1,298 research outputs found
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
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