arXiv subjects

L. R. da Silva

Publications and source records attributed to L. R. da Silva.

15 recordsLinked to original sources

arXiv2020

Connecting complex networks to nonadditive entropies

Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies adequately handles a wide class of such systems. We show here that scale-invariant networks belong to this class. We numerically study a $d$-dimensional geographically located network with weighted links and exhibit its 'energy' distribution per site at its quasi-stationary state. Our results strongly suggest a correspondence between the random geometric problem and a class of thermal problems within the generalised thermostatistics. The Boltzmann-Gibbs exponential factor is generically substituted by its $q$-generalisation, and is recovered in the $q=1$ limit when the nonlocal effects fade away. The present connection should cross-fertilise experiments in both research areas.

cond-mat.stat-mech↗

arXiv2017

The complex social network of surnames: A comparison between Brazil and Portugal

We present a study of social networks based on the analysis of Brazilian and Portuguese family names (surnames). We construct networks whose nodes are names of families and whose edges represent parental relations between two families. From these networks we extract the connectivity distribution, clustering coefficient, shortest path and centrality. We find that the connectivity distribution follows an approximate power law. We associate the number of hubs, centrality and entropy to the degree of miscegenation in the societies in both countries. Our results show that Portuguese society has a higher miscegenation degree than Brazilian society. All networks analyzed lead to approximate inverse square power laws in the degree distribution. We conclude that the thermodynamic limit is reached for small networks (3 or 4 thousand nodes). The assortative mixing of all networks is negative, showing that the more connected vertices are connected to vertices with lower connectivity. Finally, the network of surnames presents some small world characteristics.

physics.soc-ph↗

arXiv2015

Role of dimensionality in complex networks: Connection with nonextensive statistics

Deep connections are known to exist between scale-free networks and non-Gibbsian statistics. For example, typical degree distributions at the thermodynamical limit are of the form $P(k) \propto e_q^{-k/κ}$, where the $q$-exponential form $e_q^z \equiv [1+(1-q)z]^{\frac{1}{1-q}}$ optimizes the nonadditive entropy $S_q$ (which, for $q\to 1$, recovers the Boltzmann-Gibbs entropy). We introduce and study here $d$-dimensional geographically-located networks which grow with preferential attachment involving Euclidean distances through $r_{ij}^{-α_A} \; (α_A \ge 0)$. Revealing the connection with $q$-statistics, we numerically verify (for $d$ =1, 2, 3 and 4) that the $q$-exponential degree distributions exhibit, for both $q$ and $κ$, universal dependences on the ratio $α_A/d$. Moreover, the $q=1$ limit is rapidly achieved by increasing $α_A/d$ to infinity.

cond-mat.stat-mech↗

arXiv2015

Information entropy of classical versus explosive percolation

We study the Shannon entropy of the cluster size distribution in classical as well as explosive percolation, in order to estimate the uncertainty in the sizes of randomly chosen clusters. At the critical point the cluster size distribution is a power-law, i.e. there are clusters of all sizes, so one expects the information entropy to attain a maximum. As expected, our results show that the entropy attains a maximum at this point for classical percolation. Surprisingly, for explosive percolation the maximum entropy does not match the critical point. Moreover, we show that it is possible determine the critical point without using the conventional order parameter, just analysing the entropy's derivatives.

cond-mat.dis-nn↗

arXiv2014

How to efficiently destroy a network with limited information

We address the general problem of how best to attack and destroy a network by node removal, given limited or no prior information about the edges. We consider a family of strategies in which nodes are randomly chosen, but not removed. Instead, a random acquaintance (i.e., a first neighbour) of the chosen node is removed from the network. By assigning an informal cost to the information about the network structure, we show using cost-benefit analysis that acquaintance removal is the optimal strategy to destroy networks efficiently.

physics.soc-ph↗

arXiv2013

Geometrical and transport properties of sequential adsorption clusters

We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.

cond-mat.stat-mech↗

arXiv2010

Symbolic Sequences and Tsallis Entropy

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated $l$ times, with the probability distribution $p(l)\propto 1/ l^μ$. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, for a suitable choice of $q$, a linear behavior. We also study the chain as a random walk-like process and observe a nonusual diffusive behavior depending on the values of the parameter $μ$.

