Age spreads in clusters and associations: the lithium test

We report the evidence that several low-mass stars (<~0.4 Msun) of the Orion and Upper Scorpius clusters have lithium abundances well below the interstellar value. Due to time-dependent depletion, our result implies stellar ages greater than ~5 Myr, suggesting that star formation has been proceeding for a long time in these systems.Comment: to appear in IMF@50: The Initial Mass Function 50 years later, eds. E. Corbelli et al. (Kluwer Acad. Press), 2004, in pres

Diffusion in scale-free networks with annealed disorder

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost, and re-established again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results including, (1) greatly reduced growth with the time of the mean number of distinct sites visited; (2) blocking of the random walkers; (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.Comment: 18 pages including 8 figure

Avalanche Collapse of Interdependent Network

We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random damage. Divergence of their mean size signals the approach to the hybrid phase transition from one side, while there are no critical precursors on the other side. We find that this discontinuous transition occurs in scale-free multiplex networks whenever the mean degree of at least one of the interdependent networks does not diverge.Comment: 4 pages, 5 figure

Robustness of planar random graphs to targeted attacks

In this paper, robustness of planar trivalent random graphs to targeted attacks of highest connected nodes is investigated using numerical simulations. It is shown that these graphs are relatively robust. The nonrandom node removal process of targeted attacks is also investigated as a special case of non-uniform site percolation. Critical exponents are calculated by measuring various properties of the distribution of percolation clusters. They are found to be roughly compatible with critical exponents of uniform percolation on these graphs.Comment: 9 pages, 11 figures. Added references.Corrected typos. Paragraph added in section II and in the conclusion. Published versio

Revisiting the effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of controversial results. Here we re-examine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one and two-dimensional versions of Axelrod's model indicate that, contrary to previous claims in the literature, the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforces homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state

Geometrical properties of Potts model during the coarsening regime

We study the dynamic evolution of geometric structures in a poly-degenerate system represented by a $q$-state Potts model with non-conserved order parameter that is quenched from its disordered into its ordered phase. The numerical results obtained with Monte Carlo simulations show a strong relation between the statistical properties of hull perimeters in the initial state and during coarsening: the statistics and morphology of the structures that are larger than the averaged ones are those of the initial state while the ones of small structures are determined by the curvature driven dynamic process. We link the hull properties to the ones of the areas they enclose. We analyze the linear von-Neumann--Mullins law, both for individual domains and on the average, concluding that its validity, for the later case, is limited to domains with number of sides around 6, while presenting stronger violations in the former case.Comment: 12 page

Aging dynamics and the topology of inhomogenous networks

We study phase ordering on networks and we establish a relation between the exponent $a_\chi$ of the aging part of the integrated autoresponse function $\chi_{ag}$ and the topology of the underlying structures. We show that $a_\chi >0$ in full generality on networks which are above the lower critical dimension $d_L$, i.e. where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with $T_c = 0$, which are at the lower critical dimension $d_L$, we show that $a_\chi$ is expected to vanish. We provide numerical results for the physically interesting case of the $2-d$ percolation cluster at or above the percolation threshold, i.e. at or above $d_L$, and for other networks, showing that the value of $a_\chi$ changes according to our hypothesis. For $O({\cal N})$ models we find that the same picture holds in the large-${\cal N}$ limit and that $a_\chi$ only depends on the spectral dimension of the network.Comment: LateX file, 4 eps figure

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

A spherical model with directional interactions: I. Static properties

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different size. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: at low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities -- due to the competition between excluded volume and attractive interactions -- the system forms a defective network. The very same behavior has been previously observed in numerical studies of non-spherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Differently from these models, theoretical treatments devised for spherical potentials, e.g. integral equations and ideal mode coupling theory for the glass transition can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.Comment: 11 pages, 11 figure