Gustavo Castillo

Fluctuations and criticality of a granular solid-liquid-like phase transition.

We present an experimental study of density and order fluctuations in the vicinity of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. The two-dimensional projected static and dynamic correlation functions are studied. We show that density fluctuations, characterized through the structure factor, increase in size and intensity as the transition is approached, but they do not change significantly at the transition itself. The dense, metastable clusters, which present square symmetry, also increase their local order in the vicinity of the transition. This is characterized through the bond-orientational order parameter Q4, which in Fourier space shows an Ornstein-Zernike-like behavior. Depending on the filling density and vertical height, the transition can be of first- or second-order type. In the latter case, the associated correlation length ξ4, the relaxation time τ4, the zero k limit of Q4 fluctuations (static susceptibility), the pair correlation function of Q4, and the amplitude of the order parameter obey critical power laws, with saturations due to finite size effects. Their respective critical exponents are ν(perpendicular))=1, ν(parallel)=2, γ=1, η=0.67, and β=1/2, whereas the dynamical critical exponent z=ν(parallel)/ν(perpendicular)=2. These results are consistent with model C of dynamical critical phenomena, valid for a nonconserved critical order parameter (bond-orientation order) coupled to a conserved field (density).

Universality and criticality of a second-order granular solid-liquid-like phase transition.

We experimentally study the critical properties of the nonequilibrium solid-liquid-like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the bond-orientational order parameter Q(4), which measures the degree of local crystallization. Two setups are compared, which present the transition at different critical accelerations as a result of modifying the energy dissipation parameters. In both setups five independent critical exponents are measured, associated to different properties of Q(4): the correlation length, relaxation time, vanishing wavenumber limit (static susceptibility), the hydrodynamic regime of the pair correlation function, and the amplitude of the order parameter. The respective critical exponents agree in both setups and are given by ν(⊥)=1,ν(∥)=2,γ=1,η≈0.6-0.67, and β=1/2, whereas the dynamical critical exponent is z=ν(∥)/ν(⊥)=2. The agreement on five exponents is an exigent test for the universality of the transition. Thus, while dissipation is strictly necessary to form the crystal, the path the system undergoes toward the phase separation is part of a well-defined universality class. In fact, the local order shows critical properties while density does not. Being the later conserved, the appropriate model that couples both is model C in the Hohenberg and Halperin classification. The measured exponents are in accord with the nonequilibrium extension to model C if we assume that α, the exponent associated in equilibrium to the specific heat divergence but with no counterpart in this nonequilibrium experiment, vanishes.

Chile y la OCDE. La dicotomia entre lo macroeconómico y el desarrollo humano

espanolLa economia de Chile ha mostrado singular fortaleza desde la decada de 1990. El establecimiento de una trayectoria de alto crecimiento economico e inversion, el aumento del ingreso per capita, la inflacion bien contenida y los excedentes fiscales han sido hechos recurrentes. Sin embargo, persiste una preocupante dicotomia entre los buenos resultados macroeconomicos y lo limitado de aquellos relativos a las variables humanas subyacentes, especialmente en educacion, salud e innovacion, lo cual permite otorgar baja sustentabilidad a los resultados en cuanto a competitividad internacional y estabilidad macroeconomica. Este trabajo pone de relieve ese contraste, basado en la informacion comparativa disponible del Foro Economico Mundial. EnglishThe Chilean economy has exhibited a noticeable performance since the 1990s. High economic growth and investment, the sustained increase in per capita GDP, low inflation and the existence of fiscal surpluses have been repeated results along past decades. However, there prevails a worrisome dichotomy between positive macroeconomic results and poor indicators relative to the human dimension, particularly education, health and innovation, a situation that originates doubts as to the sustainability of economic results, particularly in terms of international competitiveness and macroeconomic stability. This paper illustrates the situation using comparative information available from the World Economic Forum