PER IL CENTESIMO ANNIVERSARIO DELLA TEORIA DELLE RELAZIONI STATISTICHE DI CORRADO GINI

This Note aims at highlighting Gini’s contributions to denition and measurement of the intensity of a statistical relationship, on the occcasion of the centennial anniversary of the publication of his early papers on that topic. The Note stresses the precursory value of those contributions and mentions some of their most signicant developments apropos of metrization of spaces of probability distributions and anaysis of monotone dependence.

Electrodiffusion-Mediated Swelling of a Two-Phase Gel Model of Gastric Mucus

Gastric mucus gel is known to exhibit dramatic and unique swelling behaviors in response to the ionic composition of the hydrating solution. This swelling behavior is important in the maintenance of the mucus layer lining the stomach wall, as the layer is constantly digested by enzymes in the lumen, and must be replenished by new mucus that swells as it is secreted from the gastric wall. One hypothesis suggests that the condensed state of mucus at secretion is maintained by transient bonds with calcium that form crosslinks. These crosslinks are lost as monovalent cations from the environment displace divalent crosslinkers, leading to a dramatic change in the energy of the gel and inducing the swelling behavior. Previous modeling work has characterized the equilibrium behavior of polyelectrolyte gels that respond to calcium crosslinking. Here, we present an investigation of the dynamic swelling behavior of a polyelectrolytic gel model of mucus. In particular, we quantified the rate at which a globule of initially crosslinked gel swells when exposed to an ionic bath. The dependence of this swelling rate on several parameters was characterized. We observed that swelling rate has a non-monotone dependence on the molarity of the bath solution, with moderate concentrations of available sodium inducing the fastest swelling.

Analysis of a dynamic frictional contact problem for hyperviscoelastic material with non-convex energy density

Using the time approximation method we obtain the existence of a weak solution for the dynamic contact problem with damping and a non-convex stored elastic energy function. On the contact boundary we assume the normal compliance law and the generalization of the Coulomb friction law which allows for non-monotone dependence of the friction force on the tangential velocity. The existence result is accompanied by two numerical examples, one of them showing lack of uniqueness for the numerical solution.

Non-classical gas dynamics of vapour mixtures

The non-classical gas dynamics of binary mixtures of organic fluids in the vapour phase is investigated for the first time. A predictive thermodynamic model is used to compute the relevant mixture properties, including its critical point coordinates and the local value of the fundamental derivative of gas dynamics $\Gamma $. The considered model is the improved Peng–Robinson Stryjek–Vera cubic equation of state, complemented by the Wong–Sandler mixing rules. A finite thermodynamic region is found where the nonlinearity parameter $\Gamma $ is negative and therefore non-classical gas dynamics phenomena are admissible. A non-monotone dependence of $\Gamma $ on the mixture composition is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the minimum value of $\Gamma $ in the mixture being always larger than that of its more complex component. The observed dependence indicates that non-ideal mixing has a strong influence on the gas dynamics behaviour, either classical or non-classical, of the mixture. Numerical experiments of the supersonic expansion of a mixture flow around a sharp corner show the transition from the classical configuration, exhibiting an isentropic rarefaction fan centred at the expansion corner, to non-classical ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is changed.

Topographic instability of flow in a rotating fluid

Here are presented the results of experimental and theoretical studies on a stability of zonal geostrophic flows in the rotating layer of the shallow water. In the experiments, a special apparatus by Abastumani Astrophysical Observatory Georgian Academy of Science was used. This apparatus represents a paraboloid of rotation, which can be set in a regulable rotation around the vertical axis. Maximal diameter of the paraboloid is 1.2 m, radius of curvature in the pole is 0.698 m. In the paraboloid, water spreads on walls as a layer uniform on height under the period of rotation 1.677 s. Against a background of the rotating fluid, the zonal flows are formed by the source-sink system. It consists of two concentric circular perforations on the paraboloid bottom (width is 0.3 cm, radiuses are 8.4 and 57.3 cm, respectively); water can be pumped through them with various velocities and in all directions. It has been established that under constant vertical depth of the rotating fluid the zonal flows are stable. There are given the measurements of the radial profiles for the water level and velocity in the stationary regime. It has been found that zonal flows may lose stability under the presence of the radial gradient of full depth formed by a change of angular velocity of paraboloid rotation. An instability origin results in the loss of flow axial symmetry and in the appearance of self-excited oscillations in the zonal flow. At the given angular velocity of rotation, instability is observed only in the definite range of intensities of the source-sink system. The theoretical estimations are performed in the framework of the equations of the shallow water theory, including the terms describing the bottom friction. It has been shown that the instability of zonal flows found experimentally has a topographical nature and is related with non-monotone dependence of the potential vorticity on radius.