Date of Award

Spring 2019

Document Type

Open Access Thesis

Department

Mathematics

First Advisor

Yi Sun

Abstract

Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through three events: hopping, evaporation, and condensation. Finally, we institute the ki- netic Monte Carlo method to describe the evolution of a crystalline structure and to examine how temperature influences the mobility of surface atoms.

Included in

Mathematics Commons

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