Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys

Abstract In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. * Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”.     

Mean Field Behaviour of Spin Systems with Orthogonal Interaction Matrix

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie–Weiss case.     

Symmetric Boundary Value Methods for Second Order Initial and Boundary Value Problems

We introduce symmetric Boundary Value Methods for the solution of second order initial and boundary value problems (in particular Hamiltonian problems). We study the conditioning of the methods and link it to the boundary loci of the roots of the associated characteristic polynomial. Some numerical tests are provided to assess their reliability. Dedicated to the memory of Professor Aldo Cossu     

An algorithm for the computation of consistent initial values for differential–algebraic equations

We use boundary value methods to compute consistent initial values for fully implicit nonlinear differential-algebraic equations. The obtained algorithm uses variable order formulae and a deferred correction technique to evaluate the error. A rigorous theory is stated for nonlinear index 1, 2 and 3 DAEs of Hessenberg form. Numerical tests on classical index 1, 2 and 3 DAE problems are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

Indirect fluorometric determination of diclofenac sodium.

A simple and easy method of analysis for diclofenac sodium is reported. A spectrofluorometric method for the microdetermination of diclofenac sodium has been developed through its reaction with cerium(IV) in an acidic solution and measurement of the fluorescence of the Ce(III) ions produced. Under the optimum experimental conditions for the oxidation reaction, 1.0 M H2SO4 with 90 min of heating time (100 degrees C), the range of application is 124.3-600 ng mL(-1) and the limit of detection is 72.7 ng mL(-1). The proposed method was applied to the determination of diclofenac sodium in pharmaceutical tablets. The results of the analysis show a good agreement with those obtained by the official USP 27 HPLC method.     

Analysis of saccharides in beer samples by flow injection with electrospray mass spectrometry

Saccharides in foods play important roles, as they are essential substrates for fermentation processes. In brewing, the concentration of maltooligosaccharides influences the characteristics of beers and therefore their determination is of great practical interest. Electrospray ionization mass spectrometry (ESI-MS) was applied to identify and characterise maltooligosaccharides in beer samples. The effects due to different cation concentrations and dilution of samples were studied. Furthermore, quantitative analyses of maltooligosaccharides by means of flow-injection ESI-MS (FI/ESI-MS) of 1-microL beer samples (diluted 1000-fold) are described.     

Electromagnetic coupling in near-field scattering by small homogeneous and heterogeneous nanoaggregates

Progress in near-field optical spectroscopy research on metal nanoparticles demands a better understanding of the role played by particle-particle interactions and a deeper insight of the influence of the incident field wavelength. This is particularly true for scanning near-field optical microscopy (SNOM), where the mechanism by which some components of the evanescent illuminating field are transformed into propagating field components that carry information about the sample is at the core of the image formation and where the role played by the interactions between sample and tip remains a still open problem. In this perspective, we investigate numerically the optical behavior of small aggregates of spherical nanoparticles, taking into account the electromagnetic coupling between all particles and the apertureless tip. The tip is modeled as a sphere made of different materials characterized by appropriate dielectric functions. We find that the tip material affects both qualitatively and quantitatively the SNOM images; more important, from the analysis of the calculated scattering cross section, the resonance plasmon location of the whole (aggregate + tip) system undergoes detectable changes, if the tip is constituted of the same material of the sample, as the tip is situated in different positions. This modification of the plasmon frequencies induces a nontrivial variation of the near-field intensity as a function of the tip position and the resulting SNOM image can be distorted with respect to the actual shape of the sample. No simple arguments can be used to relate the value of the local field on the tip surface to the scattering cross section value; depending on the tip material, the comparison between these two measurements can help to clarify the role of basic interactions in the scattering mechanism.     

Synthesis and properties of new glucocationic surfactants: model structures for marking cationic surfactants with carbohydrates

[reaction: see text] In this work, we report the synthesis of a new series of glucocationic surfactants, a class of surfactants we introduced very recently. The preparation of the surfactants is based on the synthesis of the 2-bromoethyl-2,3,4,6-tetra-O-acetyl-beta-D-glucopyranoside, whose preparation was studied in order to improve yields and stereoselectivity of this key intermediate. These glucocationic amphiphiles were prepared and studied as a model of cationic surfactants marked with a carbohydrate moiety. The use of carbohydrates as markers on cationic lipids was recently introduced to induce recognition by specific receptors, present on the surface of cell membranes. The chemicophysical characterization of these model structures can give more insight on the aggregation behavior. Conductivity and surface tension measurements were performed in order to characterize the compounds from the amphiphilic point of view. The results showed a different effect of the glucosidic moiety on the cmc value with respect to the glucopyridinium cationic surfactants. The surfactants also showed the tendency to form premicellar aggregates in solution when the hydrophobicity is raised.     

An analyticity bound for two-dimensional Ising model at low temperature

We study the coexistence phase in the two-dimensional Ising model. Optimizing the cluster expansion technique, we are able to prove the phase separation phenomenon, with the Onsager value for the surface tension, in a range , where estimates from above the critical within 19% and essentially coincides with the entropic bound.     

Reactions of 1,4-diaza-3-methylbutadien-2-ylpalladium(II) derivatives with chloro-bridged rhodium(I) complexes

The reactions of the organometallic 1,4-diazabutadienes, RN=C(R′)C(Me)=NR″ [R = R″ = p-C₆H₄OMe, R′ = trans-PdCl(PPh₃)₂ (DAB); R = p-C₆H₄OMe, R″ = Me, R′ = trans-PdCl(PPh₃)₂ (DAB^I; R = R″ = p-C₆H₄OMe, R′ = Pd(dmtc)-(PPh₃), dmtc = dimethyldithiocarbamate (DAB^II); R = R″ = p-C₆H₄OMe, R′ = PdCl(diphos), diphos = 1,2-bis(diphenylphosphino)ethane (DAB^III)] with [RhCl(COD)]₂ (COD = 1,5-cyclooctadiene, Pd/Rh ratio = $\text{1}\text{2}$) depend on the nature of the ancillary ligands at the Pd atom in group R′. In the reactions with DAB and DAB^I transfer of one PPh₃ ligand from Pd to Rh occurs yielding [RhCl(COD)(PPh₃)] and the new binuclear complexes [Rh(COD) {RN=C(R?)-C(Me)=NR″}], in which the diazabutadiene moiety acts as a chelating bidentate ligand. Exchange of ligands between the two different metallic centers also occurs in the reaction with DAB^II. In this case, the migration of the bidentate dmtc anion yields [Rh(COD)Pdmtc] and [Rh(COD) {RN=C(R?)C(Me)=NR″}]. In contrast, the reaction with DAB^III leads to the ionic product [Rh(COD)- (DAB^III)][RhCl₂(COD)], with no transfer of ligands. The cationic complex [Rh(COD)(DAB^III)]⁺ can be isolated as the perchlorate salt from the same reaction (Pd/Rh ratio = 1/1) in the presence of an excess of NaClO₄. In all the binuclear complexes the coordinated 1,5-cyclooctadiene can be readily displaced by carbon monoxide to give the corresponding dicarbonyl derivatives. The reaction of [RhCl(CO)₂]₂ with DAB and/or DAB^I yields trinuclear complexes of the type [RhCl(CO)₂]₂(DAB), in which the diazabutadiene group acts as a bridging bidentate ligand. Some reactions of the organic diazabutadiene RN=C(Me)C(Me)=NR (R = p-C₆H₄OMe) are also reported for comparison.