Mathematical Sciences: Dynamics in Partial Differential Equations Modeling Phase Transitions

数学科学：偏微分方程动力学相变建模

• 批准号: 8902422
• 负责人: Robert Pego
• 金额: $ 3.58万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1990-09-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902422&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Partial; Differential

8902422 Pego The main goal of this project is to develop a mathematical understanding of nonlinear dynamics appropriate for models of continua which admit phase transitions. The mathematical problems to be studied address the general questions: How do nonlinear systems relax to equilibrium? How do interfaces and transition zones propagate? Specifically, the project includes the study of the propagation of transition layers in the Cahn-Hilliard equation and phase field equations, to prove the validity of interface migration laws via the geometric approach to singular perturbations; the formal determination of the laws of migration for singularities in nematic liquid crystals using a regularized model of Lin and the geometric method; the discovery of admissibility criteria for shock waves in compressible fluids which account for metastability and homogeneous nucleation, nonequilibrium phenomena which have recently been shown to be highly relevant in experiment.

8902422 Pego 该项目的主要目标是开发一个数学 理解适合于模型的非线性动力学 允许相变的连续体。 数学 要研究的问题解决一般问题：如何 非线性系统松弛到平衡态？ 接口和 过渡区会传播吗？ 具体而言，该项目包括 研究了过渡层的传播， Cahn-Hilliard方程和相场方程，以证明 通过几何方法验证界面迁移定律的有效性 奇异摄动;法律的正式确定 使用向列型液晶中奇异点的迁移 林的正则化模型和几何方法; 冲击波容许准则的发现 可压缩流体，其考虑亚稳性， 均匀成核，非平衡现象， 最近在实验中被证明是高度相关的。