Biomedical subjects

F D A Aarão Reis

Publications and source records attributed to F D A Aarão Reis.

13 recordsLinked to original sources

PubMed2006

Scaling theory in a model of corrosion and passivation.

We study a model for corrosion and passivation of a metallic surface after small damage of its protective layer using scaling arguments and simulation. We focus on the transition between an initial regime of slow corrosion rate (pit nucleation) to a regime of rapid corrosion (propagation of the pit), which takes place at the so-called incubation time. The model is defined in a lattice in which the states of the sites represent the possible states of the metal (bulk, reactive, and passive) and the solution (neutral, acidic, or basic). Simple probabilistic rules describe passivation of the metal surface, dissolution of the passive layer, which is enhanced in acidic media, and spatially separated electrochemical reactions, which may create pH inhomogeneities in the solution. On the basis of a suitable matching of characteristic times of creation and annihilation of pH inhomogeneities in the solution, our scaling theory estimates the average radius of the dissolved region at the incubation time as a function of the model parameters. Among the main consequences, that radius decreases with the rate of spatially separated reactions and the rate of dissolution in acidic media, and it increases with the diffusion coefficient of H(+) and OH(-) ions in solution. The average incubation time can be written as the sum of a series of characteristic times for the slow dissolution in neutral media, until significant pH inhomogeneities are observed in the dissolved cavity. Despite having a more complex dependence on the model parameters, it is shown that the average incubation time linearly increases with the rate of dissolution in neutral media, under the reasonable assumption that this is the slowest rate of the process. Our theoretical predictions are expected to apply in realistic ranges of values of the model parameters. They are confirmed by numerical simulation in two-dimensional lattices, and the expected extension of the theory to three dimensions is discussed.

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PubMed2006

Universal and nonuniversal features in the crossover from linear to nonlinear interface growth.

We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1 - p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p approximately 0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q identical with p - 1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda - q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55< or =p< or =0.8, which provides numerical estimates of the crossover times tc. They scale as tc approximately lambda -phi with phi=4.1+/-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi approximately 3.

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PubMed2006

Scaling in the crossover from random to correlated growth.

In systems where deposition rates are high compared to diffusion, desorption, and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t0. This crossover is analyzed in lattice models via scaling arguments, with support from simulation results presented here and in other works. We argue that the amplitudes of the saturation roughness and of the saturation time t(x) scale as t0(1/2) and t0, respectively. For models with lateral aggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, we show that t0 approximately p(-1), where p is the probability of the correlated aggregation mechanism to take place. However, t0 approximately p(-2) is obtained in solid-on-solid models with single-particle deposition attempts. This group includes models in various universality classes, with numerical examples being provided in the Edwards-Wilkinson (EW), KPZ, and Villain-Lai-Das Sarma (nonlinear molecular-beam epitaxy) classes. Most applications are for two-component models in which random deposition, with probability 1-p, competes with a correlated aggregation process with probability p. However, our approach can be extended to other systems with the same crossover, such as the generalized restricted solid-on-solid model with maximum height difference S, for large S. Moreover, the scaling approach applies to all dimensions. In the particular case of one-dimensional KPZ processes with this crossover, we show that t0 approximately nu(-1) and nu approximately lambda(2/3), where nu and lambda are the coefficients of the linear and nonlinear terms of the associated KPZ equations. The applicability of previous results to models in the EW and KPZ classes is discussed.

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PubMed2005

Logarithmic coarsening and glassy behavior in a polymer model with mass-dependent diffusion.

We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) approximately (m-1)gamma. It shows nonuniversal logarithmic coarsening involving the exponent gamma. Strong-glass behavior is found in the typical times for disappearance of all polymers up to a given length, without reference to the equilibrium states of the macroscopic system. These features are predicted by numerical simulations, scaling theories, and an analytic solution of the master equation within an independent interval approximation, which also provides the cluster size distribution.

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PubMed2005

Numerical study of roughness distributions in nonlinear models of interface growth.

