Dynamic Scaling of Growing Interfaces

Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang
Phys. Rev. Lett. 56, 889 – Published 3 March 1986
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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.

  • Received 12 November 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.889

©1986 American Physical Society

Authors & Affiliations

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

Comments & Replies

Dynamic Scaling of Eden-Cluster Surfaces

D. Stauffer and J. G. Zabolitzky
Phys. Rev. Lett. 57, 1809 (1986)

Kardar, Parisi, and Zhang Respond

Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang
Phys. Rev. Lett. 57, 1810 (1986)

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Issue

Vol. 56, Iss. 9 — 3 March 1986

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