We study the Deffuant et al model for continuous-opinion dynamics under the influence of noise. In the original version of this model, individuals meet in random pairwise encounters after which they compromise or not depending on a confidence parameter. Free will is introduced in the form of noisy perturbations: individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside the whole opinion space. We derive the master equation of this process. One of the main effects of noise is to induce an order–disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The master equation analysis is compared with direct Monte Carlo simulations. We find that the master equation and the Monte Carlo simulations do not always agree due to finite-size-induced fluctuations that we analyze in some detail.

This letter focus on the effect of repulsive interactions on the adoption of an external message in an opinion model. With a simple change in the rules, we modify the Deffuant et al. model to incorporate the presence of repulsive interactions. We will show that information receptiveness is optimal for an intermediate fraction of repulsive links. Using the master equation as well as Monte Carlo simulations of the message-free model, we identify the point where the system becomes optimally permeable to external influence with an order-disorder transition.

Assessment of mean-field microkinetic models for CO methanation on stepped metal surfaces using accelerated kinetic Monte Carlo The Journal of Chemical Physics 147, 152705 (2017) Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model for continuous-opinion dynamics.

This work focus on the effects of an external mass media on continuous opinion dynamics with heterogeneous bounds of confidence. We modified the original Deffuant et al. and Hegselmann and Krause models to incorporate both, an external mass media and a heterogeneous distribution of confidence levels. We analysed two cases, one where only two bounds of confidence are taken into account, and other were each individual of the system has her/his own characteristic level of confidence. We found that, in the absence of mass media, diversity of bounds of confidence can improve the capacity of the systems to reach consensus. We show that the persuasion capacity of the external message is optimal for intermediate levels of heterogeneity. Our simulations also show the existence, for certain parameter values, of a counter-intuitive effect in which the persuasion capacity of the mass media decreases if the mass media intensity is too large. We discuss similarities and differences between the two heterogeneous versions of these continuous opinion dynamic models under the influence of mass media.

We study the effects of diffusing opinions on the Deffuant et al. model for continuous opinion dynamics. Individuals are given the opportunity to change their opinion, with a given probability, to a randomly selected opinion inside an interval centered around the present opinion. We show that diffusion induces an order-disorder transition. In the disordered state the opinion distribution tends to be uniform, while for the ordered state a set of well defined opinion clusters are formed, although with some opinion spread inside them. If the diffusion jumps are not large, clusters coalesce, so that weak diffusion favors opinion consensus. A master equation for the process described above is presented. We find that the master equation and the Monte-Carlo simulations do not always agree due to finite-size induced fluctuations. Using a linear stability analysis we can derive approximate conditions for the transition between opinion clusters and the disordered state. The linear stability analysis is compared with Monte Carlo simulations. Novel interesting phenomena are analyzed. PACS. 8 9.65.-s Social and economic systems.,05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion.

The behavior of different mixed oxides, including zinc titanates (ZT) and zinc ferrites modified with CuO (ZFC) or TiO2 (ZFT), as hot gas desulfurizing sorbents was investigated. The sorbents were prepared by calcination at 650 °C of a mixture of bulk oxides in three different stoichiometries in order to form new phases and modify their textural properties. Tests of stability against reduction were obtained by thermoprogrammed reduction, and kinetic studies of the sulfidation reaction were carried out in a thermobalance in the temperature range of 550−650 °C. Kinetic parameters of the intrinsic reaction were obtained assuming a grain model. The sulfidation behavior of the sorbents as extrudates was investigated in a fixed-bed reactor in terms of breakthrough curves. Fresh and sulfided samples were characterized by Hg porosimetry, X-ray diffraction, and SEM-EDX. The study shows that the addition of TiO2 or CuO to zinc ferrite based sorbents calcined at 650 °C has little effect on the stability against reduction but markedly influences their textural properties. The stabilizing effect of Ti is observed in samples calcined at higher temperature or in non-iron-containing sorbents. The calculated kinetic constants indicate that the Zn content and the incorporation of Cu have an enhancing effect on the kinetics of the sulfidation process. Including H2 in the feed gas decreases the reactivity and increases the activation energy. Extrudated sorbents showed a good performance as desulfurizing agents and maintained the H2S concentration in the outlet gas below 20 ppm. ZT sorbent exhibited a poor efficiency, which makes the addition of Ti questionable.

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