Phase transitions and partial differential equations of mixed types

相变和混合型偏微分方程

• 批准号: 354724-2008
• 负责人: Mei, Ming
• 金额: $ 1.02万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=459288
• 关键词: Phase; transitions; partial; differential; equations

Phase transitions are very common phenomena arising in thermodynamics. Two important type of models are the compressible van der Waals fluid flow and the model of viscoelastic material dynamics. In the van der Waals flow, due to the variety of the absolute temperature and the non-monotony of the pressure function, the flow usually exhibits phase transitions between water, vapor and mixtures of water and vapor. While in the model of viscoelastical material dynamics, due to the change of the non-monotonic stress function, the system behaves as three phases-soft material, hard material and the mixture of soft and hard material.

相变是热力学中非常常见的现象。两种重要的模型是可压缩的货车der Waals流体流动和粘弹性材料动力学模型。在货车范德瓦尔斯流动中，由于绝对温度的变化和压力函数的非单调性，流动通常表现为水、水蒸气以及水蒸气混合物之间的相变。而在粘弹性材料动力学模型中，由于非单调应力函数的变化，系统表现为软质材料、硬质材料和软硬混合物三种相态。