We analyze the shapes of roughness distributions of discrete models in the Kardar, Parisi, and Zhang (KPZ) and in the Villain, Lai, and Das Sarma (VLDS) classes of interface growth, in one and two dimensions. Three KPZ models in d=2 confirm the expected scaling of the distribution and show a stretched exponential tail approximately as exp(-x0.8), with a significant asymmetry near the maximum. Conserved restricted solid-on-solid models belonging to the VLDS class were simulated in d=1 and d=2. The tail in d=1 has the form exp(-x2) and, in d=2, has a simple exponential decay, but is quantitatively different from the distribution of the linear fourth-order (Mullins-Herring) theory. It is not possible to fit any of the above distributions to those of 1/f(alpha) noise interfaces, in contrast with recently studied models with depinning transitions.

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PubMed2005

Nonuniversal coarsening and universal distributions in far-from-equilibrium systems.

Anomalous coarsening in far-from-equilibrium one-dimensional systems is investigated by applying simulation and analytic techniques to minimal hard-core particle (exclusion) models. They contain mechanisms of aggregated particle diffusion, with rates epsilon<<1 , particle deposition into cluster gaps, but suppressed for the smallest gaps, and breakup of clusters that are adjacent to large gaps. Cluster breakup rates vary with the cluster length x as k x(alpha) . The domain growth law x approximately (epsilont)(z) , with z=1/ (2+alpha) for alpha>0 , is explained by a simple scaling picture involving the time for two particles to coalesce and a new particle to be deposited. The density of double vacancies, at which deposition and cluster breakup are allowed, scales as 1/ [t (epsilont)(z) ] . Numerical simulations for several values of alpha and epsilon confirm these results. A fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. The equation for a one-variable scaling function explains the above average cluster length scaling. The probability distributions of cluster lengths x scale as P (x) = [1/ (epsilont)(z) ] g (y) , with y identical with x/ (epsilont)(z) , which is confirmed by simulation. However, those distributions show a universal tail with the form g (y) approximately exp (- y(3/2) ) , which is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps. The high correlation of surviving particle displacement in the latter problem explains the failure of the independent cluster approximation to represent those rare events.

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PubMed2004

Numerical study of discrete models in the class of the nonlinear molecular beam epitaxy equation.

We study numerically some discrete growth models belonging to the class of the nonlinear molecular beam epitaxy equation, or the Villain-Lai-Das Sarma (VLDS) equation. The conserved restricted solid-on-solid model (CRSOS) with maximum height differences Delta H(max)=1 and Delta H(max)=2 was analyzed in substrate dimensions d=1 and d=2 . The Das Sarma and Tamborenea (DT) model and a competitive model involving random deposition and CRSOS deposition were studied in d=1. For the CRSOS model with Delta H(max)=1, we obtain the more accurate estimates of scaling exponents in d=1:roughness exponent alpha=0.94+/-0.02 and dynamical exponent z=2.88+/-0.04. These estimates are significantly below the values of one-loop renormalization for the VLDS theory, which confirms Janssen's proposal of the existence of higher-order corrections. The roughness exponent in d=2 is very near the one-loop result alpha=2/3, in agreement with previous works. The moments W(n) of orders n=2 , 3, 4 of the height distribution were calculated for all models, and the skewness S triple bond W3/W(3/2)(2) and the kurtosis Q triple bond W4/W(2)2-3 were estimated. At the steady states, the CRSOS models and the competitive model have nearly the same values of S and Q in d=1, which suggests that these amplitude ratios are universal in the VLDS class. The estimates for the DT model are different, possibly due to their typically long crossover to asymptotic values. Results for the CRSOS models in d=2 also suggest that those quantities are universal.

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PubMed2004

Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment, and deposition.

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for postdeposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1 ) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further ( epsilont )(1/3) coarsening of average cluster size; and t(-1/2) approach to a saturation size varying as epsilon(-1/2) . Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law [ ( epsilont )(1/2) ] cluster size coarsening through the redistribution allowed by slow detachment. The basic ( epsilont )(1/3) domain growth laws and epsilon(-1/2) saturation in model I are explained by a simple scaling picture involving the time for a particle to detach and diffuse to the next cluster. A second, fuller approach is presented that employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows, through the steady state solution of the corresponding equation for a cluster probability generating function, quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.

