arXiv subjects

F. D. A. Aarao Reis

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

24 records · Page 2Linked to original sources

arXiv2006

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. The crossover from an initial regime of slow corrosion rate (pit nucleation) to a regime of rapid corrosion (propagation of the pit) takes place at the incubation time. The model is defined in a lattice whose sites represent the possible states of the metal (bulk, reactive and passive) and the solution (neutral, acidic or basic). 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. From a suitable matching of characteristic times of creation and annihilation of pH inhomogeneities in the solution, a scaling theory gives the average radius of the dissolved region at the incubation time as a function of the model parameters. That radius decreases with the rate of spatially separated reactions and the rate of dissolution in acidic media, and increases with the diffusion coefficient of H+ and OH- ions in solution. The average incubation time is written as the sum of a series of characteristic times for the slow dissolution in neutral media. It linearly increases with the rate of dissolution in neutral media, under the reasonable assumption that this is the slowest rate of the process. The results are confirmed by numerical simulation in two-dimensional lattices, but extension to three dimensions is discussed.

cond-mat.stat-mech↗

arXiv2006

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

We study a restricted solid-on-solid (RSOS) 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~0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q=p-1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear λ-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<=p<=0.8, which provides numerical estimates of the crossover times t_c. They scale as t_c ~ 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~3.

cond-mat.stat-mech↗

arXiv2004

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 post-deposition 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 (epsilon t)^(1/3) coarsening of average cluster size; and t^(-1/2) approach to a saturation size going like 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 (epsilon t)^(1/2) cluster size coarsening through the redistribution allowed by slow detachment. The basic (epsilon t)^(1/3) domain growth laws and epsilon^(-1/2) saturation in model I are explained by a simple scaling picture. A second, 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. This allows 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.

cond-mat.stat-mech↗

arXiv2001

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

We extend a previously proposed deposition model with two kinds of particles, 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 ~ p^{-η}, with η= 3/2, which is confirmed by numerical simulations. The dynamic scaling relation W_s = p^{-η} f(tp^z) is obtained in very large substrates, with z=η.

cond-mat.stat-mech↗

arXiv1999

Universality, frustration and conformal invariance in two-dimensional random Ising magnets

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $γ/ν$, $α/ν$ and $ν$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $γ/ν$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.

cond-mat.stat-mech↗

arXiv1997

Universality and logarithmic corrections in two-dimensional random Ising ferromagnets

We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linear finite size of the system) to the temperature derivative of the correlation length. The predictions are tested by considering long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings, along which free energy, spin-spin correlation functions and specific heats are calculated by transfer-matrix methods. The ratio $γ/ν$ is calculated and has the same value as in the pure case; consequently conformal invariance predictions remain valid for this type of disorder. Semilogarithmic plots of correlation functions against distance yield average correlation lengths $ξ^{av}$, whose size dependence agrees very well with the proposed theory. We also examine the size dependence of the specific heat, which clearly suggestsa divergency in the thermodynamic limit. Thus our data consistently favour the Dotsenko-Shalaev picture of logarithmic corrections (enhancements) to pure system singularities, as opposed to the weak universality scenario.

cond-mat.stat-mech↗