Dynamics of Solidification Process and Introduction to Interfacial Stability Theory

Author: Xu Jianjun
Publisher:
Publish Date: 2006-12-01
Features: This book aims to systematically present important fundamental theoretical concepts and modern achievements in solidification dynamics, elucidate the Mullins-Sekerka instability theory for planar interfaces, explore the physical mechanisms of dendritic growth during directional solidification, introduce and review various modern analytical theories of dendritic growth dynamics, and systematically explain the new theory of interface waves in dendritic growth. The book demonstrates important analytical methods in applied mathematics, such as dimensional analysis, similarity solutions, asymptotic matching, multiple variable asymptotic expansions, and nonlinear bifurcation theory, through examples. It also explains the basic concepts and theoretical foundations of the phase-field model, which is currently widely used in numerical simulations. This book can serve as a textbook or teaching reference for senior undergraduate and graduate students in material science, physics, applied mathematics, and related fields with a focus on crystal growth and material processing. It can also be used as a reference for researchers in mathematical theory of material science and university teachers. The content of the book includes: Introduction, Solidification of Pure Melts, Stability of Solidification Processes with Planar Liquid-Solid Interfaces, Stability of Solidification Processes with Constant Curvature Curved Interfaces, etc.