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ABSTRACT: We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.
The European Physical Journal E 05/2012; 35(5):38. · 1.94 Impact Factor
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ABSTRACT: In a roughening process, the growth exponent ß describes how the roughness w grows with the time t: w ~ tß. We determine the exponent ß of a growth process generated by the spatiotemporal patterns of the one-dimensional Domany-Kinzel
cellular automaton. The values obtained for ß show a cusp at the frozen/active transition which permits determination of the
transition line. The ß value at the transition depends on the scheme used: symmetric
(b @ 0.83)(\beta \simeq 0.83) or non-symmetric
(b @ 0.61)(\beta \simeq 0.61). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas
are updated.
PACS. 05.10.-a Computational methods in statistical physics and nonlinear dynamics – 02.50.-r Probability theory, stochastic
processes, and statistics
Physics of Condensed Matter 04/2012; 16(3):501-505. · 1.53 Impact Factor
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ABSTRACT: We study a generalization of the Wolf-Villain (WV) interface growth model
based on a probabilistic growth rule. In the WV model, particles are randomly
deposited onto a substrate and subsequently move to a position nearby where the
binding is strongest. We introduce a growth probability which is proportional
to a power of the number $n_i$ of bindings of the site $i$: $p_i\propto
n_i^\nu$. Through extensively simulations, in $(1+1)$-dimensions, we find three
behavior depending of the $\nu$ value: {\it i}) if $\nu$ is small, a crossover
from the Mullins-Hering to the Edwards-Wilkinson (EW) universality class; {\it
ii}) for intermediate values of $\nu$, a crossover from the EW to the
Kardar-Parisi-Zhang (KPZ) universality class; {\it iii}) and, finally, for
large $\nu$ values, the system is always in the KPZ class. In
$(2+1)$-dimensions, we obtain three different behaviors: {\it i}) a crossover
from the Villain-Lai-Das Sarma to the EW universality class, for small $\nu$
values; {\it ii}) the EW class is always present, for intermediate $\nu$
values; {\it iii}) a deviation from the EW class is observed, for large $\nu$
values.
04/2011;
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ABSTRACT: We present a molecular-dynamics study of discharges in a granular pile evincing a catastrophic regime depending on the outlet size. The avalanche size distribution function suggests a phase transition where the height of the remaining pile is taken as the order parameter. Our results indicate that there is a critical outlet size beyond which discharges become catastrophic and the initial pile is split in two minor piles. As the system size increases, finite-size analysis indicates that the critical orifice width converges to a finite value.
Physical Review E 11/2010; 82(5 Pt 1):051303. · 2.26 Impact Factor
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ABSTRACT: 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 $p_{i}(t)=\rho$ exp$[\kappa \Gamma_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $\rho$ and $\kappa$ are two parameters and $\Gamma_{i}(t)$ 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 $\kappa$ is varied. Comment: 6 pages, 7 figures
10/2006;
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ABSTRACT: In this work, the transition between diffusion-limited (DLA) and ballistic aggregation (BA) models was reconsidered using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter lambda, which assumes the value lambda=0 (1) for the ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, an efficient algorithm was developed. For lambda (not equal to) 0 , the patterns are fractal on small length scales, but homogeneous on large ones. We evaluated the mean density of particles (-)rho in the region defined by a circle of radius r centered at the initial seed. As a function of r, (-)rho reaches the asymptotic value rho(0)(lambda) following a power law (-)rho = rho(0) +Ar(-gamma) with a universal exponent gamma=0.46 (2) , independent of lambda . The asymptotic value has the behavior rho(0) approximately |1-lambda|(beta) , where beta=0.26 (1) . The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by xi approximately |1-lambda|(-nu) , where nu=0.61 (1) , while the cluster mass at the crossover follows a power law M(xi) approximately |1-lambda(-alpha) , where alpha=0.97 (2) . We deduce the scaling relations beta=nugamma and beta=2nu-alpha between these exponents.
