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Review on relationship between the universality class of the Kardar-Parisi-Zhang equation and the ballistic deposition model

Sayfidinov Okhunjon, Bognar Gabriella

International Journal of Applied Mechanics and Engineering

2021

Vol. 26, no. 4

206--216

We have analysed the research findings on the universality class and discussed the connection between the Kardar-Parisi-Zhang (KPZ) universality class and the ballistic deposition model in microscopic rules. In one dimension and 1+1 dimensions deviations are not important in the presence of noise. At the same time, they are very relevant for higher dimensions or deterministic evolution. Mostly, in the analyses a correction scale higher than 1280 has not been studied yet. Therefore, the growth of the interface for finite system size [...] value predicted by the KPZ universality class is still predominant. Also, values of [...] obtained from literature are consistent with the expected KPZ values of [...] connection between the ballistic deposition and the KPZ equation through the limiting procedure and by applying the perturbation method was also presented.