Browsing by Author "Lima, Francisco Welington de Sousa"

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    Droplet finite-size scaling of the contact process on scale-free networks revisited.
    (2023) Alencar, David Santana Marques; Alves, Tayroni Francisco de Alencar; Ferreira, Ronan Silva; Alves, Gladstone de Alencar; Macedo Filho, Antonio de; Lima, Francisco Welington de Sousa
    We present an alternative finite-size scaling (FSS) of the contact process on scale-free networks compatible with mean-field scaling and test it with extensive Monte Carlo simulations. In our FSS theory, the dependence on the system size enters the external field, which represents spontaneous contamination in the context of an epidemic model. In addition, dependence on the finite size in the scale-free networks also enters the network cutoff. We show that our theory reproduces the results of other mean-field theories on finite lattices already reported in the literature. To simulate the dynamics, we impose quasi-stationary states by reactivation. We insert spontaneously infected individuals, equivalent to a droplet perturbation to the system scaling as N⁻¹. The system presents an absorbing phase transition where the critical behavior obeys the mean-field exponents, as we show theoretically and by simulations. However, the quasi-stationary state gives finite-size logarithmic corrections, predicted by our FSS theory, and reproduces equivalent results in the literature in the thermodynamic limit. We also report the critical threshold estimates of basic reproduction number R₀ λc of the model as a linear function of the network connectivity inverse 1/z, and the extrapolation of the critical threshold function for z→∞ yields the basic reproduction number R₀ = 1 of the complete graph, as expected. Decreasing the network connectivity increases the critical R₀ for this model.
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    Opinion dynamics systems on barabási-albert networks : biswas-chatterjee-sen model.
    (2023) Alencar, David Santana Marques; Alves, Tayroni Francisco de Alencar; Alves, Gladstone de Alencar; Macedo Filho, Antonio de; Ferreira, Ronan Silva; Lima, Francisco Welington de Sousa; Plascak, João Antônio
    A discrete version of opinion dynamics systems, based on the Biswas–Chatterjee–Sen (BChS) model, has been studied on Barabási–Albert networks (BANs). In this model, depending on a pre-defined noise parameter, the mutual affinities can assign either positive or negative values. By employing extensive computer simulations with Monte Carlo algorithms, allied with finite-size scaling hypothesis, second-order phase transitions have been observed. The corresponding critical noise and the usual ratios of the critical exponents have been computed, in the thermodynamic limit, as a function of the average connectivity. The effective dimension of the system, defined through a hyper-scaling relation, is close to one, and it turns out to be connectivity-independent. The results also indicate that the discrete BChS model has a similar behavior on directed Barabási–Albert networks (DBANs), as well as on Erdös–Rènyi random graphs (ERRGs) and directed ERRGs random graphs (DERRGs). However, unlike the model on ERRGs and DERRGs, which has the same critical behavior for the average connectivity going to infinity, the model on BANs is in a different universality class to its DBANs counterpart in the whole range of the studied connectivities.
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    The diffusive epidemic process on Barabasi–Albert networks.
    (2021) Alves, Tayroni Francisco de Alencar; Alves, Gladstone de Alencar; Macedo Filho, Antonio de; Ferreira, Ronan Silva; Lima, Francisco Welington de Sousa
    We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time tmax, exponentially distributed with mean inversely proportional to the node population in order to model the individuals’ interactions. Our simulation results of the modified model on Barabasi–Albert networks are compatible with a continuous absorbing-active phase transition when increasing the average concentration. The transition obeys the mean-field critical exponents β = 1, γ = 0 and ν⊥ = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents β = γ = −3/2 on the order parameter and its fluctuations, respectively. The most evident implication of our simulation results is if the individuals avoid social interactions in order to not spread a disease, this leads the system to have a finite threshold in scale-free graphs.