Mathematical Sciences: Selection Criteria and Metastable States for Phase Transitions in Fluids and Solids

数学科学：流体和固体相变的选择标准和亚稳态

• 批准号: 8701448
• 负责人: E. Zachmanoglou
• 金额: $ 2.12万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701448&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Selection; Criteria; Metastable

This research program is concerned with two related projects. One is the selection of equilibrium states of a three dimensional, nonlinearly elastic body undergoing a phase transformation. The selection criterion involves a singular perturbation problem for a nonconvex functional in a variational formulation. The second is the study of the long time behavior of the solutions of the Cahn-Hilliard equation which models the phase-separation of binary alloys and polymer mixtures that have been rapidly cooled. The results from these two projects are expected to have significant impact on engineering mechanics.

这项研究计划涉及两个相关的项目。其一是相变过程中三维非线性弹性体平衡态的选择。选择准则涉及变分形式中非凸泛函的奇异摄动问题。第二个是研究Cahn-Hilliard方程解的长时间行为，该方程模拟了快速冷却的二元合金和聚合物混合物的相分离。这两个项目的结果预计将对工程力学产生重大影响。