A fractal langevin equation describing the kinetic roughening growth on fractal lattices

摘要

A fractal Langevin equation partial derivative h/partial derivative t = v del(zrw)h + lambda/2(del(zrw)/(2)h)(2) +eta (z(rw) ( z(rw) is the random walk exponent on the lattice) is proposed to describe the kinetic roughening growth on fractal substrates. The scaling relation alpha + z= z(rw) can be obtained. Kinetic Monte Carlo simulations are carried out for Restricted Solid-on-solid model and Etching model growing on various fractal substrates, and the results prove this scaling relation.