need to simulate reactive hydrodynamic flows. Such problems still help drive the development of increasingly powerful computers. However, during the past three decades, simulations have become integrated elements of the toolboxes of experimentalists and theorists in many of the physical and biological sciences.

The increasing importance of modeling and simulation is evidenced for the materials science field by the recent (1992) inauguration of two new journals devoted exclusively to this topic: Computational Materials Science (Elsevier) and Modeling and Simulation in Materials Science and Engineering (Institute of Physics Publishing). Materials data modeling encompasses two quite different areas: materials R&D (both theoretical and experimental) and data handling and application activities (continuum level design calculations, process modeling, service behavior modeling, and compression, extrapolation, and interpolation of data). Other research areas in which computer simulations have become standard are in the design of optics for electromagnetic radiation and of beams of electrons and ions; flow of fluids; folding of protein molecules; interaction of enzyme molecules with their substrates, the species on which they act; melting and freezing, at the atomic level; the motions of individual atoms during reactive collisions of molecules; and collisions of gaseous atoms and molecules with surfaces.

Many simulations require repeated solution of equations of motion of the system by computer. These equations may be simple or complex, but however simple they are, the ability to solve them over and over, many millions of times, as the system they describe evolves, is a consequence of the power of electronic computers. The simulation results may be reduced to only a few summary numbers, which was the usual practice in the early years of computers. Now it is common for the results to include numerical information about entire time histories, information that can be put into tables and graphs.

Perhaps the most dramatic advance in simulations, however, has been the use of graphics, particularly animations. The information in an animation can give insights into a scientific phenomenon that could not be guessed from individual snapshot images or numerical indicators. Time may serve as a surrogate for a spatial dimension, allowing the investigator to visualize the behavior of a function of three independent variables. Animations are useful when an investigator uses a preconception to decide what indicators would be best to compute and it turns out that the situation does not correspond to that preconception. For example, one study examined the high degree of solid-like, cooperative, and collective motion of most, but not all, of the atoms in the supposedly liquid surface layer of a cluster of atoms. Instead of an amorphous swarm of atoms swirling on the surface, the outer, "molten" layer of the cluster showed organized, collective (but loose) vibrations by all but a few of the surface atoms. All the quantitative indicators showing liquid-like character arose from a few atoms displaced from the surface so that they were free to float just outside it, in almost-free fashion. The consequence of seeing the animation was the construction of a theoretical



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