论文标题
分叉分析揭示了相场模型的解决方案结构
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
论文作者
论文摘要
相位场方法在理解和预测材料和生物系统的形态演化方面起着越来越重要的作用。在这里，我们基于分叉分析开发了一种新的分析方法，以探索相位场模型的数学解决方案结构。揭示这种解决方案结构不仅具有极大的数学兴趣，而且还可以为经过电子和结构相变的材料中的实验或计算发现新的形态演化现象提供指导。为了阐明这个想法，我们将这种分析方法应用于三个代表性相位场方程：艾伦 - 卡纳方程，cahn-hilliard方程和艾伦 - 卡纳 - 奥塔·卡瓦萨基系统。这三个相位方程的解决方案结构也通过同型持续方法进行数值验证。
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.
