title: Analysis of etching at a solid-solid interface.
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.
authors.affiliation: Graduate Program in Material Science, Faculdade UnB Planaltina, Universidade de Brasília, CEP 73300-000, Planaltina, DF, Brazil.|Instituto de Física, Universidade de Brasília, CP 04513, CEP 70919-970, Brasília, DF, Brazil.
authors.forename: Washington S
authors.initials: WS
authors.lastname: Alves
authors.affiliation: Instituto de Física, Universidade de Brasília, CP 04513, CEP 70919-970, Brasília, DF, Brazil.
authors.forename: Evandro A
authors.initials: EA
authors.lastname: Rodrigues
authors.affiliation: Universidade Federal de Goiás, Campus Jataí, Br 364, Km 192, 3800, Parque Industrial, CEP 75801-615, Jataí, Goiás, Brazil.
authors.forename: Henrique A
authors.initials: HA
authors.lastname: Fernandes
authors.affiliation: IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA.
authors.forename: Bernardo A
authors.initials: BA
authors.lastname: Mello
authors.affiliation: Instituto de Física, Universidade de Brasília, CP 04513, CEP 70919-970, Brasília, DF, Brazil.|Korea Institute for Advanced Study, Seoul 130722, South Korea.
authors.forename: Fernando A
authors.initials: FA
authors.lastname: Oliveira
authors.affiliation: Graduate Program in Material Science, Faculdade UnB Planaltina, Universidade de Brasília, CEP 73300-000, Planaltina, DF, Brazil.
authors.forename: Ismael V L
authors.initials: IV
authors.lastname: Costa