materials science: block copolymers, dynamic fracture, effective moduli of composites, grain boundaries, grain growth, martensite and shape-memory materials, mushy regions, processing of semiconductor chips, stokesian dynamics for complex fluids, and superconductivity. As a basic framework for description, the committee's choice of general categories of focus or themes became the titles of this report's Chapters 2 through 8. This organization of subjects by themes is in contrast to the committee's phase-one survey (National Research Council, 1991a), which was organized around various classes or applications of materials (such as ceramics, electronic and semiconductor materials, polymers, and so on). Extensive cross-referencing has been provided between subjects or chapters when the same or a related topic is discussed elsewhere in this report. Subjects within chapters were chosen for illustration; the lists of subjects are not meant to be comprehensive. Further, the descriptions of those subjects and associated mathematical research opportunities present only a part of the much more wide-ranging totality (for example, cf. Langer, 1992; National Research Council, 1991c, 1989; Psaras and Langford, 1987). In the same way, the references given are intended to help the reader search further into the literature, with no attempt made to be complete. What appears in this report reflects the committee members' expertise and knowledge, that of the cross-section of individuals (see appendix) who were kind enough to provide information to the committee, and the project limits on time and funding.

The committee hopes that this report will help encourage research in the mathematical sciences that complements vital research in materials science, will generally raise awareness of the value of quantitative methods in materials science, and will spur researchers to explore the interface between the mathematical sciences and materials science. The committee also wishes to repeat the perspective expressed in its previous short report on the subject (National Research Council, 1991a): cross-disciplinary collaborations require long-term commitments.

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