Continuous and discontinuous absorbing-state phase transitions on Voronoi-Delaunay random lattices

We study absorbing-state phase transitions in two-dimensional Voronoi-Delaunay (VD) random lattices with quenched coordination disorder. Quenched randomness usually changes the criticality and destroys discontinuous transitions in low-dimensional nonequilibrium systems. We performed extensive simulations of the Ziff-Gulari-Barshad (ZGB) model, and verified that the VD disorder does not change the nature of its discontinuous transition. Our results corroborate recent findings of Barghatti and Vojta [Phys. Rev. Lett. {\bf 113}, 120602 (2014)] stating the irrelevance of topological disorder in a class of random lattices that includes VD and raise the interesting possibility that disorder in nonequilibrium APT may, under certain conditions, be irrelevant for the phase coexistence. We also verify that the VD disorder is irrelevant for the critical behavior of models belonging to the directed percolation and Manna universality classes.Comment: 7 pages, 6 figure

How would you integrate the equations of motion in dissipative particle dynamics simulations?

In this work we assess the quality and performance of several novel dissipative particle dynamics integration schemes that have not previously been tested independently. Based on a thorough comparison we identify the respective methods of Lowe and Shardlow as particularly promising candidates for future studies of large-scale properties of soft matter systems

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

We experimentally study the critical properties of the non-equilibrium 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 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 $\nu_{\perp} = 1$, $\nu_{\parallel} = 2$, $\gamma = 1$, $\eta \approx 0.6 - 0.67$, and $\beta=1/2$, whereas the dynamical critical exponent is $z = \nu_{\parallel}/\nu_{\perp} = 2$. 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 towards 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 non-equilibrium extension to model C if we assume that $\alpha$, the exponent associated in equilibrium to the specific heat divergence but with no counterpart in this non-equilibrium experiment, vanishes.Comment: 14 pages, 13 figures, accepted in PR

Heavy-tailed Distributions In Stochastic Dynamical Models

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics

How self-organized criticality works: A unified mean-field picture

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other non-equilibrium critical phenomena, we identify the order parameter with the density of ``active'' sites and the control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or super-critical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control parameters, the stationary state displays scaling characteristic of self-organized criticality (SOC). We show that this limit corresponds to the breakdown of space-time locality in the dynamical rules of the models. We define a complete set of critical exponents, describing the scaling of order parameter, response functions, susceptibility and correlation length in the subcritical and supercritical states. In the subcritical state, the response of the system to small perturbations takes place in avalanches. We analyze their scaling behavior in relation with branching processes. In sandpile models because of conservation laws, a critical exponents subset displays mean-field values ($\nu=1/2$ and $\gamma = 1$) in any dimensions. We treat bulk and boundary dissipation and introduce a new critical exponent relating dissipation and finite size effects. We present numerical simulations that confirm our results. In the case of the forest-fire model, our approach can distinguish between different regimes (SOC-FF and deterministic FF) studied in the literature and determine the full spectrum of critical exponents.Comment: 21 RevTex pages, 3 figures, submitted to Phys. Rev.

The Economics of Local Tourist Systems

In this paper we analyse the Local Tourist System (LTS) as a particular case of Marshallian Industrial District. The LTS allows the identification of more effective policy tools for managing tourism. First, through the concept of LTS, the policy maker can take into account the complexity of tourism, characterised by a strong heterogeneity of goods, services and subjects involved; second, LTS helps promote a stronger co-ordination between the public and the private sector, by identifying a homogeneous territory and recognising its importance in tourists' decisions; third, through the LTS the policymaker can analyze the externalities and promotes the idea of collaborating networks in a context of local development. In the LTS framework, the anticommon problem can be analysed and contrasted. As the tourist has to buy different but intertwined goods which compose the holiday package, the failure in one of the markets can lead to the overall failure of the package. A LTS policy has to: i) co-ordinate the price policy of the different firms supplying “single components” of the tourist product; ii) fix the price of the whole product; iii) impute a price to each component. We demonstrate that, through price policy co-ordination and under general conditions, the LTS can increase the size of tourism and the firms’ profits, thereby reaching a more effective and efficient target in tourism policy. The recent introduction of LTS in the Italian legislation can be seen as a positive attempt of improving co-ordination in a complex sector such as tourism.Local tourist systems, Tourism policy

Social network dynamics of face-to-face interactions

The recent availability of data describing social networks is changing our understanding of the "microscopic structure" of a social tie. A social tie indeed is an aggregated outcome of many social interactions such as face-to-face conversations or phone-calls. Analysis of data on face-to-face interactions shows that such events, as many other human activities, are bursty, with very heterogeneous durations. In this paper we present a model for social interactions at short time scales, aimed at describing contexts such as conference venues in which individuals interact in small groups. We present a detailed anayltical and numerical study of the model's dynamical properties, and show that it reproduces important features of empirical data. The model allows for many generalizations toward an increasingly realistic description of social interactions. In particular in this paper we investigate the case where the agents have intrinsic heterogeneities in their social behavior, or where dynamic variations of the local number of individuals are included. Finally we propose this model as a very flexible framework to investigate how dynamical processes unfold in social networks.Comment: 20 pages, 25 figure