In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures, that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, that seems to have a still longer ordering time.PACS numbers: 82.70. Dd, 64.60.Ak, 82.70.Gg In colloidal suspensions solid (or liquid) mesoscopic particles are dispersed in another substance. These systems, like blood, proteins in water, milk, black ink or paints, are important in our everyday lives, in biology and industry [1,2]. It is crucial, for example, to control the process of aggregation in paint and paper industries [3], or to favour the protein crystallization in the production of pharmaceuticals and photonic crystals [4,5].A practical and exciting feature of colloidal suspensions is that the interaction energy between particles can be well controlled [6][7][8]. In fact particles can be coated and stabilized leading to a hard sphere behaviour, and an attractive depletion interaction can be brought out by adding some non-adsorbing polymers. The range and strength of the potential are controlled respectively by the size and concentration of the polymer [8,9]. Recent experimental works highlighted the presence of a net charge on colloidal particles [7,10] giving rise to a long range electrostatic repulsion in addition to the depletion attraction.The competition between attractive and repulsive interactions produces a rich phenomenology and a complex behavior as far as structural and dynamical properties are concerned. For particular choices of the interaction parameters, the aggregation of particles is favoured but the liquid-gas phase transition can be avoided and the cluster size can be stabilized at an optimum value [11]. Experimentally, such a cluster phase made of small equilibrium monodisperse clusters is observed using confocal microscopy at low volume fraction and low temperature (or high attraction strength) [7,10,12]. Increasing the volume fraction, the system is transformed from an ergodic cluster liquid into a nonergodic gel [10,12], where structural arrest occurs. Using molecular dynamic simulations, we showed that such structural arrest is crucially related to the formation of a long living spanning cluster, providing evidence for the percolation nature of the colloidal gel transition at low volume fraction and low temperature [13,14]. This scenario was confirmed by recent experiments [10] and molecular dynamics simulations [15], where it was shown that increasing the volume fraction clusters coalesce into elongated structures eventually forming a disordered spanning network. A realistic framework for the modelization of these systems is represented by DLVO interaction p...

The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABM) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its "phase diagram" in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the "Mark I" ABM devised by D. Delli Gatti and collaborators. In this regard, our major finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high. We then introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-tosales ratio. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the "good" phase) or deflation (in the "bad" phase), but leaves the overall phase diagram of the model essentially unchanged. We have also explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models.It is human nature to think wisely and to act absurdly

The nonlinear dielectric susceptibilities χ (1) 3 (ω,T ) and χ (3) 3 (ω,T ), corresponding respectively to the first-and third-harmonic responses, have been measured in supercooled glycerol close to the glass transition temperature T g . By analyzing the two contributions to the nonlinear response, saturation of the polarization and glassy correlations, we show that the first one is dominant at low frequencies and verify the scaling prediction of Bouchaud and Biroli [Phys. Rev. B 72, 064204 (2005)] in what concerns the second one. Such a detailed investigation allows an accurate determination of the temperature dependence of the average number of correlated molecules N corr (T ).