A priori bounds in the Bénard problem with boundaries of finite conductivity

In questa nota, si danno alcune stime a priori per le soluzioni classiche delle equazioni che descrivono il problema di Bénard quando le frontiere hanno conduttività finita (modello di Hurle, Jakeman e Pike [3]). Adottando il metodo della funzione peso, si mostra che la velocità v e la temperatura T del fluido che a priori sono fatte crescere per grandi distanze spaziali, si mantengono in effetti uniformemente limitate a patto che siano tali la velocità e la temperatura iniziali del fluido e il suo gradiente di pressione.     

A $\Gamma$-convergence result for doubling metric measures and associated perimeters

Abstract. In this paper we study the notion of perimeter associated with doubling metric measures or strongly weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski content and can be obtained also as a -limit of Modica-Mortola type degenerate integral functionals. Received: 27 August 2001 / Accepted: 29 November 2001 / Published online: 10 June 2002 Investigation supported by University of Bologna, funds for selected research topics and by GNAMPA of INdAM, Italy. The authors are very grateful to Luigi Ambrosio and Francesco Serra Cassano for making their preprints available to them, for listening with patience and for many unvaluable suggestions.     

A Sum Operator with Applications to Self-Improving Properties of Poincaré Inequalities in Metric Spaces

We define a class of summation operators with applications to the self-improving nature of Poincaré–Sobolev estimates, in fairly general quasimetric spaces of homogeneous type. We show that these sum operators play the familiar role of integral operators of potential type (e.g., Riesz fractional integrals) in deriving Poincaré–Sobolev estimates in cases when representations of functions by such integral operators are not readily available. In particular, we derive norm estimates for sum operators and use these estimates to obtain improved Poincaré–Sobolev results.     

A highly redundant coordinate formulation for constrained rigid bodies

The paper presents a formulation for the dynamic analysis of rigid multibodies. An introductory part carries out the kinematic analysis and the definition of the highly redundant differential framework along with the choice of unknowns and equations. From the differential formulation the variational principles, either in Lagrangian or Hamiltonian form, are developed. The Hamiltonian formulation is then used to develop the numerical approximation by applying the finite element method in time. The application of the method in its multifield form is discussed and a solution algorithm is proposed. Some examples are finally presented in order to verify the effectiveness of the formulation.

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Sommario Il lavoro presenta una formulazione per lo studio della dinamica dei sistemi multicorpo rigidi. Nella parte introduttiva viene svolta l'analisi cinematica e si definisce il quadro differenziale con la scelta delle incognite e delle equazioni. Dalla formulazione differenziale vengono poi sviluppati dei principi variazionali nella forma Lagrangiana ed Hamiltoniana. La formulazione Hamiltoniana é quindi utilizzata per sviluppare l'approssimazione numerica col metodo degli elementi finiti di tempo. Viene discussa l'applicazione del metodo nella forma multi-campo e viene proposto un algoritmo di soluzione. Da ultimo, vengono discussi alcuni esempi per verificare la correttezza della formulazione.

     

Water-soluble gold nanoparticles protected by fluorinated amphiphilic thiolates

The preparation and the properties of gold nanoparticles (Au NPs) protected by perfluorinated amphiphiles are described. The thiols were devised to form a perfluorinated region close to the gold surface and to have a hydrophilic portion in contact with the bulk solvent to impart solubility in water. The monolayer protected clusters were prepared, in an homogeneous phase using sodium thiolates because of the low nucleophilicity of the alpha-perfluorinated thiols, and fully characterized with (1)H, (19)F NMR spectrometry, IR and UV-vis absorption spectroscopies, transmission electron microscopy (TEM), thermogravimetric analysis (TGA), and X-ray photoelectron spectroscopy (XPS). Au NPs with core diameters ranging from 1.6 to 2.9 nm, depending on the reaction conditions, were obtained. Water-soluble NPs (MPC-F8-PEGs) were obtained with the thiol HS-F8-PEG ending with a short poly(ethylene glycol) unit (PEG-OMe 550), whereas thiols with shorter PEG chains give rise to NPs insoluble in water. MPC-F8-PEGs undergo an exchange reaction with amphiphilic alkyl thiols. ESR investigations, using a hydrophobic radical probe, indicate that the MPC-F8-PEG monolayer shows a greater hydrophobicity compared to the analogous hydrogenated monolayer.     

Nontrivial solutions for Monge-Ampère type operators in convex domains

In this paper we prove existence and interior regularity of convex solutions of the Dirichlet problem for a class of Monge-Ampère type equations with right hand side vanishing on the boundary, by means of the fixed point index theory for Bakelman's weak solutions. The regularity in the interior follows from recent results of Caffarelli. Partially supported by M.U.R.S.T., Italy Partially supported by G.N.A.F.A. of C.N.R., Italy. This work was accomplished during a Humbold research stay at Karlsruhe and Heidelberg Universities.