Phys. Rev. Lett. 56, 889–892 (1986)Dynamic Scaling of Growing InterfacesReceived 12 November 1985; published in the issue dated 3 March 1986 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/doi/10.1103/PhysRevLett.56.889
DOI:
10.1103/PhysRevLett.56.889
PACS:
05.70.Ln, 64.60.Ht, 68.35.Fx, 81.15.Jj
See AlsoComment: D. Stauffer and J. G. Zabolitzky, Dynamic Scaling of Eden-Cluster Surfaces, Phys. Rev. Lett. 57, 1809 (1986). Comment: Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang, Kardar, Parisi, and Zhang Respond, Phys. Rev. Lett. 57, 1810 (1986). |
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