Física
URI permanente desta comunidadehttps://locus.ufv.br/handle/123456789/11779
Navegar
112 resultados
Resultados da Pesquisa
Item Robustness and fragility of the susceptible- infected- susceptible epidemic models on complex networks(Physical Review E, 2018) Cota, Wesley; Mata, Angélica S.; Ferreira, Silvio C.We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent γ<5/2, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent γ>5/2. Differences are more remarkable for γ>3, where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a k-core decomposition for γ<3 while it happens only for γ<5/2 in the standard model. For γ>3, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.Item Griffiths phases in infinite- dimensional, non- hierarchical modular networks(Scientific Reports, 2018) Cota, Wesley; Ódor, Géza; Ferreira, Silvio C.Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs.Item Eden model with nonlocal growth rules and kinetic roughening in biological systems(Physical Review, 2018-08) Ferreira, Silvio C.; Santalla, Silvia N.We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. The concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore a nonlocal dependence on the replication rule. Our simulations point out that the Kadar–Parisi–Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity, we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.Item Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge(Physical Review E, 2017-12) Rodrigues, Nathann T.; Oliveira, Tiago J.We present results from extensive Monte Carlo simulations of polymer models where each lattice site can be visited by up to K monomers and no restriction is imposed on the number of bonds on each lattice edge. These multiple monomer per site (MMS) models are investigated on the square and cubic lattices, for K=2 and 3, by associating Boltzmann weights ω0=1, ω1=eβ1, and ω2=eβ2 to sites visited by 1, 2, and 3 monomers, respectively. Two versions of the MMS models are considered for which immediate reversals of the walks are allowed (RA) or forbidden (RF). In contrast to previous simulations of these models, we find the same thermodynamic behavior for both RA and RF versions. In three dimensions, the phase diagrams, in space β2×β1, are featured by coil and globule phases separated by a line of Θ points, as thoroughly demonstrated by the metric νt, crossover ϕt, and entropic γt exponents. The existence of the Θ lines is also confirmed by the second virial coefficient. This shows that no discontinuous collapse transition exists in these models, in contrast to previous claims based on a weak bimodality observed in some distributions, which indeed exists in a narrow region very close to the Θ line when β1<0. Interestingly, in two dimensions, only a crossover is found between the coil and globule phases.Item Kardar- Parisi- Zhang growth on one- dimensional decreasing substrates(Physical Review E, 2018-07) Carrasco, I. S. S.; Oliveira, T. J.Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, here we investigate several one-dimensional KPZ models on substrates whose size changes in time as L(t)=L0+ωt, focusing on the case ω<0. From extensive numerical simulations, we show that for L0≫1 there exists a transient regime in which the statistics is consistent with that of flat KPZ systems (the ω=0 case), for both ω<0 and ω>0. Actually, for a given model, L0 and |ω|, we observe that a difference between ingrowing (ω<0) and outgrowing (ω>0) systems arises only at long times (t∼tc=L0/|ω|), when the expanding surfaces cross over to the statistics of curved KPZ systems, whereas the shrinking ones become completely correlated. A generalization of the Family-Vicsek scaling for the roughness of ingrowing interfaces is presented. Our results demonstrate that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless of their curvature. This is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces, but it is in contrast with the apparent observation of curved statistics in colloidal deposition at the edge of evaporating drops. A possible explanation for this last result, as a consequence of the very small number of monolayers analyzed in this experiment, is given. This is illustrated in a competitive growth model presenting a few-monolayer transient and an asymptotic behavior consistent, respectively, with the curved and flat statistics.Item Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks(Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018) Silva, Diogo H.; Ferreira, Silvio C.We investigate a fermionic susceptible-infected-susceptible model with the mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions P(k)∼k−γP(k)∼k−γ of exponents 2<γ<32<γ<3. Two diffusive processes with diffusion rate DD of an infected vertex are considered. In the standard diffusion, one of the nearest-neighbors is chosen with equal chance, while in the biased diffusion, this choice happens with probability proportional to the neighbor’s degree. A non-monotonic dependence of the epidemic threshold on DD with an optimum diffusion rate D∗D∗, for which the epidemic spreading is more efficient, is found for standard diffusion while monotonic decays are observed in the biased case. The epidemic thresholds go to zero as the network size is increased and the form that this happens depends on the diffusion rule and the degree exponent. We analytically investigated the dynamics using quenched and heterogeneous mean-field theories. The former presents, in general, a better performance for standard and the latter for biased diffusion models, indicating different activation mechanisms of the epidemic phases that are rationalized in terms of hubs or max kk-core subgraphs. Nowadays, we live in an interwoven world where information, goods, and people move through a complex structure with widely diversified types of interactions such as on-line friendship and airport connections. These and many other systems of completely distinct nature can be equally suited in a theoretical representation called complex networks, in which the elements