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Dynamic Scaling of Growing Interfaces
Physical Review Letters · 1986 · Vol. 56(9) · pp. 889–892
Mehran Kardar✉(Harvard University)Giorgio Parisi(Sapienza University of Rome)Yi-Cheng Zhang(Brookhaven National Laboratory)
Abstract
A model is proposed for the evolution of the profile of a growing interface. The deterministic growth is solved exactly, and exhibits nontrivial relaxation patterns. The stochastic version is studied by dynamic renormalization-group techniques and by mappings to Burgers's equation and to a random directed-polymer problem. The exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations. Predictions are made for more dimensions.
Theoretical and Computational PhysicsMaterial Dynamics and PropertiesStochastic processes and statistical mechanicsDynamic scalingScalingStatistical physicsBurgers' equationRenormalization groupRelaxation (psychology)Interface (matter)Functional renormalization groupPhysicsComputer science
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References
The surface statistics of a granular aggregate
Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1982 · 1,502 citations
Large-distance and long-time properties of a randomly stirred fluid
Physical review. A, General physics · 1977 · 1,307 citations
Current Topics in Materials Science
Journal of The Electrochemical Society · 1980 · 2,266 citations
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