Dynamic transition in deposition with a poisoning species

Surface properties and scaling behavior of a generalized ballistic deposition model

The surface exponents, scaling behavior, and bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely nonsticky to fully sticky. Such particles may adhere to any one of the successively encountered surfaces, depending on a sticking probability that is governed by the underlying stochastic mechanism. The microscopic configurations possible in this model are much larger than those allowed in existing models of ballistic deposition and competitive growth models that seek to mix ballistic and random deposition processes. In this article, we find the scaling exponents for surface width and porosity for the proposed GBD model. In terms of scaled width W[over ̃] and scaled time t[over ̃], the numerical data collapse onto a single curve, demonstrating successful scaling with sticking probability p and system size L. Similar scaling behavior is also found for the porosity.

Nonuniversal effects in mixing correlated-growth processes with randomness: interplay between bulk morphology and surface roughening

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height field. A distinction between growth processes X that do and do not create voids in the bulk leads to the definition of the effective probability p(eff) of the process X that is a measurable property of the bulk morphology and depends on the activation probability p of X in the competitive process RD+X. The bulk morphology is reflected in the surface roughening via nonuniversal prefactors in the universal scaling of the surface width that scales in p(eff). The equation and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or Edwards-Wilkinson universality class in (1+1) dimensions and are illustrated by an example of X being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all p∈(0;1]. We outline the generalizations to (1+n) dimensions and to many-component competitive growth processes.

Adsorbed films of three-patch colloids: continuous and discontinuous transitions between thick and thin films

We investigate numerically the role of spatial arrangement of the patches on the irreversible adsorption of patchy colloids on a substrate. We consider spherical three-patch colloids and study the dependence of the kinetics on the opening angle between patches. We show that growth is suppressed below and above minimum and maximum opening angles, revealing two absorbing phase transitions between thick and thin film regimes. While the transition at the minimum angle is continuous, in the directed percolation class, that at the maximum angle is clearly discontinuous. For intermediate values of the opening angle, a rough colloidal network in the Kardar-Parisi-Zhang universality class grows indefinitely. The nature of the transitions was analyzed in detail by considering bond flexibility, defined as the dispersion of the angle between the bond and the center of the patch. For the range of flexibilities considered we always observe two phase transitions. However, the range of opening angles where growth is sustained increases with flexibility. At a tricritical flexibility, the discontinuous transition becomes continuous. The practical implications of our findings and the relation to other nonequilibrium transitions are discussed.

Langevin equations for competitive growth models

Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension ν and the nonlinear coefficient λ of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p→0. The superposition of those scaling factors gives ν~p(2) for random deposition with surface relaxation (RDSR) as the CD, and ν~p, λ~p(3/2) for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p dependence of λ, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients.

Surface and bulk properties of deposits grown with a bidisperse ballistic deposition model

We study roughness scaling of the outer surface and the internal porous structure of deposits generated with the three-dimensional bidisperse ballistic deposition (BBD), in which particles of two sizes are randomly deposited. Systematic extrapolation of roughness and dynamical exponents and the comparison of roughness distributions indicate that the top surface has Kardar-Parisi-Zhang (KPZ) scaling for any ratio F of the flux between large and small particles. A scaling theory predicts the characteristic time of the crossover from random to correlated growth in BBD and provides relations between the amplitudes of roughness scaling and F in the KPZ regime. The porosity of the deposits monotonically increases with F and scales as F{12} for small F, which is also explained by the scaling approach and illustrates the possibility of connecting surface growth rules and bulk properties. The suppression of relaxation mechanisms in BBD enhances the connectivity of the deposits when compared to other ballisticlike models, so that they percolate down to F approximately 0.05. The fractal dimension of the internal surface of the percolating deposits is D{F} approximately 2.9, which is very close to the values in other ballistic-like models and suggests universality among these systems.

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.

Universal scaling in mixing correlated growth with randomness

We study two-component growth that mixes random deposition (RD) with a correlated growth process that occurs with probability p. We find that these composite systems are in the universality class of the correlated growth process. For RD blends with either Edwards-Wilkinson or Kardar-Parisi-Zhang processes, we identify a nonuniversal exponent in the universal scaling in p.

Roughening of the interfaces in (1+1) -dimensional two-component surface growth with an admixture of random deposition

We simulate competitive two-component growth on a one-dimensional substrate of L sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early nonscaling phase in the interface evolution. The length of this initial phase is a nonuniversal parameter, but its presence is universal. We introduce a method to measure the length of this initial nonscaling phase. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.

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.

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.