study the molecular mass distribution and number of species in narrow-range (2-pH-unit wide, in the nominal pI 2-4 or 3-5 interval) carrier ampholytes from four commercial sources (Bio-Lyte, Servalyt, Ampholine and Pharmalyte), a 2-D technique was adopted, consisting of a preparative focusing step in a Rotofor instrument, followed by analysis of every other collected fraction (10 out of 20) by CE-MS. It was found that Ampholine pH 3.5-5 contains 105 different molecular mass (M(r)) compounds, in the M(r) interval 205-965 Da, for a total of 446 isoforms. Bio-Lyte pH 3-5 consists of 84 different M(r) species, in the M(r) range 216-965 Da, for a total of 383 isoforms. Servalyt pH 2-4 is made of 227 different M(r) compounds, in the M(r) interval 204-929 Da, for a total of 1201 isoforms. Pharmalyte pH 2.5-5 comprises 245 amphoteres, in the M(r) range 203-857 Da, for a total of 857 isoforms. Pharmalyte appears to be the best brand, with the vast majority of species focusing sharply at their pI position and almost no 'poor' species, distributed along the entire pH gradient, denoting an extremely shallow pH/mobility curve across the pI value. Due to some overlap with the adjacent acidic pH 4-6 interval, the species in common have been evaluated: the most extended overlaps are found in Ampholine (55% of the species appearing in the two neighbouring intervals) and in Servalyt (47% coincidence). The lowest overlaps are found in Pharmalyte (23%) and in Bio-Lyte (20%).     

Regioselectivity and diasteroselectivity in Pt(II)-mediated "green" catalytic epoxidation of terminal alkenes with hydrogen peroxide: mechanistic insight into a peculiar substrate selectivity

Recently developed electron-poor Pt(II) catalyst 1 with the "green" oxidant 35% hydrogen peroxide displays high activity and complete substrate selectivity in the epoxidation of terminal alkenes because of stringent steric and electronic requirements. In the presence of isolated dienes bearing terminal and internal double bonds, epoxidation is completely regioselective toward the production of terminal epoxides. Insight into the mechanism is gained by means of a reaction progress kinetic analysis approach that underlines the peculiar role of 1 in activating both the alkene and H2O2 in the rate-determining step providing a rare example of nucleophilic oxidation of alkenes by H2O2.     

Reversible microwave-assisted cycloaddition of aziridines to carbon nanotubes

We report a new approach that uses microwaves to rapidly functionalize carbon nanotubes by using 1,3-dipolar cycloaddition of aziridines, well-known precursors to azomethine ylides, in solvent-free conditions. The efficiency of our microwave-mediated protocol is confirmed by comparison to a similar protocol in classical conditions for the azomethine ylides in DMF. Under these latter conditions, the reaction proceeds in 5 days (against 1 h under microwave irradiation), and the functionalization degree is much lower, as confirmed by thermogravimetric analysis and Raman spectroscopy. With our procedure, we easily scale-up the reaction up to 250 mg of functionalized MWNT in 1 h. We also provide an indirect proof of the covalent sidewall functionalization of the tubes.     

PNA-based probe for quantitative chemiluminescent in situ hybridisation imaging of cellular parvovirus B19 replication kinetics

To allow the ultrasensitive localization and the quantitative detection of parvovirus B19 nucleic acids in single infected cells at various times post-infection, a peptide nucleic acid (PNA)-based in situ hybridisation (ISH) assay with chemiluminescent detection has been developed. The assay is based on the use of a biotin-labelled PNA probe detected by a streptavidin-linked alkaline phosphatase and a chemiluminescent dioxetane phosphate derivative substrate. The luminescent signal was quantified and imaged with an ultrasensitive nitrogen-cooled CCD camera connected to an epifluorescence microscope. The assay was used to analyze the parvovirus B19 infection process in cell cultures and to quantify the amount of viral nucleic acids at different times after infection.The chemiluminescent ISH-PNA assay is characterized by high resolution providing a sharp localization of B19 nucleic acids within single cells, with higher sensitivity with respect to conventional colorimetric ISH detection. Thanks to the high detectability and wide linear range of chemiluminescence detection, an objective evaluation of the percentage of infected cells, which reached its maximum at 24 h after infection, following a B19 virus infectious cycle could be accurately evaluated. Chemiluminescence detection also allowed the quantitative analysis of viral nucleic acids at the single-cell level, showing a continuous increase of the content of viral nucleic acids in infected cells with time after infection.The developed chemiluminescent ISH-PNA assay could thus represent a potent tool for the assessment of viral infections and for the quantitative evaluation of the virus nucleic acid load of infected cells in virus studies and diagnostics.