Pattern formation in reaction diffusion systems and ion bombardment of surfaces - Hashmi, Bahaudin A., author; Shipman, Patrick D., advisor; Liu, Jiangguo, advisor; Thompson, Stephen, committee member; Bates, Daniel J., committee member (Colorado State University. Libraries, 2017)
We have analyzed pattern formation in two different systems: (1) Vapor-to-particle reaction diffusion systems and (2) Highly ordered square arrays in ion bombardment. The vapor-to-particle reaction exhibits oscillatory behavior and produces a spatial pattern called Liesegang rings. In this thesis, we develop a finite element scheme to model the hydrogen chloride and ammonia vapor-to-particle reaction. In our simulations, we develop parametric regions for different patterns and corroborate data obtained from experiments of this reaction. For the ion bombardment of a planar surface, we add the Ehrlich-Schwoebel barrier terms to the Bradley-Shipman equations of motion and see the impact of ion bombardment at normal incidence on a binary crystalline material. A weakly nonlinear stability analysis was conducted and regions were determined where highly ordered square pyramids formed.
Keywords: ion bombardment; threshold kinetics; nucleation and growth; finite element methods