Ballistic deposition and Kardar-Parisi-Zhang universality class - Zevnik, Domen (Matrika, 2022)
The paper focuses on modeling the growth of interface, best pictured as deposition of snow. In the first part a heuristic derivation of the Kardar-Parisi-Zhang (KPZ) equation is provided based on simple symmetry arguments. Next, the KPZ universality class is defined through an example of a simple discrete model, called Ballistic deposition. Numerical evidence is provided, which suggest that the KPZ equation is indeed in the KPZ universality class. Lastly, an experimental realisation is described, which shows characteristic KPZ statistics in boundary growth in liquid crystals.
Keywords: balistično odlaganje; ballistic deposition; Kadar-Parisi-Zhang enačba; Kardar-Parisi-Zhang equation; parcialne diferencialne enačbe; partial differential equations