From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure
From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure
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 …