Earthquake events are well-known to prams a variety of empirical scaling laws. Accordingly, renormalization methods offer some hope for understanding why earthquake statistics behave in a similar way over orders of magnitude of energy. We review the progress made in the use of renormalization methods in approaching the earthquake problem. In particular, earthquake events have been modeled by previous investigators as hierarchically organized bundles of fibers with equal load sharing. We consider by computational and analytic means the failure properties of such bundles of fibers, a problem that may be treated exactly by renormalization methods. We show, independent of the specific properties of an individual fiber, that the stress and time thresholds for failure of fiber bundles obey universal, albeit different, staling laws with respect to the size of the bundles. The application of these results to fracture processes in earthquake events and in engineering materials helps to provide insight into some of the observed patterns and scaling-in particular, the apparent weakening of earthquake faults and composite materials with respect to size, and the apparent emergence of relatively well-defined stresses and times when failure is seemingly assured.

The study of intermediate-energy heavy-ion nuclear reactions is reported. This work has two foci: the properties of nuclear matter under abnormal conditions, in this energy domain, predominately low densities and the study of the relevant reaction mechanisms. Nuclear matter properties, such as phase transitions, are reflected in the dynamics of the reactions. The process leads to an understanding of the reaction mechanism themselves and therefore to the response characteristics of finite, perhaps non-equilibrium, strongly interacting systems. The program has the following objectives: to study energy, mass, and angular momentum deposition by studying incomplete fusion reactions; to gain confidence in the understanding of how highly excited systems decompose by studying all emissions from the highly excited systems; to push these kinds of studies into the intermediate energy domain (where intermediate mass fragment emission is not improbable) with excitation function studies; and to learn about the dynamics of the decays using particle-particle correlations. The last effort focuses on simple systems, where definitive statements are possible. These avenues of research share a common theme, large complex fragment production. It is this feature, more than any other, which distinguishes the intermediate energy domain.