arXiv subjects

J. G. Moreira

Publications and source records attributed to J. G. Moreira.

12 recordsLinked to original sources

arXiv2015

Analysis of the velocity field of granular hopper flow

We report the analysis of radial characteristics of the flow of granular material through a conical hopper. The discharge is simulated for various orifice sizes and hopper opening angles. Velocity profiles are measured along two radial lines from the hopper cone vertex: along the main axis of the cone and along its wall. An approximate power law dependence on the distance from the orifice is observed for both profiles, although differences between them can be noted. In order to quantify these differences, we propose a Local Mass Flow index that is a promising tool in the direction of a more reliable classification of the flow regimes in hoppers.

cond-mat.soft↗

arXiv2006

New method to study stochastic growth equations: a cellular automata perspective

We introduce a new method based on cellular automata dynamics to study stochastic growth equations. The method defines an interface growth process which depends on height differences between neighbors. The growth rule assigns a probability $p_{i}(t)=ρ$ exp$[κΓ_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $ρ$ and $κ$ are two parameters and $Γ_{i}(t)$ is a function which depends on height of the site $i$ and its neighbors. Its functional form is specified through discretization of the deterministic part of the growth equation associated to a given deposition process. In particular, we apply this method to study two linear equations - the Edwards-Wilkinson (EW) equation and the Mullins-Herring (MH) equation - and a non-linear one - the Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical analysis of the height distributions of the profiles, we recover the values for roughening exponents, which confirm that the processes generated by the method are indeed in the universality classes of the original growth equations. In addition, a crossover from Random Deposition to the associated correlated regime is observed when the parameter $κ$ is varied.

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↗

arXiv2002

Phase diagram of a probabilistic cellular automaton with three-site interactions

We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\it three} sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter, $p_3$, representing the probability for a site to be active at time $t$, given that its nearest neighbors and itself were active at time $t-1$. We study phase transitions and critical behavior for the activity {\it and} for damage spreading, using one- and two-site mean-field approximations, and simulations, for $p_3=0$ and $p_3=1$. We find evidence for a line of tricritical points in the ($p_1, p_2, p_3$) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For $p_3 =0$, the phase diagram is similar to the DKCA, but the damage spreading transition exhibits a reentrant phase. For $p_3=1$, the growth-exponent method reproduces the two absorbing states, first and second-order phase transitions, bicritical point, and damage spreading transition recently identified by Bagnoli {\it et al.} [Phys. Rev. E{\bf 63}, 046116 (2001)].

cond-mat.stat-mech↗

arXiv2002

Growth model with restricted surface relaxation

We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson linear model, but only within a distance s. If the local minimum is out from this distance, the particle evaporates through a refuse mechanism similar to the Kim-Kosterlitz nonlinear model. In d=1, the growth exponent beta, measured from the temporal behavior of roughness, indicates that in the coarse-grained limit, the linear term of the Kardar-Parisi-Zhang equation dominates in short times (low-roughness) and, in asymptotic times, the nonlinear term prevails. The crossover between linear and nonlinear behaviors occurs in a characteristic time t_c which only depends on the magnitude of the parameter s, related to the nonlinear term. In d=2, we find indications of a similar crossover, that is, logarithmic temporal behavior of roughness in short times and power law behavior in asymptotic times.

cond-mat.stat-mech↗

arXiv2001

Lattice Model for Approximate Self-Affine Soil Profiles

A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation dimension, $D_f$, and the maximum mass of the deposited aggregates, $M_{max}$. The fragmentation dimension is related to the particle size distribution through the relation $N(r \ge R) \sim R^{D_f}$, where $N(r \ge R)$ is the accumulative number of particles with radius greater than $R$. The size of the deposited aggregates are chose following the power law above, and the morphology of the aggregate is random selected using a bond percolation algorithm. The deposition rules are the same used in the model of solid-on-solid deposition with surface relaxation. A comparison of the model with real data shows that the Hurst exponent, $H$, measured {\it via} semivariogram method and detrended fluctuation analysis, agrees in statistical sense with the simulated profiles.

cond-mat.stat-mech↗

arXiv2001

Growth Exponent in the Domany-Kinzel Cellular Automaton

In a roughening process, the growth exponent $β$ describes how the roughness $w$ grows with the time $t$: $w\sim t^β$. We determine the exponent $β$ of a growth process generated by the spatiotemporal patterns of the one dimensional Domany-Kinzel cellular automaton. The values obtained for $β$ shows a cusp at the frozen/active transition which permits determination of the transition line. The $β$ value at the transition depends on the scheme used: symmetric ($β\sim 0.83$) or non-symmetric ($β\sim 0.61$). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.

cond-mat.stat-mech↗

arXiv2001

Scaling Exponents of Rough Surfaces Generated by the Domany-Kinzel Cellular Automaton

The critical behavior at the frozen/active transition in the Domany-Kinzel stochastic cellular automaton (DKCA) is studied {\it via} a surface growth process in (1+1) dimensions. At criticality, this process presents a kinetic roughening transition; we measure the critical exponents in simulations. Two update schemes are considered: in the symmetric scheme, the growth surfaces belong to the Directed Percolation (DP) universality class, except at one terminal point. At this point, the phase transition is discontinuous and the surfaces belong to the Compact Directed Percolation universality class. The relabeling of space-time points in the nonsymmetric scheme alters the surface growth dramatically. The critical behavior of rough surfaces at the nonchaotic/chaotic transition is also studied using the damage spreading technique; the exponents confirm DP values for the symmetric scheme.

cond-mat.stat-mech↗

arXiv2001

Failure regime in (1+1) dimensions in fibrous materials

In this paper, we introduce a model for fracture in fibrous materials that takes into account the rupture height of the fibers, in contrast with previous models. Thus, we obtain the profile of the fracture and calculate its roughness, defined as the variance around the mean height. We investigate the relationship between the fracture roughness and the fracture toughness.

cond-mat.stat-mech↗

arXiv2000

Kinetic roughening model with opposite Kardar-Parisi-Zhang nonlinearities

We introduce a model that simulates a kinetic roughening process with two kinds of particles: one follows the ballistic deposition (BD) kinetic and, the other, the restricted solid-on-solid (KK) kinetic. Both of these kinetics are in the universality class of the nonlinear KPZ equation, but the BD kinetic has a positive nonlinear constant while the KK kinetic has a negative one. In our model, called BD-KK model, we assign the probabilities p and (1-p) to the KK and BD kinetics, respectively. For a specific value of p, the system behaves as a quasi linear model and the up-down symmetry is recuperated. We show that nonlinearities of odd-order are relevant in these low nonlinear limit.

cond-mat.stat-mech↗

arXiv2000

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density $ρ$ scales with the system size $L$, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation.

cond-mat.stat-mech↗

arXiv1994

Model for Fracture in Fibrous Materials

A fiber bundle model in $(1+1)$-dimensions for the breaking of fibrous composite matrix is introduced. The model consists of $N$ parallel fibers fixed in two plates. When one of the plates is pulled in the direction parallel to the fibers, these can be broken with a probability that depends on their elastic energy. The mechanism of rupture is simulated by the breaking of neighbouring fibers that can generate random cracks spreading up through the system. Due to the simplicity of the model we have virtually no computational limitation. The model is sensitive to external conditions as temperature and traction time-rate. The energy {\it vs.} temperature behaviour, the diagrams of stress {\it vs.} strain and the histograms of the frequency {\it vs.} size of cracks are obtained. (to appear in Phys. Rev. B)

cond-mat↗