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Phys. Rev. Lett. 56, 889–892 (1986)

[Issue 9 – 3 March 1986 ]

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Dynamic Scaling of Growing Interfaces

Mehran Kardar

Physics Department, Harvard University, Cambridge, Massachusetts 02138

Giorgio Parisi

Physics Department, University of Rome, I-00173 Rome, Italy

Yi-Cheng Zhang

Physics Department, Brookhaven National Laboratory, Upton, New York 11973

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.

©1986 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v56/p889
DOI: 10.1103/PhysRevLett.56.889
PACS: 05.70.Ln, 64.60.Ht, 68.35.Fx, 81.15.Jj

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