Bifurcation Analysis Reveals Solution Structures of Phase Field Models

扫码查看

原文链接

NETL
NSTL
万方数据

外文摘要：The 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 the 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 com-putationally 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:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continua-tion method.

外文关键词：

Phase field modelingBifurcationsMultiple solutions

作者：

Xinyue Evelyn Zhao、Long-Qing Chen、Wenrui Hao、Yanxiang Zhao

展开 >

作者单位：

Department of Mathematics,Vanderbilt University,Nashville,TN 37212,USA

Department of Materials Science and Engineering,Pennsylvania State University,University Park,PA 16802,USA

Department of Mathematics,Pennsylvania State University,University Park,PA 16802,USA

Department of Mathematics,The George Washington University,Washington,DC 20052,USA

展开 >

基金：

Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy SciencesSimons Foundation国家自然科学基金

项目编号：

DE-SC0020145357963DMS-2142500

出版年：

2024

DOI：

10.1007/s42967-022-00221-1

应用数学与计算数学学报

上海大学

应用数学与计算数学学报

影响因子：0.165

ISSN：1006-6330

年,卷(期)：2024.6(1)

参考文献量78