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specialty about a generation ago. In recent years, the same nonequilibrium concepts being tested in the design of alloys are also being applied to galaxy formation in the cosmos, climatic changes on the Earth, and the growth of forms in biological systems.

The Brinkman report1 was remarkably prescient in its discussion of nonequilibrium physics. Its authors recognized the growing importance of topics such as pattern formation, chaotic behavior, turbulence, and fractal geometries. Understandably, they missed today's emerging interests in friction, fracture, and granular materials and the speculations that some of these spatially extended chaotic phenomena might be exhibiting previously unanticipated collective behaviors. They also could not have predicted the invention of the scanning-probe microscopes and optical tweezers that are only just now beginning to open the world of biological phenomena to first-principles physical investigations.

In the last decade or so—the period since the Brinkman report—important progress has been made in many of these areas. We now understand in much more systematic ways how complex patterns emerge from simple ingredients in hydrodynamic, metallurgical, and chemical systems. Notable progress has been made in sorting out the mechanisms that control pattern formation, for example, in convecting liquid crystals, on the surfaces of vibrating fluids, in chemical reaction-diffusion systems, and in some biological phenomena such as cellular aggregation and membrane morphology. New understanding of spiral waves in active media has found application in the analysis of cardiac arrhythmia. We are beginning to understand how complex systems—for example, those in which fluid flow and chemical reactions are occurring simultaneously—sometimes become intrinsically self-organized, sometimes exhibit large critical fluctuations, sometimes become chaotic, and sometimes do all three of those things at the same time.

Nonequilibrium physics has grown into a major enterprise, one that cannot be described fully in this report. The committee has therefore selected a special set of topics as illustrative examples of the themes and issues to emphasize. The first of these topics is pattern formation and turbulence in fluid flow. The next two are in the areas of processing and performance of structural materials, specifically, microstructural pattern formation in solidification and a group of topics in solid mechanics: friction, fracture, granular materials, and polymers and adhesives. The final section includes some brief remarks about nonequilibrium phenomena in biology and in the quantum domain. Each of these topics, in different ways, illustrates the four themes listed below:

1. Much of the most important progress in recent years has consisted simply of recognizing that fundamental questions remain unanswered in the physics of

1National Research Council [W.F. Brinkman, study chair], Physics Through the 1990s, National Academy Press, Washington, D.C. (1986).

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