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An analytical formulation for roughness based on celular automata | Ismael V. L. Costa
; Henrique A. Fernandes
; Bernardo A. Mello
; Fernando A. Oliveira
; | Date: |
24 Aug 2012 | Abstract: | We present a method to derive the analytical expression of the roughness of a
fractal surface whose dynamics is ruled by cellular automata. Starting from the
automata, we write down the the time derivative of the height’s average and
variance. By assuming the equiprobability of the surface configurations and
taking the limit of large substrates we find the roughness as a function of
time. As expected, the function behaves as $t^eta$ when $tll t_ imes$ and
saturate at $w_s$ when $tgg t_ imes$. We apply the methodology to describe
the etching model citep{Bernardo}, however, the value of $eta$ we obtained
are not the one predicted by the KPZ equation and observed in numerical
experiments. That divergence may be due to the equiprobability assumption. We
redefine the roughness with an exponent that compensate the nonuniform
probability generated by the celular automata, resulting in an expression that
perfectly matches the experimental results. | Source: | arXiv, 1208.5063 | Services: | Forum | Review | PDF | Favorites |
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