Mathematical Sciences: Nonlinear Partial Differential Equations and Models for Phase Change

数学科学：非线性偏微分方程和相变模型

• 批准号: 8901771
• 负责人: Paul Fife
• 金额: $ 16.7万
• 依托单位: University of Utah
• 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: 1989-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901771&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Partial; Differential

This research concerns mathematical questions relating to models for phase change, especially phase separation. The existing models for phase separation are the Cahn-Hilliard equation (for a binary alloy) and the phase field equations (for a pure material with latent heat). The mathematical issues relate to the initial phase separation events and the subsequent coarsening of the material. Also, the research will include a study of the connections between different stationary states and, in one case, the motion of internal layers, characteristic of the later stages of coarsening. The research is in the general area of applied mathematics and in the specific area mathematical models for the dynamics of phase changes. The project supports a group effort of four researchers.

这项研究涉及的数学问题， 相变模型，尤其是相分离模型。的 现有的相分离模型是Cahn-Hilliard 方程（对于二元合金）和相场方程（对于 具有潜热的纯材料）。 数学问题 与最初的相分离事件和随后的 材料的粗化。 此外，该研究将包括一个 研究不同定态之间的联系 在一种情况下，内部层的运动， 在粗化的后期。 这项研究属于应用数学的一般领域 在特定领域的数学模型的动力学 阶段变化。 该项目支持四个小组的努力， 研究人员