Microscopic Properties and Physical Behavior of Materials and Media

DMS奖摘要奖号：0104531PI: Bruno，奥斯卡机构：加州理工学院项目：应用数学项目经理：Catherine mavriplis标题：材料和介质的微观性质和物理行为本文提出了两个不同领域的研究，即1)估计包含微观失配的非均匀材料的整体（均质）行为，以及2)评估非均匀介质的波传播和散射。微观失配是复合材料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，混合物的两种基本成分具有不同的热膨胀系数；因此，加热会导致不匹配-即，如果没有陶瓷和金属之间边界弹性位移连续性的约束，微观变形将是不匹配的。因此，不匹配产生的微观应力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对不适合的理论理解，以便可以设计具有改进性能的材料。例如，我们的目标之一是寻求设计出在高温下不会破碎的陶瓷，因此适合用于高温下的涡轮叶片。另一方面，非均匀介质的散射问题在包括雷达、声纳和遥感、医学显微镜、光通信和非侵入性评估在内的各种应用中发挥着核心作用。这里提出的工作将寻求为工程实践中出现的各种配置开发快速高阶求解器。鉴于最近的结果，我们设想所提出的技术将大大提高我们在材料科学和计算波传播方面的预测能力。拟议的工作影响联邦战略利益的许多领域，包括高性能计算、材料研究、医学、生物学和国家安全。具体研究在两个不同的领域，即1)估计包含微观失配的非均匀材料的整体行为，以及2)评估非均匀介质的波传播和散射。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以及与雷达和声纳有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