Collaborative Research: CMG: Cellular Automata, Directed Graphs, and the Modeling of Earthquake and Landforms

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This project examines some of the mathematical foundations of self-organization in complex systems that occur in geophysics. The approach is based on studying the properties of a number of discrete phenomenological models of geophysical and environmental phenomena including: the spread of forest fires, earthquakes, and landform evolution. One goal is to identify the universal aspects of the behavior of such nonlinear systems, extending results on universality already seen in studies drainage networks, diffusion-limited aggregation, and forest fire models. Questions to be addressed include the dependence of behavior on the representation of interactions between elements, the effect of representing unresolved physical processes as random noise, their forecastability, and whether continuum analogues can be found. The investigators hope that the understanding gained may have practical applications in the prediction and risk assessment of natural hazards, including better predictive models of earthquakes, the assessment of land-slide hazards, and the assessment of forest fire hazards.