physics.data-an↗

arXiv2009

New efficient methods to calculate watersheds

We present an advanced algorithm for the determination of watershed lines on Digital Elevation Models (DEMs), which is based on the iterative application of Invasion Percolation (IIP). The main advantage of our method over previosly proposed ones is that it has a sub-linear time-complexity. This enables us to process systems comprised of up to 10^8 sites in a few cpu seconds. Using our algorithm we are able to demonstrate, convincingly and with high accuracy, the fractal character of watershed lines. We find the fractal dimension of watersheds to be Df = 1.211 +/- 0.001 for artificial landscapes, Df = 1.10 +/- 0.01 for the Alpes and Df = 1.11 +/- 0.01 for the Himalaya.

cond-mat.dis-nn↗

arXiv2009

Diffusion in stochastic sandpiles

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is only possible over a very narrow interval near the critical point. We also develop a series expansion, in inverse powers of the density. for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with $n$ particles is $n(n-1)$, and compare the theoretical prediction with simulation results.

cond-mat.stat-mech↗

arXiv2006

Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation

We analyse a bidimensional nonlinear Fokker-Planck equation by considering an anisotropic case, whose diffusion coefficients are $D_x \propto |x|^{-θ}$ and $D_y \propto |y|^{-γ}$ with $θ, γ\in {\cal{R}}$. In this context, we also investigate two situations with the drift force $\vec{F}(\vec{r},t)=(-k_{x}x, -k_y y)$. The first one is characterized by $k_x/k_y=(2+γ)/(2+θ)$ and the second is given by $k_{x}=k$ and $k_{y}=0$. In these cases, we can verify an anomalous behavior induced in different directions by the drift force applied. The found results are exact and exhibit, in terms of the $q$-exponentials, functions which emerge from the Tsallis formalism. The generalization for the $D$-dimensional case is discussed.

nucl-th↗

arXiv2006

Preferential attachment scale-free growth model with random fitness

We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by obeying a power law distribution.

cond-mat.stat-mech↗

arXiv2001

Remarks on $(1-q)$ expansion and factorization approximation in the Tsallis nonextensive statistical mechanics

The validity of (1-q) expansion and factorization approximations are analysed in the framework of Tsallis statistics. We employ exact expressions for classical independent systems (harmonic oscillators) by considering the unnormalized and normalized constrainsts. We show that these approxiamtions can not be accurate in the analysis of systems with many degrees of freedom.

cond-mat.stat-mech↗

arXiv2001

Spin wave specific heat in quasiperiodic Fibonacci structures

The energy spectra of a variety of collective modes on quasiperiodic structures exhibit a complex fractal profile. Among the modes that have attracted particular attention in this context, are the spin wave spectra of quasiperiodic magnetic multilayers that obey a substitutional sequence of the Fibonacci type. They are described within the framework of the Heisenberg theory. In order to have a deep insight on the relevant thermodynamical implications of the above mentioned energy spectra's fractal profile, we have performed analytical and numerical calculations of the spin wave specific heat associated with successive hierarchical sequences of the Fibonacci quasiperiodic structures. The spectra show interesting oscillatory behavior in the low-temperature region, which can be traced back to the spin wave's self-similar energy spectrum.

cond-mat.stat-mech↗

arXiv2000

Reply to ``Comment on `Critical behavior of a two-species reaction-diffusion problem' ''

Our recent Monte Carlo results [Phys. Rev. E 61 (2000) 6330] for the one-dimensional reaction-diffusion process A+B->2B and B->A lead to the correlation length exponent estimate nu=2.21 +/- 0.05. In a comment on our work [cond-mat/0007366] the exact value is claimed to be nu=2. We reply that the arguments advanced in the comment fail to prove the claim.

cond-mat.stat-mech↗

arXiv1998

Connection between energy-spectrum self-similarity and specific heat log-periodicity

As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations associated with succesive hierarchical approximations to multiscale fractal energy spectra. We show that, in a certain range of temperatures, the specific heat displays log-periodic oscillations as a function of the temperature. We exhibit scaling arguments that allow for relating the mean value as well as the amplitude and period of the oscillations to the characteristic scales of the spectrum.

cond-mat.stat-mech↗