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Article overview
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Analysis of etching at a solid-solid interface | | Washington S. Alves
; Evandro A. Rodrigues
; Henrique A. Fernandes
; Bernardo A. Mello
; Fernando A. Oliveira
; Ismael V. L. Costa
; | | Date: |
18 Jul 2017 | | Abstract: | 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. | | Source: | arXiv, 1707.5687 | | Services: | Forum | Review | PDF | Favorites | |
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