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

数学科学：沉积系统空间模式的细胞建模和动力系统分析

• 批准号: 9316078
• 负责人: Christopher Paola
• 金额: $ 6.85万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-03-01 至 1996-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9316078&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cellular; Modeling; Dynamical

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. ***

9316078各个领域的Paola研究人员表明，在对抗拒常规分析形式的复杂的，空间扩展的系统的研究中，细胞计算（“晶格”）模型可能具有很大的实用性。 在这样的模型中，晶格的细胞根据规则的规则基于管理系统的物理学的抽象相互作用。 这种方法研究了系统的各个部分之间的相互作用 - 导致整个系统行为的间隔 - 并允许评估基础详细物理的哪些方面最重要的是总体动态。 拟议研究的主要目标是开发编织流的细胞计算模型，该模型结合了可移动珠的基本物理。 迄今为止，由于缺乏对模型和实际系统数据之间的比较方法的定量方法，因此通常仅在定性上评估了此类模型。 该项目的第二个主要目标是开发新的数据分析技术基础= d = d动态系统数学的最新进展，这些技术将促进细胞计算方法的定量测试。 我们的方法是处理在空间扩展系统中的下游测量序列，例如动态系统的时间序列。 空间“吸引子”的图表表征了各种几何变量的下游开发以及离散的迭代图，这些迭代图显示了这些变量的价值如何影响下游值，这既量化了空间扩展系统的各个部分之间的相互作用并表征整个系统的行为。 诸如此类的分析应用于自然系统，实验室实验和计算模型的数据，将对现有技术的模型提供更有效的定量测试。 在拟议的项目中，这些测试将应用于上述编织的模型，并使用所有三个系统的实验室和现场示例，将其现有的风体和水下床形模型应用于现有模型。 ***