Roughening of the interfaces in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional two-component surface growth with an admixture of random deposition

Kolakowska, A.; Novotny, M. A.; Verma, Poonam

doi:10.1103/physreve.70.051602

Phys. Rev. E

2004

DOI: 10.1103/physreve.70.051602

|View full text |Cite

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

A. Kolakowska

M. A. Novotny

Poonam Verma

Abstract: 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 … Show more

Help me understand this report

View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2006

2024

Publication Types

Select...

Article7

Relationship

Self Cite1

Independent6

Authors

Journals

Cited by 17 publications

(28 citation statements)

References 75 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Parameter-free scaling relation for nonequilibrium growth processes

Chou

Pleimling

2009

Phys. Rev. E

View full text Add to dashboard Cite

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...

show abstract

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

View full text Add to dashboard Cite

show abstract

“…The system retains the memory of this initial condition for t 0 steps, where t 0 depends on the particulars of the model, i.e., t 0 is a nonuniversal parameter. In this start-up regime w(t) does not scale [7]; scaling occurs only for t > t 0 (Fig. 1).…”

mentioning

confidence: 99%

“…This case is in the KPZ universality class [7]. Model D simulates, e.g., conservative updates in a system of asynchronous processors [7,11]. We stress that, although in one universality class for p = 1, Models C and D are essentially different simulations (as is the pair A and B).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Universal scaling in mixing correlated growth with randomness

2006

Self Cite

View full text Add to dashboard Cite

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 KardarParisi-Zhang processes, we identify a nonuniversal parameter in the universal scaling in p. PACS numbers: 68.90.+g, 89.75.Da, 02.50.Fz Many properties of complex systems can be uncovered by statistical analysis of some representative nonequilibrium interfaces. Mainstream studies of surface growth and interface roughening focus on one-component growth, or homoepitaxy, and large-scale properties. On the microscopic level, nonequilibrium interfaces have been studied in a variety of discrete simulation models such as ballistic deposition (BD), Eden or solid-on-solid models. While one-component growths are well understood [1], the same can not be claimed about composite systems, even as simple as binary growth in one spatial dimension. Several mixed-growth models studied in the recent decade [2,3] reveal new and nontrivial properties. But the theory behind these is in the initial stages.In this first systematic study of two-component growth, we examine a system whose dynamics is governed by two simultaneously present processes: one is a process that builds up correlations (a pure-correlated growth) and the other process is totally uncorrelated, i.e., random deposition (RD). The pure-correlated growth occurs with probability p. Questions that we address here concern the universality of such composite systems. As we shall show, the presence of randomness slows down the dynamics of the correlation processes. Nevertheless, the universality class of the combined processes is the same as the universality class of a correlation process. This is an outcome of scaling in p. One consequence of this observation is a magnifying-glass effect that RD-blending has on the time-evolution of the surface roughness. This effect can be useful in revealing hidden features of a correlated growth when designing simulation models. Intuitively, since RD carries no correlations of its own, it may be expected that its admixtures should not lead to a new universality class. Yet, demonstration of this is not so trivial since, as we shall make evident by the results of several simulations, some of the parameters involved in the universal scaling may be nonuniversal. Results presented here for (1 + 1) dimensions can be easily extended to multidimensions.Consider aggregation models where particles fall onto a one-dimensional substrate of L sites, where they may be accepted in accordance to a rule that generates correlations among the sites. This pure-correlated growth occurs with probability p and competes with RD growth that occurs with probability q = 1 − p. When a particle is accepted at a site, the site increases its height by ∆h. Roughness of the growing surface is measured by the interface width w(t) at time t:, where h k (t) is the height at site k andh(t) is it...

show abstract

Scaling behavior of roughness in the two-dimensional Kardar–Parisi–Zhang growth

Jiang

Yang

2007

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

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

Cited by 17 publications

References 75 publications

Parameter-free scaling relation for nonequilibrium growth processes

Parameter-free scaling relation for nonequilibrium growth processes

Universal scaling in mixing correlated growth with randomness

Scaling behavior of roughness in the two-dimensional Kardar–Parisi–Zhang growth

Contact Info

Product

Resources

About