### Speaker

Prof.
Fernando Oliveira
(Universidade de Brasília)

### Description

In a recent work [1] a method to derive analytically the roughness evolution was exposed. The method allows to obtain analytically the growths exponents of a surface of $1+1$ dimensions whose dynamics is ruled by cellular automata. The method was successfully applied to the etching model[2,3] and the dynamical exponents where obtained. Those exponents are exact and they are the same as those exhibited by the KPZ model[4] for this dimension. Here we revisit the dynamics of corrosion of an interface and we define a distribution of height difference $P(h_i - h_j)$, between a site $i$ and its first neighbour $j$. We present a simple proof that in the continuous limit the etching mechanism leads us to the Kardar-Parisi-Zhang (KPZ) equation in a $d+1$ dimensional space. We show that the parameter $\lambda$ associated with the nonlinear term of the KPZ equation is not phenomenological, rather it stems from $P(h_i-h_j)$. The Galilean invariance is recovered independent of $d$, and we illustrate this via very precise numerical simulations. Moreover, we strengthen the argument that there is no upper critical limit for the KPZ equation [6].\\
references
[1] W. S. Alves, E. A. rodrigues, H. A. Fernandes, B. A. Mello, F. A. Oliveira and I. V. L. Costa. Phys. Rev. E 94, 042119 (2016).
[2] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. Rev. E \textbf{63}, 041113 (2001).
[3] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. Phys. A {\bf 48}, 035001 (2015).
[4] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. {\bf 56}, 9, 889 (1986).
[5] Halpin-Healy T J and Zhang C-Y, Phys. Rep. 254 215 (1995);
Marsili M, Maritan A, Toigo F and Banavar J R Rev. Mod. Phys. 68 963 (1996).
[6] W. R. J. Gomes and F. A. Oliveira to be published.

### Primary author

Prof.
Fernando Oliveira
(Universidade de Brasília)

### Co-authors

Waldenor Gomes
(University of Brasilia)
Washington Alves
(University of Brasilia)