Mathematical Sciences: Parallel and Distributed Diffusion Models for Heterogeneous Media

数学科学：异构介质的并行分布式扩散模型

• 批准号: 9500920
• 负责人: Ralph Showalter
• 金额: $ 10.41万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500920&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Parallel; Distributed; Diffusion

DMS-9500920 Showalter Mathematical models of diffusion in heterogeneous media will be developed as nonlinear systems of partial differential equations. These diffusion processes include examples of diffusion through porous or fissured media (with saturation, absorption, or phase change) and conduction through composite semiconductor materials. The singular or degenerate nature of these systems arise from material properties and from the geometry of the composition. Major objectives include the development by homogenization theory of two-scale models, proof of well-posedness results in appropriate function spaces, and the investigation of properties of solutions for the various systems. Mathematical models of diffusion in composite media will be developed. These diffusion processes include examples of heat conduction (with solid - liquid phase change), diffusion of fluid through porous or fissured media (with saturation), absorption by granulated substance, and the macroscopic description of current flow in semi-conductor materials. The singular or degenerate nature of these systems arise from properties of the materials and from the geometry of the composition. Major objectives include the development of exact small-scale models to describe the flow across the intricate interface between the components of the media and averaged large-scale models which are necessary for the computation of solutions.

DMS-9500920 Showalter非均质介质中扩散的数学模型将被开发为偏微分方程的非线性系统。这些扩散过程包括通过多孔或裂缝介质（具有饱和、吸收或相变）的扩散和通过复合半导体材料的传导的示例。这些系统的奇异性或退化性来自材料性质和组成的几何形状。主要目标包括两个尺度模型的均匀化理论的发展，适定性结果在适当的函数空间的证明，以及各种系统的解决方案的性质的调查。 将建立复合介质中扩散的数学模型。这些扩散过程包括热传导（固-液相变）、流体通过多孔或裂隙介质（饱和）的扩散、颗粒物质的吸收以及半导体材料中电流流动的宏观描述。这些系统的奇异或退化性质来自材料的性质和组合物的几何形状。主要目标包括开发精确的小规模模型，以描述穿过介质组分之间复杂界面的流动，以及计算解决方案所需的平均大规模模型。