Anomalous Surface Roughening: Experiment and Models

  • S. Havlin
  • A.-L. Barabási
  • S. V. Buldyrev
  • C. K. Peng
  • M. Schwartz
  • H. E. Stanley
  • T. Vicsek
Part of the NATO ASI Series book series (NSSB, volume 304)


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.


Correlate Noise Directed Percolation Directed Polymer Roughness Exponent Invasion Percolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • S. Havlin
    • 1
    • 2
  • A.-L. Barabási
    • 1
  • S. V. Buldyrev
    • 1
  • C. K. Peng
    • 1
  • M. Schwartz
    • 1
    • 3
  • H. E. Stanley
    • 1
  • T. Vicsek
    • 4
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Department of PhysicsBar-Ilan UniversityRamat-GanIsrael
  3. 3.Department of Physics and AstronomyTel-Aviv UniversityRamat-AvivTel-AvivIsrael
  4. 4.Department of Atomic PhysicsEötvös UniversityBudapestHungary

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