MODELING ROUGH SURFACES WITH LORENTZ EQUATIONS

Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is model ed with stochastic partial differential equations. However, we apply a new approach by the use of the famous Lorentz equations to simulate and predict such patterns. It has been ear lier reported that at early times, during sputterin g, surface displays a chaotic pattern, with stable domains that nucleate and grow linearly in time until ripples domains of two different orientations are formed. The numerical solutions of the Lorentz model, being an unstable and chaotic m odel, give a pattern similar to modern surface evolution simulations. Th e ultimate goal was to predict the most common surf ace morphology by constantly varying the parameters of the Lorentz mo del and study the effects on the simulated surface patterns. Almost all of the recent experimentally observed and theoreticall y predicted formations are accurately obtainable wi th this concept.