The 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