The processes that are used to produce industrial materials—casting alloys for jet engines or fabricating microscopically small features of computer chips—are all exercises in what we call “nonequilibrium physics,” the study of systems that are changing their shapes or properties as we exert forces on them, freeze them, or otherwise disturb their states of equilibrium. Predicting and controlling these processes with the precision that will be needed for applications requires fundamental understanding of the nonequilibrium phenomena underlying them and is a challenge for physicists.

For example, snowflakes form by a branching process that is called “dendritic crystal growth.” Research in this area has been driven not only by our natural curiosity about snow-flakes, but also by the need to understand and control metallurgical microstructures. The interior of a grain of a freshly solidified alloy, when viewed under a microscope, often looks like a collection of overly ambitious snowflakes. Each grain is formed by a dendritic mechanism in which a crystal of the primary composition grows out rapidly in a cascade of branches and side branches, leaving solute-rich melt to solidify more slowly in the interstices. The speed at which the dendrites grow and the regularity and spacing of their side branches determine the observed microstructure, which in turn governs many of the properties of the solidified material such as its mechanical strength and its response to heating and deformation. We cannot yet predict microstructures accurately, but much progress has been made in the last decade. Figure 3.1 shows one of the best new theoretical efforts in this direction.

Much of the most important recent progress in nonequilibrium physics has consisted simply of recognizing that fundamental questions remain unanswered in many familiar situations. The recent growth of interest in fracture and friction, for example, has led us to realize that we need to establish first-principles understanding of the difference between brittleness and ductility, especially in noncrystalline materials. We are learning about the dynamics of granular materials, systems that are like liquids in some respects, like solids in others, and unlike either in many of the most important ways. And we are just beginning to learn which questions to ask in a search for understanding the dynamics of fracture at crack tips, failure at interfaces between different solids, or rupture on earthquake faults.


Because of the astonishingly rapid advances in both hardware and software, the small workstations or PCs that sit on almost every scientist's desk these days have the power of machines that we called supercomputers little more than a decade ago. Today's supercomputers can simulate the behavior of hundreds of millions of interacting classical molecules or follow the transitions among comparable numbers of quantum states. This exponential growth in computational power will continue for at least another decade.

Computers play a central role in modern experiments, controlling apparatus, acquiring and storing data, and analyzing data. Theorists also find them essential for solving mathematical problems that once seemed intractable. But the computer is now emerging as much more than just a tool for assisting the work of scientists; it is making a qualitative change in the kinds of research that will be done in the near future. Consider just a few examples.

Starting from little more than the masses and charges of electrons and atomic nuclei, as well as the rules of quantum mechanics, we are approaching the point where we will be able to predict accurately the properties of molecules, of atoms at solid surfaces and interfaces, of defects in solids, and even of larger structures such as the recently discovered fullerenes (see page 21).

In situations that justify neglecting quantum effects, multimillion-molecule simulations are beginning to provide valuable information about complex solid-state phenomena such as fluid flow, fracture, friction, and deformation. The great advantage of such computational investigations is that they can tell us in detail about the behavior of individual molecules. Thus, computer-based studies of this kind have features of both experimental and theoretical research.

FIGURE 3.1 Computer simulation of dendritic growth in the solidification of a nickel-copper alloy. The colors indicate relative concentration of copper, from low (red) to high (blue). The orange and red regions are solid; the green and blue regions are liquid. (Courtesy of the National Institute of Standards and Technology.)

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