2022/10/13 by Xinyue Evelyn Zhao, Long‐Qing Chen, Zhao, Xinyue Evelyn +5
Materials Science · Physics and Astronomy · Engineering · #Solidification and crystal growth phenomena #Theoretical and Computational Physics #Fluid Dynamics and Thin Films
paper · pdf · doi:10.48550/arxiv.2210.06691
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: Allen-Cahn equation, Cahn-Hilliard equation, and Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.