Dynamical Systems Special Topics: Dynamics of granular materials: jamming, avalanches, disorder, and localization

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A simple analytic theory of the dynamics of sheared granular materials near the jamming transition is needed to guide current experiments, simulations, and applications. Here such a model is developed that:(1) identifies the key parameters that control the intermittent dynamics of sheared granular materials near the jamming transition,(2) provides predictions for the dependence of the slip avalanche statistics on the key parameters, both near and far from the jamming transition, and(3) provides a unified understanding of the interplay between structure and dynamics of granular materials and related systems. Granular materials, such as powders, sand, gravel, and grain, either flow if pushed, similar to fluids, or they jam, with intermittent sudden stops and slips, similar to earthquakes. A simple mathematical tool to quickly predict the behavior of pushed granular materials is being developed that is expected to have wide applications in processes that use molecular liquids, powders, construction materials, and agricultural grains. The tool can be used to predict the results of new experiments, in computer simulations, and in industrial applications, where jamming of granular matter poses a significant operational problem. The results of this research are relevant also to other physical systems, over a wide range of scales, from the deformation of metallic crystals and amorphous materials to the deformation of the earth's crust in earthquakes. The model provides new approaches to nondestructive materials testing and hazard prediction. The project also provides broad interdisciplinary training to a graduate student and an advanced undergraduate student. The students learn modern mathematical modeling tools from physics, materials science and engineering, dynamical systems theory, mathematical physics, and computational science. Collaboration with theorists, experimentalists, engineers, and geophysicists broaden the students? perspectives and increase their versatility in solving new problems.