Prominence and control: the weighted rich-club effect

Complex systems are often characterized by large-scale hierarchical organizations. Whether the prominent elements, at the top of the hierarchy, share and control resources or avoid one another lies at the heart of a system's global organization and functioning. Inspired by network perspectives, we propose a new general framework for studying the tendency of prominent elements to form clubs with exclusive control over the majority of a system's resources. We explore associations between prominence and control in the fields of transportation, scientific collaboration, and online communication.     

Cast-extruded syndiotactic polypropylene films: preliminary structural and mechanical results

Syndiotactic polypropylene (sPP) was cast-extruded with a laboratory single screw extruder, obtaining a crystalline and still highly transparent film. The structural studies showed that the film crystallized at room temperature in the disordered helical form I, containing a fraction of a mesophase with the chains in trans-planar conformation. X-ray patterns, taken either along the extrusion direction (MD) or along the orthogonal directions (TD and ND), indicated a low orientation of the c axis parallel to the machine direction (MD) and a partial orientation of the a axis along the transverse direction (TD). Mechanical properties performed in either direction showed a very similar behaviour, but a different strain at the breaking point. The mechanical parameters were derived in both directions.     

Elastic Behaviour of Oriented Syndiotactic Poly(propylene)

A syndiotactic poly(propylene) film (sPP), quenched from the melt at 0°C, was drawn at room temperature up to a draw ratio of λ = 6. The fibre was analysed under tension by X‐ray analysis and FTIR spectroscopy, showing the presence of the oriented crystalline form III described by Chatani, with the chains in trans‐planar conformation. Then it was unhooked, undergoing a large shrinkage, and reaching a length corresponding to a draw ratio of λ = 3.8. X‐ray and FTIR analysis showed that in the relaxed fibre, a conformational transition from the trans‐planar to the helical form occurred. The relaxed fibre was again submitted to increasing extensions up to λ = 6, step by step, and the elastic behaviour was analysed through the Mullins' curve and hysteresis cycles. It showed good elastic properties, which appear to be closely correlated to the conformational transition between helical and trans‐planar forms.     

Recognition of the syndiotactic polypropylene polymorphs via dynamic-mechanical analysis

Three syndiotactic polypropylene samples were crystallized under different conditions in order to obtain different polymorphs. A first sample was crystallized at high temperature, obtaining the helical form I; a second was crystallized from the melt at 0°C for many days obtaining the trans-planar mesophase; a third sample was obtained by solvent induced crystallization followed by annaeling of the trans-planar mesophase, leading to a mixture of both the helical forms I and II. In the dynamic-mechanical analysis the helical form I showed only one peak of tan δ corresponding to the amorphous glass transition. The other polymorphs also showed this transition centered at about the same temperature. Beside the peak corresponding to the Tg, the trans-planar mesophase was characterized by a peak appearing at 70°C, and the helical form II by a peak at 100°C. These peaks, unambiguously associated to transitions of the different forms, can be considered a distinctive evidence for the polymorphs obtained in different processing conditions.     

Transport properties of an hydrophobic-hydrophilic copolymer

Sorption and diffusion properties of a copolymer composed by hydrophilic and hydrophobic blocks have been analyzed. The material, obtained as a film by moulding the powders under pressure, was submitted to thermal treatments, and the structural organization of the samples was investigated using water vapour and dichloromethane as permeants. The polar solvent (water) has been useful to investigate the hydrophilic amorphous regions, while the apolar one (methylene chloride) gave information about the organization of the hydrophobic amorphous phases.     

Influence of water on the physical aging of poly(ethylene terephtalate)

Physical aging in polyethylene terephtalate (PET) has been studied on samples well characterized in terms of aging history and their content of water. This allows us to better understand the role played by water in the complex phenomenology of the physical aging in a hygroscopic material as PET. No appreciable changes in the thermal behavior in the sample aged in water at room temperature for one month were noted, while substantial changes were observed in samples aged in more severe conditions like 50°C under vacuum and 50°C in water for one month. The results are consistent with the formation of small regions in which segments of chains are closely packed.     

Resonant ionic bonding and high TC superconductivity

The implications of an electronic coupling model in high T_C superconductors of YBCO are discussed in which the pairing mechanism is based upon the ionic bonding. Specifically,the bonding reaction Cu + O [rlhar2] Cu^-- resonates at a frequency of I/2π ; in the CuO planes, where I = 0.4 eV is the ionic bonding energy. We formulate an Hamiltonian which allows for the reduction of the total energy by I each time two holes or two electrons form a pair. The total energy consists of kinetic energy calculable from band theory, and the ionic bonding energy proportional to I. We calculate (i) the effective Ginzburg-Landau free energy for all T < T_c, (ii) the energy gap, (iii) the anisotropic London penetration depths, and (iv) the anisotropic coherence lengths. General agreement is found between our calculations and experimental data.     

Drawing and dynamic-mechanical behavior of syndiotactic polystyrene an introduction

The drawing behavior of syndiotactic polystyrene was analyzed at different temperatures. Amorphous films were used and, depending on drawing temperature, strain-induced or thermal-induced cold crystallization was observed. This phenomenon, when present, greatly affects the drawing behavior. The dynamic-mechanical behavior of drawn samples was analyzed, and the obtained results indicate that the glass transition is affected by drawing, and that the effect depends drastically on the drawing temperature. Particularly interesting is the dynamic behavior at high temperature where the elastic modulus is weakly affected by temperature also near the melting point.     

Log-Sobolev inequalities for semi-direct product operators and applications

In this paper, we prove some type of logarithmic Sobolev inequalities (with parameters) for operators in semi-direct product forms (see Sect. 1 for a precise definition). This generalizes the tensorization procedure for this type of inequalities and allows to deal with some operators with varying coefficients. We provide many examples of applications and obtain ultracontractive bounds for some of these operators by using appropriate Hardy’s type inequalities necessary for our method. This theory is developed in the setting of carré du champ with diffusion property.