are represented by vertices and the interactions among them by edges connecting these vertices. The study of epidemic processes on complex networks represents one of the cornerstones in modern network science and can aid the prevention (or even stimulation) of disease or misinformation spreading. The relevance of the interplay between diffusion and epidemic spreading in real systems is self-evident since hosts of infectious agents, such as people and mobile devices, are constantly moving, being the carriers that promote the quick transition from a localized outbreak to a large scale epidemic scenario. In this work, we perform a theoretical analysis and report nontrivial roles played by mobility of infected agents on the efficiency of epidemic spreading running on the top of complex networks. We expect that our results will render impacts for forthcoming research related to the area.Item Mathematical modeling of dengue epidemic: control methods and vaccination strategies(Theory in Biosciences, 2018-04) Carvalho, Sylvestre Aureliano; Silva, Stella Olivia da; Charret, Iraziet da CunhaDengue is, in terms of death and economic cost, one of the most important infectious diseases in the world. So, its mathematical modeling can be a valuable tool to help us to understand the dynamics of the disease and to infer about its spreading by the proposition of control methods. In this paper, control strategies, which aim to eliminate the Aedes aegypti mosquito, as well as proposals for the vaccination campaign are evaluated. In our mathematical model, the mechanical control is accomplished through the environmental support capacity affected by a discrete function that represents the removal of breedings. Chemical control is carried out using insecticide and larvicide. The efficiency of vaccination is studied through the transfer of a fraction of individuals, proportional to the vaccination rate, from the susceptible to the recovered compartments. Our major find is that the dengue fever epidemic is only eradicated with the use of an immunizing vaccine because control measures, directed against its vector, are not enough to halt the disease spreading. Even when the infected mosquitoes are eliminated from the system, the susceptible ones are still present, and infected humans cause dengue fever to reappear in the human population.Item Loop quantization of a model for D = 1 + 2 (anti)de sitter gravity coupled to topological matter(Classical and Quantum Gravity, 2015) Oporto, Zui; Constantinidis, Clisthenis P.; Piguet, OlivierWe present a complete quantization of Lorentzian D = 1 + 2 gravity with cosmological constant, coupled to a set of topological matter fields. The approach of loop quantum gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) × SU(2). A pair of quantum observables is con- structed, which are non-trivial despite being gauge-equivalent to zero at the classical level. A semi-classical approximation based on appropriately defined coherent states shows non-vanishing expectation values for them, thus not reproducing their classical behaviour.Item Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice(Journal of Physics A: Mathematical and Theoretical, 2016) Oliveira, Tiago J.The exact grand-canonical solution of a generalized interacting self-avoid walk (ISAW) model, placed on a Husimi lattice built with squares, is presented. In this model, beyond the traditional interaction ω1=eϵ1/kBT between (nonconsecutive) monomers on nearest-neighbor (NN) sites, an additional energy ϵ2 is associated to next-NN (NNN) monomers. Three definitions of NNN sites/interactions are considered, where each monomer can have, effectively, at most 2, 4 or 6 NNN monomers on the Husimi lattice. The phase diagrams found in all cases have (qualitatively) the same thermodynamic properties: a non-polymerized (NP) and a polymerized (P) phase separated by a critical and a coexistence surface that meet at a tricritical (θ-) line. This θ-line is found even when one of the interactions is repulsive, existing for ω1 in the range [0,∞), i. e., for ϵ1/kBT in the range [−∞,∞). Counterintuitively, a θ-point exists even for an infinite repulsion between NN monomers (ω1=0), being associated to a coil-"soft globule" transition. In the limit of an infinite repulsive force between NNN monomers, however, the coil-globule transition disappears and only a NP-P continuous transition is observed. This particular case, with ω2=0, is also solved exactly on the square lattice, using a transfer matrix calculation, where a discontinuous NP-P transition is found. For attractive and repulsive forces between NN and NNN monomers, respectively, the model becomes quite similar to the semiflexible-ISAW one, whose crystalline phase is not observed here, as a consequence of the frustration due to competing NN and NNN forces. The mapping of the phase diagrams in canonical ones is discussed and compared with recent results from Monte Carlo simulations.Item Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices(Journal of Physics A: Mathematical and Theoretical, 2014) Rodrigues, Nathann T; Oliveira, Tiago JWe study a generalized interacting self-avoiding walk (ISAW) model with nearest- and next nearest-neighbor (NN and NNN) interactions on square and cubic lattices. In both dimensions, the phase diagrams show coil and globule phases separated by continuous transition lines. Along these lines, we calculate the metric νt, crossover phgrt and entropic γt exponents, all of them in good agreement with the exact values of the Θ universality class. Therefore, the introduction of NNN interactions does not change the class of the ISAW model, which still exists even for repulsive forces. The growth parameters μt are shown to change monotonically with temperature along the Θ-lines. In the square lattice, the Θ-line has an almost linear behavior, which was not found in the cubic one. Although the region of repulsive NNN interactions, with attractive NN ones, leads to stiff polymers, no evidence of a transition to a crystalline phase was found.