Noise reduction in Eden models: II. Surface structure and intrinsic width

Kertész, János; Wolf, D. E.

doi:10.1088/0305-4470/21/3/030

Cited by 138 publications

(73 citation statements)

References 28 publications

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“…1, it is apparent that there are fluctuations in the location of the interface between the reactive and CO-poisoned states, and that these are particularly dramatic for small h. The total amplitude of these fluctuations, , is naturally decomposed into contributions due to intrinsic fluctuations, i , and due to long-wavelength fluctuations, 0 , where 2 Ϸ i 2 ϩ 0 2 . 6,16 For hϭ0, large intrinsic fluctuations occur when p CO ϭ p* ͓and these are the dominant feature in Fig. 1͑a͔͒, although they are significantly reduced when p CO Ͻ p*.…”

Section: Structure Of the Chemical Wave Frontmentioning

confidence: 91%

“…For p CO Ͻp*, where the long-wavelength fluctuations are of the KPZ-type, the amplitude, i , of the intrinsic fluctuations can in principle be extracted from the total amplitude, , for a system of width L, from the asymptotic slope of 2 /LϷ i 2 /Lϩ␥/(24v) vs 1/L. 16 On the other hand, in the regime of large h of interest here, the intrinsic fluctuations dominate on the characteristic length scale Lϳh 1/2 ͑recalling that vϳh͒. Some insight into the behavior of i in this regime comes from the analysis of ''diffusion fronts'' in nonreactive systems.…”

Section: Appendix B: Fluctuations At the Chemical Wave Frontmentioning

confidence: 99%

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Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility

Tammaro

Evans

1998

The Journal of Chemical Physics

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We analyze the spatiotemporal behavior in a lattice-gas model for the monomer-dimer reaction on surfaces. This model, which mimics catalytic CO-oxidation, includes a mobilemonomer adspecies (representing CO), an immobile dissociatively adsorbed dimer species (representing O), and afinitereaction rate (for CO2 production). We characterize in detail the propagation of the chemical wave or reaction front produced when the stable reactive steady-state of the model displaces the metastable CO-poisoned state. In the regime of high CO-mobility, such propagation can be described directly within a "hydrodynamic" reaction-diffusion equation formalism. However, we show that the chemical diffusivity of CO is dependent on the O coverage, reflecting the percolative nature of CO-transport through a background of immobile O. We also emphasize that gradients in the coverage of immobile O induce a diffusive flux in the highly mobile CO. These features significantly influence wave propagation and reaction front structure. In addition, our analysis accounts for the feature that in this hydrodynamic regime, correlations persist in the distribution of adsorbed immobile O, and that these influence the reaction kinetics, the steady states, and the percolation and diffusion properties. To this end, we utilize a "hybrid" approach which incorporates a mean-field reaction-diffusion treatment of adsorbed CO, coupled with a lattice- Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility We analyze the spatiotemporal behavior in a lattice-gas model for the monomer-dimer reaction on surfaces. This model, which mimics catalytic CO-oxidation, includes a mobile monomer adspecies ͑representing CO͒, an immobile dissociatively adsorbed dimer species ͑representing O͒, and a finite reaction rate ͑for CO 2 production͒. We characterize in detail the propagation of the chemical wave or reaction front produced when the stable reactive steady-state of the model displaces the metastable CO-poisoned state. In the regime of high CO-mobility, such propagation can be described directly within a ''hydrodynamic'' reaction-diffusion equation formalism. However, we show that the chemical diffusivity of CO is dependent on the O coverage, reflecting the percolative nature of CO-transport through a background of immobile O. We also emphasize that gradients in the coverage of immobile O induce a diffusive flux in the highly mobile CO. These features significantly influence wave propagation and reaction front structure. In addition, our analysis accounts for the feature that in this hydrodynamic regime, correlations persist in the distribution of adsorbed immobile O, and that these influence the reaction kinetics, the steady states, and the percolation and diffusion properties. To this end, we utilize a ''hybrid'' approach which incorporates a mean-field reaction-diffusion treatment of adsorbed CO, coupled with a lattice-gas treatment of adsorbed O ͓Tammaro et al., J. Chem. Phys. 103, 10277...

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Section: Structure Of the Chemical Wave Frontmentioning

confidence: 91%

Section: Appendix B: Fluctuations At the Chemical Wave Frontmentioning

confidence: 99%

Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility

Tammaro

Evans

1998

The Journal of Chemical Physics

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“…(9). The sticking probability acts as a noise reduction parameter [29] in discrete growth models, as was shown in Ref. [30] for the multiparticle biased di usion limited aggregation (MBDLA) model, used to study ECD growth.…”

Section: Instantaneous Surface Kineticsmentioning

confidence: 99%

Possible origin for the experimental scarcity of KPZ scaling in non-conserved surface growth

Cuerno

Castro

2002

Physica A: Statistical Mechanics and its Applications

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The Kardar-Parisi-Zhang (KPZ) equation is generically expected to describe the scaling properties of rough surfaces growing in the absence of conservation laws. However, very few experimental realizations are known of this universality class. Here we focus on the role of instabilities, whether of di usional origin or other, as physical mechanisms hindering the observation of KPZ scaling. Examples are drawn from various growth processes, such as electrochemical deposition (ECD), chemical vapor deposition (CVD), and erosion by ion-beam sputtering. We moreover consider an interface equation which, starting from the corresponding constitutive equations, can be derived to describe growth by either ECD or CVD depending on the interpretation of the quantities appearing. This approach makes contact with phenomenological parameters, and suggests that a more generic description of non-conserved growth may be provided by the KuramotoSivashinsky equation and generalizations thereof. In this case, the experimental scarcity of KPZ scaling would be due to exceedingly long transients determined by the instabilities that occur.

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“…A correction in the squared interface width W 2 for the Eden model [5] was proposed long ago as a constant additive term in the Family-Vicsek [33] ansatz, so that [34] …”

Section: Introductionmentioning

confidence: 99%

Origins of scaling corrections in ballistic growth models

2014

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We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtained scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in divide the surface in bins of size ε and use only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class were found. The binning method allowed the accurate determination of the height distributions of the ballistic models in both growth and steady state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in 2 + 1 dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.

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Noise reduction in Eden models: II. Surface structure and intrinsic width

Cited by 138 publications

References 28 publications

Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility

Chemical diffusivity and wave propagation in surface reactions: Lattice-gas model mimicking CO-oxidation with high CO-mobility

Possible origin for the experimental scarcity of KPZ scaling in non-conserved surface growth

Origins of scaling corrections in ballistic growth models

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