Autômatos celulares e crescimento de interfaces rugosas - Thiago Gomes de Mattos (2005)
In this work we apply the methodology of CA modeling to study interface growth processes which depend on height differences between neighbours. The rules associate a probability pi(t) for site i to receive a particle at time t, where pi(t) = ½ exp[·¡i(t)]. Here, ½ and · are two parameters and ¡i(t) is a kernel that depends on the height hi(t) of the site i and on the heights of its neighbours, at time t. We specify the functional form of this kernel by the discretization of the deterministic part of theequation associated to a given growth process. For example, in processes where surface relaxation plays a major role, we have a Laplacian as the main term in the growth equation (Edwards-Wilkinson equation) and, in this case, ¡i(t) = hi+1(t) + hi¡1(t) ¡ 2hi(t), which follows from the discretization of r2h. Furt hermore, we study dynamics with rules depending on r4h term (equation of growth with diffusion). By means ofsimulations and statistical analysis of the height distributions of the generated profiles, we obtain the growth, roughness and dynamic exponents, ¯, ® and z, whose values confirm that the defined processes are indeed in the universality class of the original growth equation.