Analysis of etching at a solid-solid interface

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E 2016-10, Vol.94 (4-1), p.042119-042119, Article 042119
Main Authors: Alves, Washington S, Rodrigues, Evandro A, Fernandes, Henrique A, Mello, Bernardo A, Oliveira, Fernando A, Costa, Ismael V L
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height variance (roughness). We apply this method to the etching model in 1+1 dimensions, and then we obtain the roughness exponent. Using this in conjunction with the Galilean invariance we obtain the other exponents, which perfectly match the numerical results obtained from simulations. These exponents are exact, and they are the same as those exhibited by the Kardar-Parisi-Zhang (KPZ) model for this dimension. Therefore, our results provide proof for the conjecture that the etching and KPZ models belong to the same universality class. Moreover, the method is general, and it can be applied to other cellular automata models.
ISSN:2470-0045
2470-0053
DOI:10.1103/PhysRevE.94.042119