L.S. Lucena

Self-organization in growth of branched polymers

We propose a growth mechanism for branched polymers where self-organization leads the system to criticality. By incorporating a dynamical rule which simply regulates the flux of monomers available for aggregation, the system is spontaneously driven to the critical branching probability which separates the finite from infinite growth regimes. The fact that the system reaches and maintains itself close to a critical state without the need of a fine tuning of the parameters is thus discussed in terms of the self-organized criticality (SOC) concept. Finally, we also demonstrate the feasibility of the method in association with a practical implementation of the theoretical model.

Seismic ground roll time–frequency filtering using the gaussian wavelet transform

Seismic signal processing is an important task in geophysics sounding and represents a permanent challenge in petroleum exploration. Although seismograms could in principle give us a picture of a geological structure, they are very contaminated by spurious signals (having the ground roll as the main component). This fact demands a big effort in developing new filtering methodologies. Using the Gaussian wavelet transform, a filtering method for ground roll removal is developed. The filter allows a local extraction of the ground roll, it is adaptative to trace and it has an attenuation factor that keeps the average frequency spectrum. This method is tested for a land-based seismic signal leading to promising results.

Crossover from extensive to nonextensive behavior driven by long-range d=1 bond percolation

We present a Monte Carlo study of a linear chain (d=1) with long-range bonds whose occupancy probabilities are given by pij=p/rijα(0⩽p⩽1;α⩾0) where rij=1,2,… is the distance between sites. The α→∞(α=0) corresponds to the first-neighbor (“mean field”) particular case. We exhibit that the order parameter P∞ equals unity ∀p>0 for 0⩽α⩽1, presents a familiar behavior (i.e., 0 for p⩽pc(α) and finite otherwise) for 1 2. Our results confirm recent conjecture, namely that the nonextensive region (0⩽α⩽1) can be meaningfully unfolded, as well as unified with the extensive region (α>1), by exhibiting P∞ as a function of p∗ where (1−p∗)=(1−p)N∗(N∗≡(N1−α/d−1)/(1−α/d),N being the number of sites of the chain). A corollary of this conjecture, now numerically verified, is that pc∝(α−1) in the α→1+0 limit.

Invasion percolation between two sites

We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the nontrapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) Pe at the extraction site. For Pe = 0, we show that the mass distribution of invaded clusters P(M) follows a power-law P(M) approximately M(-alpha) for intermediate values of the mass M, with an exponent alpha = 1.39+/-0.03. When the local pressure is set to Pe = Pc, where Pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent alpha = 1.02+/-0.03. This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these differences, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depend significantly on the local pressure Pe and it is consistent with the fractal dimension values reported for standard invasion percolation. Finally, we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self-organized critical behavior of the invasion percolation process.

Bose–Einstein and Fermi–Dirac distributions in nonextensive Tsallis statistics: an exact study

Generalized Bose–Einstein and Fermi–Dirac distributions are analyzed in nonextensive Tsallis statistics by considering the normalized constraints in the effective temperature approach. These distributions are worked in D-dimension by employing a general density of states g(e)∝eD−1(D=D/2+D/n and D>0). Thermodynamic functions such as internal energy and average number of particles are also obtained in this context.

Efficient search of critical points in Ising-like systems

We propose a simulation method inspired by self-organization that drives Ising-like magnetic systems rapidly to criticality. We develop a feedback control rule with very few parameters for use with the standard methods of local spin updatings that spontaneously leads the system to the critical temperature. This method for predicting the critical values requires small lattices. It gives good results eg., 1% accuracy for TC in 3-D for 103 systems, with reduced computer times, for both Glauber and Metropolis dynamics.

The small-world of economy: a speculative proposal

Using the small-world approach we suggest a network model for the economy. Our basic assumption is that the economic agents prefer to make business with the big business. This assumption makes the preferential attachment the main mechanism for the evolution of the economic network. We hypothesize that the connectivity of the economic network should reflect the wealth distribution of the society which is considered to be an exponential truncated power law. The objective of this paper is to model qualitatively the wealth distribution of a society using concepts based on evolving network. Several alternatives of evolving networks are discussed in an economic context.

Percolation as a dynamical phenomenon

We consider a percolation process where the probability p of having one site (or bond) occupied increases linearly with time. We study the total number of clusters as a function of time or p, the statistical distribution of jumps in the size of the major cluster, as well as the frequency of these jumps. We find that both distributions are power-laws, with different exponents below and above percolation threshold and we discuss these results.

Nonlinear fractional diffusion equation: Exact results

The nonlinear fractional diffusion equation ∂tρ=r1−d∂rμ′{rd−1D(r,t;ρ)∂rμρν}−r1−d∂r{rd−1F(r,t)ρ}+α¯(t)ρ is studied by considering the diffusion coefficient D(r,t;ρ)=D(t)r−θργ and the external force F(r,t)=−k1(t)r+kαrα. In addition, a rich class of diffusive processes, including normal and anomalous ones, is obtained from the study present in this work.

Effects of site dilution on the one-dimensional long-range bond-percolation problem

Abstract The effects of the dilution of sites (with an occupancy probability ps for an active site) on the long-range bond-percolation problem, on a linear chain (d=1), are analyzed by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance rij is given by pij=p/rijα (α⩾0), where p represents the usual occupancy probability between nearest-neighbor sites. The percolation order parameter, P∞, is investigated numerically for different values of α and ps, in such a way that a crossover between a nonextensive regime and an extensive regime is observed.