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

Chame, Anna; Reis, F. D. A. Aarão

doi:10.1103/physreve.66.051104

Cited by 33 publications

(41 citation statements)

References 31 publications

(56 reference statements)

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“…In other models with crossover between different growth dynamics, it is observed that matching the scaling relations for the roughness of both dynamics leads to correct predictions of t c [9,12]. Following this reasoning, the W values in Eqs.…”

Section: Scaling Of Surface Roughnessmentioning

confidence: 75%

Crossover of interface growth dynamics during corrosion and passivation

Reis

Stafiej

2007

J. Phys.: Condens. Matter

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We study a model of corrosion and passivation of a metalic surface in contact with a solution using scaling arguments and simulation. The passive layer is porous so that the metal surface is in contact with the solution. The volume excess of the products may suppress the access of the solution to the metal surface, but it is then restored by a diffusion mechanism. A metalic site in contact with the solution or with the porous layer can be passivated with rate p and volume excess diffuses with rate D. At small times, the corrosion front linearly grows in time, but the growth velocity shows a t −1/2 decrease after a crossover time of order t c ∼ D/p 2 , where the average front height is of order h c ∼ D/p. A universal scaling relation between h/h c and t/t c is proposed and confirmed by simulation for 0.00005 ≤ p ≤ 0.5 in square lattices. The roughness of the corrosion front shows a crossover from Kardar-Parisi-Zhang scaling to Laplacian growth (diffusion-limited erosion -DLE) at t c . The amplitudes of roughness scaling are obtained by the same kind of arguments as previously applied to the other competitive growth models. The simulation results confirm their validity. Since the proposed model captures the essential ingredients of different corrosion processes, we also expect these universal features to appear in real systems.

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Section: Scaling Of Surface Roughnessmentioning

confidence: 75%

Crossover of interface growth dynamics during corrosion and passivation

Reis

Stafiej

2007

J. Phys.: Condens. Matter

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“…Likewise, large scales are essential in simulation studies of roughening in the two-component growth models that combine one process governed by linear EW dynamics with another process governed by nonlinear KPZ dynamics [24]. Recently, Chame and Reis [25] simulated in (1+1) dimension a mixed growth where particles aggregated either by ballistic deposition (with probability p) or by random deposition with surface relaxation (with probability 1 − p). They show that for small p and sufficiently large L, the interface width has three well-defined evolution stages.…”

Section: Introductionmentioning

confidence: 99%

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

2004

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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 non-scaling 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 non-scaling 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.

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“…This is fundamentally different in more complex systems where the initial regime can extend over very large times [12,13,14,15,16,17,18,19,20,21,22,23,25]. As already mentioned, the Family-Vicsek scaling relation (3) assigns a new set of coordinates to the second crossover point.…”

mentioning

confidence: 99%

“…[12,13,14,15,16,17,18,19,20,21,22,23]. In a competitive growth model one considers a mixture of two different deposition processes where one of them takes place with probability p whereas the other takes place with probability 1−p.…”

mentioning

confidence: 99%

Parameter-free scaling relation for nonequilibrium growth processes

Chou

Pleimling

2009

Phys. Rev. E

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We discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this new scaling relation through various growth models, as for example the competitive growth model RD/RDSR (random deposition/random deposition with surface diffusion) and the RSOS (restricted solid-on-solid) model with different nearest-neighbor height differences, as well as through a new deposition model with temperature dependent diffusion. The new scaling relation is compared to the familiar Family-Vicsek relation and the limitations of the latter are highlighted.PACS numbers: 64.60.Ht,68.35.Ct,05.70.Np The study of growing interfaces has been a very active field for many years [1,2,3]. Many studies focus on the technologically relevant growth of thin films or nanostructures, but growing interfaces are also encountered in various other physical, chemical, or biological systems, ranging from bacterial growth to diffusion fronts. Over the years important insights into the behavior of nonequilibrium growth processes have been gained through the study of simple model systems that capture the most important aspects of real experimental systems [4,5].In their seminal work, Edwards and Wilkinson investigated surface growth phenomena generated by particle sedimentation under the influence of gravity [6]. They proposed to describe this process in (d + 1) dimensions by the following stochastic equation of motion for the surface height h(x, t), now called the Edwards-Wilkinson (EW) equation,where ν is the diffusion constant (surface tension), whereas η(x, t) is a Gaussian white noise with zero mean and covariance η(x, t)η(y, s) = Dδ d (x − y)δ(t − s). Since Eq. 1 is linear, it can be solved exactly by Fourier transformations [2,4,6]. Later, Family [7] discussed the random deposition (RD) and random deposition with surface relaxation (RDSR) processes. RD [3,7] is one of the simplest surface growth processes. In this lattice model particles drop from randomly chosen sites over the surface and stick directly on the top of the selected surface site. Since there is no surface diffusion, the independently growing columns yield an uncorrelated and never-saturated surface. The RDSR process is realized by adding surface diffusion which allows particles just deposited on the surface to jump to the neighboring site with lowest height. This diffusion step smoothes the surface and limits the maximum interface width W (t), defined at deposition time t as the standard deviation of the surface height h from its mean value h: W (t) = h − h 2 . Starting from an initially flat surface, RDSR yields at very early times, with t < t 1 ∼ 1 (we assume here that one layer is deposited per unit time), a surface growing in the same way as for the RD process since no (or only very few) diffusion steps occur in that regime. For t > t 1 the width increases as a power law of time with a growth exponent β before entering a saturation regime after a crossover time t 2 , see Fig. 1. Both...

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

Cited by 33 publications

References 31 publications

Crossover of interface growth dynamics during corrosion and passivation

Crossover of interface growth dynamics during corrosion and passivation

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

Parameter-free scaling relation for nonequilibrium growth processes

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