intermediate length scales, where continuum models are appropriate. Examples of topics in the latter category include fracture mechanics and microstructural pattern formation in alloys. Finally, there is work at macroscopic length scales, in which the bulk properties of materials are used as inputs to models of manufacturing processes and performance. Historically, research in each of these three areas has been carried out by separate communities of scientists—applied mathematicians, physicists, chemists, metallurgists, ceramists, mechanical engineers, manufacturing engineers, and so on. One of the committee’s principal theses is that the distinction between these areas of research is properly being blurred by modern developments.

The principal recommendations of the committee are the following:

  • Analysis, modeling, and computation should play a significant role in both the educational and the research components of academic programs in materials science and engineering. Renewed attention should be paid to mathematical analysis (as distinct from—and in addition to—computer programming) in educational curricula.

  • New support is needed both to make high-level computational facilities available for materials research and to develop validated data bases, algorithms, and numerical simulations.

  • Special attention should be paid to the need for accurate models of nonequilibrium phenomena, particularly processes relevant to manufacturability and performance of materials. Work toward the development of integrated approaches, combining science-based simulations with optimization of features regarding quality and cost, should be strongly encouraged.

PROPERTIES OF MATERIALS AT MICROSCOPIC LENGTH SCALES

Particularly interesting developments of the past few years are apparently feasible schemes for carrying out “first-principles” computations of complex atomic arrangements in materials starting with nothing more than the identities of the atoms and the rules of quantum mechanics. To put these developments in perspective, it will be best to mention some more conventional—and still very productive—approaches to atomistic modeling of materials before turning to this remarkably ambitious new point of view.

Statistical Mechanics

One conventional picture of how huge numbers of atoms collectively determine the bulk properties of materials is the classical statistical mechanics of Boltzmann, Gibbs, Einstein, and others, dating back to the turn of the century. Quantum theory plays only a subsidiary role in this picture. In



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