Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r ^γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.     

Investigation of ion-selective electrodes with neutral ionophores and ionic sites by EIS. I. Theory

Models of an ion selective electrode involving an ionophore and mobile sites in a membrane are proposed. The first model, called the phase boundary potential model, supposed thermodynamic equilibrium; it allows the concentrations of the various species to be calculated. Then, a kinetic model, which takes into account the ionic transfer at the membrane|solution interfaces, was derived. The impedance of the membrane was calculated. It shows that a membrane with nernstian behavior shows only one capacitive loop in the impedance diagram, which is related to the conductivity and dielectric properties of the material of the membrane. Non-nernstian behavior is related to slow ionic transfer at the membrane|solution interfaces or/and transport limitation of the species in the membrane. Finite rate constants of the ionic transfer lead to a capacitive loop in the middle frequency range, whereas finite rate transport leads to a diffusional impedance in the low frequency range.     

Vectorial photoinduced electron transfer in phospholipid vesicles and LB bilayers

Summary Photoinduced electron transfer (PET) was studied in phospholipid vesicles and in Langmuir-Blodgett bilayers in the attempt to produce a model for electron transfer processes in biological media. Spatial organization of the reaction centers in lipid membranes needs to be controlled in order to provide high efficiency of light-to-chemical energy conversion. We designed a phospholipid system where the donor is localized in the inner bilayer whereas the acceptor is at the polar groups-water interface. We used dipalmitoylphosphatidic acid vesicles containing low molar fractions of dipalmitoylphosphatidylcholine with pyrene (donor) bound to one of the alkyl chains. Methylviologen (acceptor) was added to the external aqueous phase; upon photoexcitation of the donor we observed the electron transfer to take place in a unidirectional manner from the inside of the bilayer to the interface. Information about the location of the donor was obtained studying the photophysical properties of the pyrene chromophore in vesicles and in LB layers. The photoinduced electron transfer reaction was evidenced by quenching of pyrene fluorescence in the presence of increasing concentrations of acceptor, the process was studied both with steady-state and time-resolved fluorescence emission. Fluorescence intensity was found to decrease with increasing concentration of methylviologen, similar results were obtained for vesicles and LB layers of analog composition immersed in a methylviologen solution. Lifetimes of the excited species were found to be of the same order of magnitude in vesicle and LB-layer systems. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Fast chromatographic determination of the bile salt critical micellar concentration

In a line of research focused on the design, synthesis and development of new bile acid-based compounds, the physico-chemical profile of the molecules must be thoroughly explored and analyzed. In this scenario, a fast and reliable information on the critical micellar concentration (CMC) of specific compounds through a profitable chromatographic parameter can be of aid to rationally direct the synthesis of new molecular entities, mainly during the early stages of the drug-discovery process. The derived ‘chromatographic hydrophobicity index’ (CHI), usually employed for a fast access to the log P/log D value of physico-chemically diverse compounds and obtained via RP-gradient elution, was for the first time engaged in the bile acid field. Accordingly, 14 unconjugated bile acids harboured with a different number, position and orientation of hydroxy groups, as well as other substituents onto the steroidal backbone and side chain, were selected to build up a calibration curve. Such a collection of compounds was rationally assembled in order to manage an almost continuous range of CMC values (spanning the spectrophotometrically obtained CMCs between 5 and 25 mM). A high degree of correlation between CMC and CHI values was obtained (R ² and cross-validated R _xv² of the pCMC vs CHI plot equal to 0.975 and 0.966, respectively). A selected new subset of five confidential research bile acids with experimental CMCs in the range 6–19 mM was finally recruited to validate the proposed method. The high statistical quality of the established mathematical model turned out into a very appreciable predictive power.     

Tracing the biological origin of animal glues used in paintings through mitochondrial DNA analysis

We report the development of a suitable protocol for the identification of the biological origin of binding media on tiny samples from ancient paintings, by exploitation of the high specificity and high sensitivity offered by the state-of-the art DNA analysis. In particular, our aim was to molecularly characterize mitochondrial regions of the animal species traditionally employed for obtaining glues. The model has been developed using aged painting models and then tested to analyze the organic components in samples from the polychrome terracotta Madonna of Citerna by Donatello (1415-1420), where, by GC-MS and FTIR spectroscopy, animal glues and siccative oils were identified. The results obtained are good in terms of both sensibility and specificity of the method. First of all, it was possible to confirm that Donatello used animal glue for the preparation of the painted layers of the Madonna of Citerna and, specifically, glue derived from Bos taurus. Data obtained from sequencing confirm that each sample contains animal glue, revealing that it was mostly prepared from two common European taurine lineages called T2 and T3. There is one remarkable exception represented by one sample which falls into a surviving lineage of the now extinct European aurochs.     

Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model

In this paper we present a novel method to reconstruct global topological properties of a complex network starting from limited information. We assume to know for all the nodes a non-topological quantity that we interpret as fitness. In contrast, we assume to know the degree, i.e. the number of connections, only for a subset of the nodes in the network. We then use a fitness model, calibrated on the subset of nodes for which degrees are known, in order to generate ensembles of networks. Here, we focus on topological properties that are relevant for processes of contagion and distress propagation in networks, i.e. network density and k-core structure, and we study how well these properties can be estimated as a function of the size of the subset of nodes utilized for the calibration. Finally, we also study how well the resilience to distress propagation in the network can be estimated using our method. We perform a first test on ensembles of synthetic networks generated with the Exponential Random Graph model, which allows to apply common tools from statistical mechanics. We then perform a second test on empirical networks taken from economic and financial contexts. In both cases, we find that a subset as small as 10 % of nodes can be enough to estimate the properties of the network along with its resilience with an error of 5 %.     

Monolayers of proteins

Summary Monolayers of various proteins were studied at airwater interface. An equation of state of the virial type, as developed byM. L. Huggins, was applied to the surface pressure-area measurements. It was found that theHuggins equation based on statistical thermodynamics was applicable to the proteins. From this treatment of the results, the degree of submersion of protein could be determined, which was found to be dependent on the degree of unfolding of the protein at the interface.     

Polylaurylmethacrylate in bidimensional mixtures with low and high molecular weight substances: effect of the chain mobility on mutual miscibility

Bidimensional two-component mixtures of polylaurylmethacrylate with polyoctadecylmethacrylate, polymethylmethacrylate and stearic acid were studied in the 15–30 °C temperature range at the air-water interface, in order to determine the effect of the state of the hydrophobic side chains on the bidimensional miscibility.We showed that bidimensional miscibility depends on whether the two components have the same interfacial orientation, and that the fluidity of the polymer side chains also plays a very important role.