arXiv subjects

S. G. Alves

Publications and source records attributed to S. G. Alves.

13 recordsLinked to original sources

arXiv2011

Universal fluctuations in KPZ growth on one-dimensional flat substrates

We present a numerical study of the evolution of height distributions (HDs) obtained in interface growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. The growth is done on an initially flat substrate. The HDs obtained for all investigated models are very well fitted by the theoretically predicted Gaussian Orthogonal Ensemble (GOE) distribution. The first cumulant has a shift that vanishes as $t^{-1/3}$, while the cumulants of order $2\le n\le 4$ converge to GOE as $t^{-2/3}$ or faster, behaviors previously observed in other KPZ systems. These results yield a new evidence for the universality of the GOE distribution in KPZ growth on flat substrates. Finally, we further show that the surfaces are described by the Airy$_{1}$ process.

cond-mat.stat-mech↗

arXiv2011

Universal fluctuations in radial growth models belonging to the KPZ universality class

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy$_2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.

cond-mat.stat-mech↗

arXiv2011

Effects of the mean free path and relaxation in a model for the aggregation of particles in superfluid media

In this paper, we study a two-dimensional model for the growth of molecular clusters in superfluid helium at low temperature. In the model, particles of diameter a follow random ballistic moves of length δ= a-256a. Upon attachment on the cluster surface, particles allow one-step relaxation to the nearest twofold coordinated site. Average coordination numbers of particles show that in the presence of relaxation the screening for incoming particles modifies the microscopic structure of the cluster. These results are in qualitative agreement with experimental aggregation of methane in He droplets, in which large abundance of fully coordinated sites is observed. The average coordination number increases with δ, showing that screening is relevant when relaxation is present. As the cluster size increases, the corresponding structure clusters changes from a compact to a fractal, typical of ballistic and diffusion limited models, respectively. A scaling ansatz describing the crossover between the two regimes is proposed.

physics.atm-clus↗

arXiv2010

Cluster-cluster aggregation with particle replication and chemotaxy: a simple model for the growth of animal cells in culture

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and \textit{in vitro} drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture.

cond-mat.stat-mech↗

arXiv2008

Contact process on a Voronoi triangulation

We study the continuous absorbing-state phase transition in the contact process on the Voronoi-Delaunay lattice. The Voronoi construction is a natural way to introduce quenched coordination disorder in lattice models. We simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios. Our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice, i.e., that of directed percolation.

cond-mat.stat-mech↗

arXiv2008

Strategies for Optimize Off-Lattice Aggregate Simulations

We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended to distinct off-lattice aggregation processes are discussed. The computer efficiencies of the distinct algorithms are compared.

cond-mat.stat-mech↗

arXiv2006

Pitfalls on the determination of the universality class of radial clusters

The self-affinity of growing systems with radial symmetry, from tumors to grain-grain displacement, has devoted increasing interest in the last decade. In this work, we analyzed features about the interface scaling of these clusters through large scale simulations (up to $3\times 10^7$ particles) of two-dimensional growth processes with special emphasis on the off-lattice Eden model. The central objective is to discuss an important pitfall associated to the evaluation of the growth exponent $β$ of these systems. We show that the $β$ value depends on the choice of the origin used to determine the interface width. We considered two strategies frequently used. When the width is evaluated in relation to the center of mass (CM) of the border, the exponent obtained for the Eden model was $β_{CM}=0.404\pm0.013$, in very good agreement with previous reported values. However, if the border CM is replaced by the initial seed position (a static origin), the exponent $β_0=0.333\pm 0.010$, in complete agreement with the KPZ value $β_{KPZ}=1/3$, was found. The difference between $β_{CM}$ and $β_{0}$ was explained through the border CM fluctuations that grow faster than the overall interface fluctuations. Indeed, we show that the exponents $β_0$ and $β_{CM}$ characterize large and small wavelength fluctuations of the interface, respectively. These finds were also observed in three distinct lattice models, in which the lattice-imposed anisotropy is absent.

cond-mat.stat-mech↗

arXiv2006

Aggregation in a mixture of Brownian and ballistic wandering particles

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as, their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability $P_{ba}$, or random ones, with probability $P_{rw}=1-P_{ba}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{ba}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{ba}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{ba}=1$. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba}\approx1/2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba}>1/2$, in agreement with recent results concerning the asymptotic scaling of DLA clusters.

cond-mat.stat-mech↗

arXiv2006

Morphological transition between diffusion-limited and ballistic aggregation growth patterns

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $λ$, which assumes the value $λ=0$ (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For $λ\ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\barρ$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\barρ$ reaches the asymptotic value $ρ_0(λ)$ following a power law $\barρ=ρ_0+Ar^{-γ}$ with a universal exponent $γ=0.46(2)$, independent of $λ$. The asymptotic value has the behavior $ρ_0\sim|1-λ|^β$, where $β= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $ξ\sim|1-λ|^{-ν}$, where $ν=0.61(1)$, while the cluster mass at the crossover follows a power law $M_ξ\sim|1 -λ|^{-α}$, where $α=0.97(2)$. We deduce the scaling relations $β=\n uγ$ and $β=2ν-α$ between these exponents.

cond-mat.stat-mech↗

arXiv2006

Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^ν$, was proposed. The exponent $ν$ has a nonuniversal critical value $ν_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $ν<ν_c$ and the rotated one (diagonal) for $ν>ν_c$. The values $ν_c = 1.395\pm0.005$ and $ν_c = 0.82\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $ν=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.

cond-mat.stat-mech↗

arXiv2002

Electoral surveys influence on the voting processes: a cellular automata model

Nowadays, in societies threatened by atomization, selfishness, short-term thinking, and alienation from political life, there is a renewed debate about classical questions concerning the quality of democratic decision-making. In this work a cellular automata (CA) model for the dynamics of free elections based on the social impact theory is proposed. By using computer simulations, power law distributions for the size of electoral clusters and decision time have been obtained. The major role of broadcasted electoral surveys in guiding opinion formation and stabilizing the ``{\it status quo}'' was demonstrated. Furthermore, it was shown that in societies where these surveys are manipulated within the universally accepted statistical error bars, even a majoritary opposition could be hindered from reaching the power through the electoral path.

cond-mat.stat-mech↗

arXiv2001

Granular fingers in Hele-Shaw experiments

Granular materials constitute an intermediate state of matter between fluids and solids. Here we investigate the pattern formation when a grain is displaced by another type of grain in a radial Hele-Shaw cell. We show that several morphologies can occur, ranging from rounded to fingered patterns, interconnected by a continuous crossover. Fourier analyses shows that, in contrast to the rounded patterns, the fingered shapes present mode selection.

cond-mat.stat-mech↗

arXiv2000

A Cellular Automata Model for Citrus Variagated Chlorosis

A cellular automata model is proposed to analyze the progress of Citrus Variegated Chlorosis epidemics in São Paulo oranges plantation. In this model epidemiological and environmental features, such as motility of sharpshooter vectors which perform Lévy flights, hydric and nutritional level of plant stress and seasonal climatic effects, are included. The observed epidemics data were quantitatively reproduced by the proposed model varying the parameters controlling vectors motility, plant stress and initial population of diseased plants.

cond-mat.stat-mech↗