Mathematical Sciences: Interacting Particle Systems and Random Cellular Automata

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Professors Bramson and Griffeath propose to further the rigorous theory of various random and deterministic complex systems in the area of interacting particle systems and random cellular automata. These include systems of annihilating random walks and billiards, random and deterministic growth models, and random and deterministic interface dynamics. The methodology for studying these processes often combines traditional rigorous mathematical analysis with interactive computer visualization. Professors Bramson and Griffeath study random processes known as interacting particle systems and random cellular automata. These are "toy universe" models that evolve over time, e.g. on a computer graphics display, offering insights into the behavior of complex dynamics from many areas of applied science. The investigators have two main objectives: to understand the kinds of aggregate behavior that such dynamics manifest, and to explain how these behaviors arise by using the traditional analytical techniques, theorems and proofs of mathematics. The phenomena they study include such fundamental physical processes as contagion, clustering, turbulence, and nucleation.