Work

Analysis of etching at a solid-solid interface

Year: 2016

Type: article

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: Physical review. E

DOI: 10.1103/physreve.94.042119

Authors: Washington S. Alves, Evandro A. Rodrigues, Henrique A. Fernandes, Bernardo A. Mello, Fernando A. Oliveira, Ismael V. L. Costa

Institutions: Universidade de Brasília, Universidade Federal de Goiás, IBM Research - Thomas J. Watson Research Center, Korea Institute for Advanced Study

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Apoio à Pesquisa do Distrito Federal

OpenAlex ID: W2535801264

FWCI: 0.598

Cites: 35

Cited by: 15

Related to: 10