Phase diagrams of the Ziff-Gulari-Barshad model on random networks.

In this study, we revisited the Ziff-Gulari-Barshad (ZGB) model in order to study the behavior of its phase diagram when two well-known random networks play the role of the catalytic surfaces: the random geometric graph and the Erdös-Rényi network. The connectivity and, therefore, the average number of neighbors of the nodes of these networks can vary according to their control parameters, the neighborhood radius α, and the linking probability p, respectively. In addition, the catalytic reactions of the ZGB model are governed by the parameter y, the adsorption rate of carbon monoxide molecules on the catalytic surface. So, to study the phase diagrams of the model on both random networks, we carried out extensive steady-state Monte Carlo simulations in the space parameters (y, α) and (y, p) and showed that the continuous phase transition is greatly affected by the topological features of the networks while the discontinuous one remains present in the diagram throughout the interval of study.

Mobility helps problem-solving systems to avoid groupthink.

Groupthink occurs when everyone in a group starts thinking alike, as when people put unlimited faith in a leader. Avoiding this phenomenon is a ubiquitous challenge to problem-solving enterprises and typical countermeasures involve the mobility of group members. Here we use an agent-based model of imitative learning to study the influence of the mobility of the agents on the time they require to find the global maxima of NK-fitness landscapes. The agents cooperate by exchanging information on their fitness and use this information to copy the fittest agent in their influence neighborhoods, which are determined by face-to-face interaction networks. The influence neighborhoods are variable since the agents perform random walks in a two-dimensional space. We find that mobility is slightly harmful for solving easy problems, i.e., problems that do not exhibit suboptimal solutions or local maxima. For difficult problems, however, mobility can prevent the imitative search being trapped in suboptimal solutions and guarantees a better performance than the independent search for any system size.

Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models.

In this paper we revisited the Ziff-Gulari-Barshad model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We use a method proposed recently to locate the nonequilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the continuous phase transition of the model, as well as its upper spinodal point, a pseudocritical point located near the discontinuous phase transition. The static critical exponents ß, ν_{∥}, and ν_{⊥}, as well as the dynamic critical exponents θ and z for the continuous transition point, were also estimated and are in excellent agreement with results found in literature.