Microscopic Properties and Physical Behavior of Materials and Media

DMS Award AbstractAward #： 0104531 PI： 布鲁诺，奥斯卡机构： 加州理工学院课程： 应用数学项目经理：Catherine Mavriplis职务：材料和介质的微观特性和物理行为本文提出了两个不同领域的研究，即1）估计的整体（均匀化）的行为，包含微观失配的非均匀材料，和，2）评估波的传播和散射的非均匀介质。微观失配是复合材料的微观组分所经历的某些类型的变形和电/磁极化。 例如，在陶瓷-金属复合材料（金属陶瓷）中，混合物的两种基本组分具有不同的热膨胀系数;因此，加热会产生失配，即，微观变形，这将是不匹配的，如果不是在陶瓷和金属之间的边界处的弹性位移的连续性的约束。 因此，失配产生微观应力，其在很大程度上决定了宏观复合材料的行为。 在这些方面提出的努力将寻求提供一个理论上的理解失配，使材料具有更好的性能可以设计。例如，我们的目标之一是设计在高温下不会破碎的陶瓷，因此适用于高温下的涡轮机叶片。 另一方面，非均匀介质的散射问题在雷达、声纳和遥感、医学显微镜、光通信和非侵入性评估等各种应用中发挥着核心作用。 这里提出的工作将寻求开发快速的高阶求解器，在工程实践中产生的各种配置。鉴于最近的研究结果，可以预见，所提出的技术将显着提高我们的预测能力，在材料科学和计算波propagation.The拟议的工作影响了一些领域的联邦战略利益，包括高性能计算，材料研究，医学，生物学和国家安全。具体的研究是在两个不同的领域，即1）包含微观失配的非均匀材料的整体行为的估计，和，2）波的传播和散射的非均匀介质的评估。这些努力旨在为具有特定特性的材料工程，光学和显微镜问题的解决方案以及与雷达和声纳相关的遥感问题提供高效的计算方法。日期：2001年6月18日

DMS Award AbstractAward #: 0104531PI: Bruno, OscarInstitution: California Institute of TechnologyProgram: Applied MathematicsProgram Manager: Catherine MavriplisTitle: Microscopic Properties and Physical Behavior of Materials and MediaThe present text proposes research in two distinct areas, namely 1) estimation of the overall (homogenized) behavior of inhomogeneous materials containing microscopic misfits, and, 2) evaluation of wave propagation and scattering by inhomogeneous media. Microscopic misfits are certain types of deformations and electrical/magnetic polarizations that are experienced by the microscopic components of a composite material. In a ceramic-metal composite (cermet), for example, the two basic components of the mixture have different coefficients of thermal expansion; heating, therefore, gives rise to misfits - i.e., microscopic deformations which would be mismatched, were it not for constraints of continuity of elastic displacements at the boundaries between ceramic and metal. Misfits thus produce microscopic stresses that determine, to a substantial extent, the macroscopic composite behavior. The proposed efforts in these regards will seek to provide a theoretical understanding of misfits, so that materials with improved properties can be designed. One of our goals, for example, seeks to design ceramics that do not shatter at elevated temperatures, and are thus appropriate for use in turbine blades at high temperatures. Problems of scattering by inhomogeneous media, on the other hand, play central roles in a wide variety of applications, including radar, sonar and remote sensing, medical microscopy, optical communications and non-invasive evaluation. The work proposed here will seek to develop fast high-order solvers for a variety of configurations arising in engineering practice. In view of recent results, it is envisioned that the proposed techniques will significantly enhance our prediction capabilities in both materials science and computational wave propagation.The proposed work impacts a number of areas of federal strategic interest, including high-performance computing, materials research, medicine, biology and national security. The specific research is in two distinct areas, namely 1) estimation of the overall behavior of inhomogeneous materials containing microscopic misfits, and, 2) evaluation of wave propagation and scattering by inhomogeneous media. These efforts seek to produce highly efficient computational methods for engineering of materials with specified properties, for the solution of problems in optics and microscopy, and for remote sensing problems related to radar and sonar. Date: June 18, 2001