Transient bimodality in interacting particle systems

We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor ^–2, then, in the limit 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each the system is in a finite interval ofZ with ^–1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order ^–1/2 propagation of chaos does not hold any more and, in the limit as 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale ^–1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.     

Escape from the unstable equilibrium in a random process with infinitely many interacting particles

We consider a one-dimensional version of the model introduced in Ref. l. At each site of Z there is a particle with spin ± 1. Particles move according to the Stirring Process and spins change according to the Glauber dynamics. In the hydrodynamical limit, with the stirring process suitably speeded up, the local magnetic densitym _t(r) is proven in Ref. 1 to satisfy the reaction-diffusion equation (*) $$\partial _t m_t (r) = \tfrac{1}{2}\partial _r^2 m_t (r) - V'(m_t )$$ \(V(m) = - \tfrac{1}{2}\alpha m^2 + \tfrac{1}{4}\beta m^4 \) ,α andβ being determined by the parameters of the Glauber dynamics. In the present paper we consider an initial state with zero magnetization,m ₀(r)=0. We then prove that at long times, before taking the hydrodynamical limit, the evolution departs from that predicted by (*) and that the microscopic state becomes a nontrivial mixture of states with different magnetizations.     

A self-diffusion study of poly(ethylene-oxide) alkyl alcohols

The self-diffusion coefficients of HDO and some surfactants in aqueous mixtures at different concentrations, below the critical micelle concentration, have been determined by means of the NMR, spin-echo pulsed field gradient method. The surfactant solutes chosen were ethylene glycol-pentyl alcohol (diethylene glycolpentylalcohol, ethylene glycol-hexyalcohol, diethylene glycol-hexyl alcohol, triethylene glycol-hexyl alcohol, tetraethylene glycol-hexyl alcohol, pentaethylene glycol-hexyl alcohol). The interactions in solution are studied by analyzing the solute self-diffusion coefficients extrapolated to infinite dilution. These values are compared with those of 1-alkanols. The slope of the self diffusion coefficientsvs. the solute concentration are correlated with the microscopic friction coefficients. A model for interpreting the experimental data is suggested.     

Constrained minima of nonlocal free energy functionals

We consider variational problems involving nonlocal free energy functionals that arise from Gibbs measures with Kac potentials and are related to the characterization of the optimal (i.e., typical) shape of an interface under given constraints on the magnetization profile.     

Surface tension in Ising systems with Kac potentials

We consider an Ising spin system with Kac potentials in a torus of ^d,d>-2, and fix the temperature below its Lebowitz-Penrose critical value. We prove that when the Kac scaling parameter vanishes, the log of the probability of an interface becomes proportional to its area and the surface tension, related to the proportionality constant, converges to the van der Waals surface tension. The results are based on the analysis of the rate functionals for Gibbsian large deviations and on the proof that they -converge to the perimeter functional of geometric measure theory (which extends the notion of area). Our considerations include nonsmooth interfaces, proving that the Gibbsian probability of an interface depends only on its area and not on its regularity.     

Interfaces and typical Gibbs configurations for one-dimensional Kac potentials

Summary We consider a one dimensional Ising spin system with a ferromagnetic Kac potential J(|r|),J having compact support. We study the system in the limit, »0, below the Lebowitz-Penrose critical temperature, where there are two distinct thermodynamic phases with different magnetizations. We prove that the empirical spin average in blocks of size ^–1 (for any positive ) converges, as »0, to one of the two thermodynamic magnetizations, uniformly in the intervals of size ^–p , for any given positivep1. We then show that the intervals where the magnetization is approximately constant have lengths of the order of exp(c ^–1),c>0, and that, when normalized, they converge to independent variables with exponential distribution. We show this by proving large deviation estimates and applying the Ventsel and Friedlin methods to Gibbs random fields. Finally, if the temperature is low enough, we characterize the interface, namely the typical magnetization pattern in the region connecting the two phases.The research has been partially supported by CNR, GNFM, GNSM and by grant SC1CT91-0695 of the Commission of European Communities     

Enantiomeric separation of acidic compounds of pharmaceutical interest by capillary electrochromatography employing glycopeptide antibiotic stationary phases

Enantiomeric separation of some selected acidic compounds of pharmaceutical interest belonging to the group of non-steroidal anti-inflammatory drugs were separated by capillary electrochromatography employing silica based glycopeptide antibiotic stationary phases, namely vancomycin or a teicoplanin derivatives (Hepta-Tyr). The vancomycin stationary phase allowed to achieve the chiral resolution of some racemic studied compounds only using mobile phases containing ammonium formate at a relatively low pH 2.5-3.5 and acetonitrile. Employing the teicoplanin derivative stationary phase, good enantiomeric resolution was achieved eluting with mobile phases containing sodium phosphate pH 6-acetonitrile. Enantiomers were moved to the detector because a relatively high reversed electroosmotic flow (due to the positive charge of the stationary phase) and to the electrophoretic mobility of analytes.     

Separation and characterisation of sphingoceramides by high-performance liquid chromatography-electrospray ionisation mass spectrometry

We developed a simple and reliable analytical method for the quantification and the characterization of ceramides extracted from biological samples by high-performance liquid chromatography (HPLC) coupled to electrospray ionisation tandem mass spectrometry (ESI/MS/MS). The chromatographic separation of analytes was carried out in a RP8 column, eluting with a methanol-water mixture in gradient elution mode. The separated lipids were detected by total ion monitoring and characterised by MS/MS spectra; quantitative analysis was performed by integrating the extracted ion peaks obtained in the negative ion mode. Good repeatability was obtained for retention time (0.3-2%), peak area ratio (A(S)/A(IS), 2-8%), as well as limit of detection (LOD, 5-26 pg) and quantification (LOQ, 13-53 pg). The method was validated for the analysis of N-palmitoyl-D-erythro-sphingosine (Cer16), N-stearoyl-D-erythro-sphingosine (Cer18), N-tetracosanoyl-D-erythro-sphingosine (N24:0, lignoceric ceramide, Cer24:0), and N-tetracos-15'-enoyl-D-erythro-sphingosine (N24:1, nervonic ceramide, Cer24:1), giving good results. Lipid mixtures, extracted from skin and epidermal cells, were analysed for their content of the studied ceramides.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

Influence of CaCO<Subscript>3</Subscript> nanoparticles shape on thermal and crystallization behavior of isotactic polypropylene based nanocomposites

Summary The influence of calcium carbonate nanoparticles with different shapes (spherical and elongated) on the thermal properties and crystallization behavior of isotactic polypropylene was investigated. CaCO₃ nanoparticles were covered by an appropriate coating agent to improve the interfacial adhesion between the filler and the polyolefin matrix. The nanocomposites were prepared by melt mixing and subsequent compression molding. A remarkable effect of CaCO₃ on the thermal properties of iPP was observed. Moreover, the analysis of crystallization kinetics showed that CaCO₃ nanopowder coated with PP-MA are efficient nucleating agents for iPP, and the overall crystallization rate results higher than plain iPP.