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.     

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.     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

Time evolution of infinite classical systems with singular,long range,two body interactions

Existence of dynamics for infinitely many hard-spheres inv dimensions is proven in a set of full equilibrium measure.Singular unbounded perturbations are considered with pair potentials diverging as (x – a)^–, >2 anda is the hard-core diameter. Long range forces are allowed with potentials decreasing at infinity asx , <v. The result corrects and generalizes a proof given in a previous paper by the same authors.Research partially supported by a CNR fellowship Posit. 204530.Research partially supported by a CNR fellowship.     

Exploring the Parallel G-Quadruplex Nucleic Acid World: A Spectroscopic and Computational Investigation on the Binding of the c-myc Oncogene NHE III1 Region by the Phytochemical Polydatin

Trans-polydatin (tPD), the 3-β-D-glucoside of the well-known nutraceutical trans-resveratrol, is a natural polyphenol with documented anti-cancer, anti-inflammatory, cardioprotective, and immunoregulatory effects. Considering the anticancer activity of tPD, in this work, we aimed to explore the binding properties of this natural compound with the G-quadruplex (G4) structure formed by the Pu22 [d(TGAGGGTGGGTAGGGTGGGTAA)] DNA sequence by exploiting CD spectroscopy and molecular docking simulations. Pu22 is a mutated and shorter analog of the G4-forming sequence known as Pu27 located in the promoter of the c-myc oncogene, whose overexpression triggers the metabolic changes responsible for cancer cells transformation. The binding of tPD with the parallel Pu22 G4 was confirmed by CD spectroscopy, which showed significant changes in the CD spectrum of the DNA and a slight thermal stabilization of the G4 structure. To gain a deeper insight into the structural features of the tPD-Pu22 complex, we performed an in silico molecular docking study, which indicated that the interaction of tPD with Pu22 G4 may involve partial end-stacking to the terminal G-quartet and H-bonding interactions between the sugar moiety of the ligand and deoxynucleotides not included in the G-tetrads. Finally, we compared the experimental CD profiles of Pu22 G4 with the corresponding theoretical output obtained using DichroCalc, a web-based server normally used for the prediction of proteins’ CD spectra starting from their “.pdb” file. The results indicated a good agreement between the predicted and the experimental CD spectra in terms of the spectral bands’ profile even if with a slight bathochromic shift in the positive band, suggesting the utility of this predictive tool for G4 DNA CD investigations.