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PubMed2004

Universality in two-dimensional Kardar-Parisi-Zhang growth.

We analyze simulation results of a model proposed for etching of a crystalline solid and results of other discrete models in the (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W(n) of orders n=2,3,4 of the height distribution are estimated. Results for the etching model, the ballistic deposition model, and the temperature-dependent body-centered restricted solid-on-solid model suggest the universality of the absolute value of the skewness S identical with W(3)/W(3/2)(2) and of the value of the kurtosis Q identical with W(4)/W(2)(2)-3. The sign of the skewness is the same as of the parameter lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are absolute value of S=0.26+/-0.01 and Q=0.134+/-0.015. For this model, the roughness exponent alpha=0.383+/-0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605< or =z< or =1.64 and beta=0.229+/-0.005, respectively, which are consistent with the relations alpha+z=2 and z=alpha/beta.

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PubMed2003

Dynamic transition in etching with poisoning.

We study a lattice model for etching of a crystalline solid including the deposition of a poisoning species. The model considers normal and lateral erosion of the columns of the solid by a flux of etching particles and the blocking effects of impurities formed at the surface. As the probability p of formation of this poisoning species increases, the etching rate decreases and a continuous transition to a pinned phase is observed. The transition is in the directed percolation (DP) class, with the fraction of the exposed columns as the order parameter. This interpretation is consistent with a mapping of the interface problem in d+1 dimensions onto a d-dimensional contact process, and is confirmed by numerical results in d=1 and d=2. In the etching phase, the interface width scales with Kardar-Parisi-Zhang (KPZ) exponents, and shows a crossover from the critical DP behavior (W approximately t) to KPZ near the critical point, at etching times of the order of (pc-p)(-nu(||)). Anomalous roughening is observed at criticality, with the roughness exponent related to DP exponents as alphac=nu(||)/nu(perpendicular)>1. The main differences from previously studied DP transitions in growth models and isotropic percolation transitions in etching models are discussed. Investigations in real systems are suggested.

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PubMed2002

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling.

We simulated a growth model in (1+1) dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient lambda of the nonlinear term of the KPZ equation, giving lambda approximately p(gamma), with gamma=2.1+/-0.2. Our numerical results confirm the interface width scaling in the growth regime as W approximately lambda(beta)t(beta) and the scaling of the saturation time as tau approximately lambda(-1)L(z), with the expected exponents beta=1/3 and z=3/2, and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t(c) approximately lambda(-4) approximately p(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.

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PubMed2002

Dynamic transition in deposition with a poisoning species.

In deposition with a poisoning species, we show that the transition to a blocked or pinned phase may be viewed as an absorbing transition in the directed percolation (DP) class. We consider a ballisticlike deposition model with an active and an inactive species that represents the basic features of the process and exhibits a transition from a growing phase to a blocked phase, with the deposition rate as the order parameter. In the growing phase, the interface width shows a crossover from the critical W approximately t behavior to Kardar-Parisi-Zhang (KPZ) scaling, which involves DP and KPZ exponents in the saturation regime. In the pinned phase, the maximum heights and widths scale as H(s) approximately W(s) approximately (p-p(c))(-nu). The robustness of the DP class suggests investigations in real systems.

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PubMed2002

Static phase and dynamic scaling in a deposition model with an inactive species.

We extend a previously proposed deposition model with two kinds of particle, considering the restricted solid-on-solid condition. The probability of incidence of particle C (A) is p (1-p). Aggregation is possible if the top of the column of incidence has a nearest neighbor A and if the difference in the heights of neighboring columns does not exceed 1. For any value of p>0, the deposit attains some static configuration, in which no deposition attempt is accepted. In 1+1 dimensions, the interface width has a limiting value W(s) approximately p(-eta), with eta=3/2, which is confirmed by numerical simulations. The dynamic scaling relation W(s)=p(-eta)f(tp(z)) is obtained in very large substrates, with z=eta.

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