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

这个项目考察了地球物理学中复杂系统中自组织的一些数学基础。该方法基于对地球物理和环境现象的若干离散唯象模型的性质的研究，这些唯象模型包括：森林火灾的蔓延、地震和地形演变。一个目标是确定这类非线性系统行为的普遍方面，扩大已在排水网络、扩散限制聚集和森林火灾模型研究中看到的普遍性结果。要解决的问题包括行为对元素之间相互作用的表示的依赖性，将未分解的物理过程表示为随机噪声的影响，它们的可预测性，以及是否可以找到连续统类似物。研究人员希望，所取得的了解可能在自然灾害的预测和风险评估方面有实际应用，包括更好的地震预测模型、滑坡风险评估和森林火灾风险评估。

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.