Computational studies of dendritic crystal growth.

摘要

In this dissertation, I will review my research on developing and validating novel ways to model dendritic crystal growth---the formation of snowflake-like patterns during the solidification of crystalline substances. After giving a brief introduction to the sharp-interface model and phase-field model, I will discuss the following topics: the universal dynamics of different phase-field models and the range of validity of the asymptotic analysis of Karma and Rappel; the creation of an improved level set method that is used to solve the sharp-interface model and compute time-dependent solidification microstructures; a review of two sidebranching mechanisms and suggestions on how to verify tip-oscillations by using different models of solidification; and an attempt to create an efficient cell dynamical system model to study universal features of dendritic growth.