Physical Review E 06/2005; 71(5 Pt 1):051402. · 2.26 Impact Factor
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ABSTRACT: 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 $\lambda$, which assumes the value $\lambda=0$ (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 $\lambda \ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\bar{\rho}$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\bar{\rho}$ reaches the asymptotic value $\rho_0(\lambda)$ following a power law $\bar{\rho}=\rho_0+Ar^{-\gamma}$ with a universal exponent $\gamma=0.46(2)$, independent of $\lambda$. The asymptotic value has the behavior $\rho_0\sim|1-\lambda|^\beta$, where $\beta= 0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $\xi\sim|1-\lambda|^{-\nu}$, where $\nu=0.61(1)$, while the cluster mass at the crossover follows a power law $M_\xi\sim|1 -\lambda|^{-\alpha}$, where $\alpha=0.97(2)$. We deduce the scaling relations $\beta=\n u\gamma$ and $\beta=2\nu-\alpha$ between these exponents. Comment: 7 pages, 8 figures
04/2005;
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ABSTRACT: We study a (1+1)-dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel stochastic-cellular automaton (DKCA), but in which the update of a given site depends on the state of 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 it and its nearest neighbors were active at time t-1. We study phase transitions and critical behavior for the activity 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 et al. [Phys. Rev. E 63, 046116 (2001)].
Physical Review E 02/2003; 67(1 Pt 2):016107. · 2.26 Impact Factor
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ABSTRACT: 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 discrete surface relaxation 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.
Physical Review E 01/2003; 66(6 Pt 1):061604. · 2.26 Impact Factor
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ABSTRACT: The critical behavior at the frozen-active transition in the Domany-Kinzel stochastic cellular automaton is studied 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 significantly the surface growth, changing the values of the critical exponents. 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.
Physical Review E 08/2002; 66(1 Pt 2):016113. · 2.26 Impact Factor
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ABSTRACT: 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.
11/2001;
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ABSTRACT: In a roughening process, the growth exponent $\beta$ describes how the roughness $w$ grows with the time $t$: $w\sim t^{\beta}$. We determine the exponent $\beta$ of a growth process generated by the spatiotemporal patterns of the one dimensional Domany-Kinzel cellular automaton. The values obtained for $\beta$ shows a cusp at the frozen/active transition which permits determination of the transition line. The $\beta$ value at the transition depends on the scheme used: symmetric ($\beta \sim 0.83$) or non-symmetric ($\beta \sim 0.61$). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.
10/2001;
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ABSTRACT: We introduce a model that simulates a kinetic roughening process with two kinds of particle: one follows ballistic deposition (BD) kinetics and the other restricted solid-on-solid Kim-Kosterlitz (KK) kinetics. Both of these kinetics are in the universality class of the nonlinear Kardar-Parisi-Zhang equation, but the BD kinetics has a positive nonlinear constant while the KK kinetics has a negative one. In our model, called the 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 quasilinear model and the up-down symmetry is restored. We show that nonlinearities of odd order are relevant in this low nonlinear limit.
Physical Review E 05/2001; 63(4 Pt 1):041601. · 2.26 Impact Factor
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ABSTRACT: 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.
Physical Review E 03/2001; 63(2 Pt 2):025104. · 2.26 Impact Factor
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ABSTRACT: 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. Comment: 4 pages, 4 figures.eps, Revtex
11/2000;
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ABSTRACT: 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 $\rho$ 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.
09/2000;
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ABSTRACT: 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 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.
Physics of Condensed Matter 12/1999; 13(2):313-318. · 1.53 Impact Factor
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ABSTRACT: In the time evolution of populations, many attractors can be found: fixed points, limit cycles and chaotic regimes. Usually,
chaotic behaviour is observed in species which have well defined breeding seasons and a high fertility rate. Different mathematical
models have been used in order to simulate those regimes. In this paper, we use the bitstring model introduced to simulate
the evolution of age-structured populations -- the Penna Model -- to simulate a sort of cyclic and chaotic behaviours. In
comparison with the standard logistic map, our results show a time changing parameter.
Physics of Condensed Matter 01/1998; 1(3):393-396. · 1.53 Impact Factor
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ABSTRACT: 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) Comment: 13 pages (RevTex) and 5 figures (.ps)
02/1994;
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ABSTRACT: We investigate the existence of self-organized criticality on a model to describe the failure process in fibrous materials. This model consists of identical parallel fibers which are pulled with constant velocity. The rupture probability of each fiber depends on the elastic energy of the fiber and on the number of unbroken neighboring fibers. In the brittle-ductile transition, we have observed a power law behaviour on the number of cracks versus its size. This indicates that, in this region, the model shows self-organized criticality and the fracture pattern can be a fractal. The power law exponent is not universal, but depends on the temperature and traction velocity.
http://dx.doi.org/10.1051/jp1:1995187.
