Showing papers by "Albert-László Barabási published in 1993"
TL;DR: A set of coupled equations are introduced to describe the nonequilibrium roughening of an interface covered with a thin surfactant layer that may drive the system into a novel phase, in which the surface roughness is negative, corresponding to a flat surface.
Abstract: A number of recent experiments have shown that surfactants can modify the growth mode of an epitaxial film, suppressing islanding and promoting layer-by-layer growth. Here I introduce a set of coupled equations to describe the nonequilibrium roughening of an interface covered with a thin surfactant layer. The surfactant may drive the system into a novel phase, in which the surface roughness is negative, corresponding to a flat surface
24 citations
01 Jan 1993
TL;DR: In this paper, the authors study the probability distribution of the height fluctuations in d = 1 + 1 by mapping the surface to a Levy walk and suggest a model based on propagation and pinning of a selfafflne interface in the presence of quenched disorder, with erosion of overhangs.
Abstract: We review briefly recent studies based on power law distribution of noise to explain the anomalous surface roughening found in several experiments. We study the probability distribution of the height fluctuations in d = 1 + 1 by mapping the surface to a Levy walk. We also review numerical studies for the effect of long-range correlated noise on (i) the KPZ equation and the related directed-polymer (DP) problem and (H) the ballistic deposition (BD) model. We describe measurements of the interface formed when a wet front propagates in paper with anomalous roughening exponent α = 0.63 ± 0.04. We suggest a model based on propagation and pinning of a self-afflne interface in the presence of quenched disorder, with erosion of overhangs. By mapping our model to directed percolation, we find α ≃ 0.63.
3 citations
TL;DR: In this article, a set of coupled equations are introduced to describe the coupling between a growing interface and a thin surfactant layer deposited on the top of the non-equilibrium surface.
Abstract: A number of recent experiments have shown that surfactants can modify the growth mode of an epitaxial film, suppressing islanding and promoting layer-by-layer growth. Here a set of coupled equations are introduced to describe the coupling between a growing interface and a thin surfactant layer deposited on the top of the non-equilibrium surface. The equations are derived using the main experimentally backed characteristics of the system and basic symmetry principles. The system is studied using a dynamic-renormalization-group scheme, which provides scaling relations between the roughness exponents. It is found that the surfactant may drive the system into a novel phase, in which the surface roughness is negative, corresponding to a flat surface.
2 citations
TL;DR: In this paper, the effect of a gradient ∇p on the scaling properties of the interface in (1+1 and (2+1) dimensions was investigated, and the critical concentration, pc, and exponents γ and α from which ν⊥ and ν|| can be determined.
Abstract: We study the effect on interface roughening of a gradient ∇p in the density of pinning sites p. We identify a new correlation length, ξ, which is a function of ∇p: ξ~(∇p)−γ/α, where α=ν⊥/ν|| is the roughness exponent, and γ=ν⊥/(1+ν⊥). The exponents ν⊥ and ν|| characterize the transverse and longitudinal correlation lengths. To investigate the effect of ∇p on the scaling properties of the interface in (1+1) and (2+1) dimensions, we calculate the critical concentration, pc, and the exponents γ and α from which ν⊥ and ν|| can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.
1 citations
TL;DR: In this paper, a set of coupled equations are introduced to describe the coupling between a growing interface and a thin surfactant layer deposited on the top of the nonequilibrium surface.
Abstract: A number of recent experiments have showed that surfactants can modify the growth mode of an epitaxial film, suppressing islanding and promoting layer-by-layer growth. Here a set of coupled equations are introduced to describe the coupling between a growing interface and a thin surfactant layer deposited on the top of the nonequilibrium surface . The equations are derived using the main experimentally backed characteristics of the system and basic symmetry principles. The system is studied using a dynamic-renormalization-group scheme, which provides scaling relations between the roughness exponents. It is found that the surfactant may drive the system into a novel phase, in which the surface roughness is negative, corresponding to a flat surface.