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Mark Lewis
The physics involved in the collisions of hard spheres is quite straightforward. The behaviors of colliding pool balls, for example, can be understood and modeled with only a basic knowledge of mechanics. Our understanding of the dynamics becomes much less clear when the number of particles being considered is increased significantly and even slight complications are added to the natural behaviors of the particles. This is the case in a number of systems including granular flows, planetary rings, and even the early stages of planetary accretion.
Analytic methods often fail when trying to understand such systems, so instead we turn to numerical methods. I have been using numerical methods to understand the collisional dynamics of planetary rings for several years in both serial and parallel codes for systems up to 10 million particles. I have had students involved in advancing this research both for improving methodologies and for exploring systems that can be modeled this way.