We study the dynamics of an interface driven far from equilibrium in three dimensions. We first derive the equations of motion which describe this physics. Numerical results are then obtained for three models which simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We show that the three models belong to the same dynamical universality class by estimating the dynamical scaling exponents and the scaling functions. We confirm the results by a careful study of the crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this phenomenon by monitoring the surface step energy which shows a drastic jump at a finite temperature for a given driving force. At the same temperature, a finite size scaling analysis on the bond energy fluctuation shows a diverging peak.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.70226 |
| Date | January 1991 |
| Creators | Grossman, Bruno |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001254642, proquestno: AAINN72134, Theses scanned by UMI/ProQuest. |
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