Modeling rough surfaces with Lorentz equations

Abstract

Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled 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 earlier reported that at early times, during sputtering, 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 model, give a pattern similar to modern surface evolution simulations. The ultimate goal was to predict the most common surface morphology by constantly varying the parameters of the Lorentz model and study the effects on the simulated surface patterns. Almost all of the recent experimentally observed and theoretically predicted formations are accurately obtainable with this concept.