From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure
Open Access
- 1 July 1998
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 58 (1), 700-703
- https://doi.org/10.1103/physreve.58.700
Abstract
We show a direct connection between the ballistic deposition and the Kardar-Parisi-Zhang (KPZ) equation. We derive the KPZ equation from the ballistic deposition models, using an important limiting procedure. The cellular automaton rule is transformed into an integrable difference-difference equation through the limiting procedure. By applying the perturbation method to the difference-difference equation, the difference-difference equation is reduced to the KPZ equation through the Burgers equation. We apply the procedure to several types of ballistic deposition models.Keywords
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