Mathematical Sciences: Cellular Modeling and Dynamical- Systems Analysis of Spatial Patterns in Sedimentary Systems

9316078 Paola Researchers in various fields have shown that cellular computational ('lattice gas') models can be of great utility in the study of complex, spatially extended systems that resist conventional forms of analysis. In such models the cells of a lattice interact according to rules based on abstractions of the physics governing a system. This approach examines the interactions between the parts of a system--interactions that lead to the behavior of the system as a whole--and allows evaluation of what aspects of the underlying detailed physics are most import to the overall dynamics. One main goal of the proposed research is the development of a cellular-computational model of braided streams that incorporates the basic physics of free-surface flow over a movable bead. To date such models have usually been evaluated only qualitatively due to a lack of a quantitative method of comparison between the models and data from real systems. The second main goal of this project is to develop new data-analysis techniques base=d on recent advances in dynamical-systems mathematics that will facilitate quantitative testing of cellular-computational methods. Our approach is to treat downstream series of measurements in spatially extended systems like the time series of dynamical systems. Graphs of spatial 'attractors' that characterize the downstream development of various geometrical variables, and discrete iterative plots that show how the value of these variables influence the values further downstream, both quantify the interactions between the parts of a spatially extended system and characterize the behavior of a system as a whole. Analyses such as these, applied to data from natural systems, laboratory experiments, and computational models, will provide a more effective quantitative test of the models that existing techniques. In the proposed projects such tests will be applied to the braided-stream model mentioned above and to existing models of aeolian and subaqueous bedforms, using data collected form laboratory and field examples of all three systems. ***