Anomalous Surface Roughening: Experiment and Models
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 Lévy 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.
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