Dynamic scaling of growing interfaces
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 Burger'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.
- Publication:
-
Physical Review Letters
- Pub Date:
- March 1986
- DOI:
- 10.1103/PhysRevLett.56.889
- Bibcode:
- 1986PhRvL..56..889K
- Keywords:
-
- 05.70.Ln;
- 64.60.Ht;
- 68.35.Fx;
- 81.15.Jj;
- Nonequilibrium and irreversible thermodynamics;
- Dynamic critical phenomena;
- Diffusion;
- interface formation;
- Ion and electron beam-assisted deposition;
- ion plating