Effect of hydrophobic solutes on the liquid-liquid critical point

Jagla ramp particles, interacting through a ramp potential with two characteristic length scales, are known to show in their bulk phase thermodynamic and dynamic anomalies, similar to what is found in water. Jagla particles also exhibit a line of phase transitions separating a low density liquid phase and a high density liquid phase, terminating in a liquid-liquid critical point in a region of the phase diagram that can be studied by simulations. Employing molecular dynamics computer simulations, we study the thermodynamics and the dynamics of solutions of hard spheres (HS) in a solvent formed by Jagla ramp particles. We consider the cases of HS mole fraction x = 0.10, 0.15 and 0.20, and also the case x = 0.50 (a 1:1 mixture of HS and Jagla particles). We find a liquid-liquid critical point, up to the highest HS mole fraction; its position shifts to higher pressures and lower temperatures upon increasing x. We also find that the diffusion coefficient anomalies appear to be preserved for all the mole fractions studied.Comment: 8 pages, 7 figures, 1 table. In press (Phys. Rev. E

The Italian primary school-size distribution and the city-size: a complex nexus

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.Comment: 16 pages, 10 figure