Spatially correlated ballistic deposition on one- and two-dimensional surfaces

Extensive numerical simulations of surface growth with temporally correlated noise

Surface growth processes can be significantly affected by long-range temporal correlations. In this work, we perform extensive numerical simulations of a (1+1)- and (2+1)-dimensional ballistic deposition (BD) model driven by temporally correlated noise, which is regarded as the temporal correlated Kardar-Parisi-Zhang universality class. Our results are compared with the existing theoretical predictions and numerical simulations. When the temporal correlation exponent is above a certain threshold, BD surfaces develop gradually faceted patterns. We find that the temporal correlated BD system displays nontrivial dynamic properties, and the characteristic roughness exponents satisfy α≃α_{loc}<α_{s} in (1+1) dimensions, which is beyond the existing dynamic scaling classifications.

Understanding the mechanisms of solid-water reactions through analysis of surface topography

The topography of a reactive surface contains information about the reactions that form or modify the surface and, therefore, it should be possible to characterize reactivity using topography parameters such as surface area, roughness, or fractal dimension. As a test of this idea, we consider a two-dimensional (2D) lattice model for crystal dissolution and examine a suite of topography parameters to determine which may be useful for predicting rates and mechanisms of dissolution. The model is based on the assumption that the reactivity of a surface site decreases with the number of nearest neighbors. We show that the steady-state surface topography in our model system is a function of, at most, two variables: the ratio of the rate of loss of sites with two neighbors versus three neighbors (d(2)/d(3)) and the ratio of the rate of loss of sites with one neighbor versus three neighbors (d(1)/d(3)). This means that relative rates can be determined from two parameters characterizing the topography of a surface provided that the two parameters are independent of one another. It also means that absolute rates cannot be determined from measurements of surface topography alone. To identify independent sets of topography parameters, we simulated surfaces from a broad range of d(1)/d(3) and d(2)/d(3) and computed a suite of common topography parameters for each surface. Our results indicate that the fractal dimension D and the average spacing between steps, E[s], can serve to uniquely determine d(1)/d(3) and d(2)/d(3) provided that sufficiently strong correlations exist between the steps. Sufficiently strong correlations exist in our model system when D>1.5 (which corresponds to D>2.5 for real 3D reactive surfaces). When steps are uncorrelated, surface topography becomes independent of step retreat rate and D is equal to 1.5. Under these conditions, measures of surface topography are not independent and any single topography parameter contains all of the available mechanistic information about the surface. Our results also indicate that root-mean-square roughness cannot be used to reliably characterize the surface topography of fractal surfaces because it is an inherently noisy parameter for such surfaces with the scale of the noise being independent of length scale.

Interface roughening dynamics: temporal width fluctuations and the correlation length

In this work we study experimentally and numerically the temporal width fluctuations obtained in kinetic roughening of single interfaces. This fluctuative behavior, which results from competing mechanisms in the interface growth process, is shown to contain information on the growth process of the specific interface. We define a measure of the temporal interface width fluctuations in order to extract the correlation length of the interface from the fluctuating data. We study numerically the quenched Kardar-Parisi-Zhang (QKPZ) equation for single interfaces in order to assess the role of the different mechanisms, such as normal growth and surface tension, on the fluctuations. We analyze experimental data of mercury droplets spreading on various metal films (silver and gold) in various thicknesses, as well as data of water spreading on paper (imbibition), in order to demonstrate the validity of our method in a wide range of growing interfaces.

Kardar-Parisi-Zhang equation with temporally correlated noise: a self-consistent approach

In this paper we discuss the well known Kardar-Parisi-Zhang (KPZ) equation driven by temporally correlated noise. We use a self-consistent approach to derive the scaling exponents of this system. We also draw general conclusions about the behavior of the dynamic structure factor Phiq(t) as a function of time. The approach we use here generalizes the well known self-consistent expansion (SCE) that was used successfully in the case of the KPZ equation driven by white noise, but unlike SCE, it is not based on a Fokker-Planck form of the KPZ equation, but rather on its Langevin form. A comparison to two other analytical methods, as well as to the only numerical study of this problem is made, and a need for an updated extensive numerical study is identified. We also show that a generalization of this method to any spatiotemporal correlations in the noise is possible, and two examples of this kind are considered.

Self-consistent expansion for the Kardar-Parisi-Zhang equation with correlated noise

A minor modification of the self-consistent expansion (SCE) for the Kardar-Parisi-Zhang (KPZ) system with uncorrelated noise is used to obtain the exponents in systems where the noise has spatial long-range correlations. For d-dimensional systems with correlations of the form D((-->)r-(-->)r',t-t')=2D(0)/(-->)r-(-->)r'/2 rho-d)delta(t-t'), (rho>0), we find a lower critical dimension d(0)(rho)=2+2 rho, above which a perturbative Edwards-Wilkinson (EW) solution appears. Below the lower critical dimension two solutions exist, each in a different, distinct region of rho. For small rho's the solution of KPZ with uncorrelated noise is recovered. For large rho's a rho-dependent solution is found. The existence of only one solution in each region of rho is not a result of a competition between two solutions but a direct outcome of the SCE equation.