Statistical Modeling and Predictability of Nonlinear Dispersive Waves

非线性色散波的统计建模和可预测性

• 批准号: 0206679
• 负责人: David Cai
• 金额: $ 15.3万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0206679&HistoricalAwards=false
• 关键词: Statistical; Modeling; Predictability; Nonlinear; Dispersive

NSF Award Abstract - DMS-0206679Mathematical Sciences: Statistical modeling and predictability of nonlinear dispersive wavesAbstract0206679 CaiThe central theme of this research is the statistical predictability and the development of effective dynamics for spatially extended, multi-scale nonlinear systems in general, and nonlinear dispersive waves in particular. Modeling complex behavior exhibited by multi-scale nonlinear dynamics often entails an effective description of large scale, coarse-grained dynamics. Their resolution requires a precise mathematical characterization of all spatial and temporal excitations present in systems. The issue of quantification of statistical properties of long-time, large-scale dynamics of spatiotemporal chaos will be addressed in a near-integrable setting and in a system in which the separation of scales, as well as instability, can be precisely tuned and controlled. Once a good statistical characterization is obtained, it can provide not only guidance in modeling coarse-grained dynamics but also statistical calibrations of these effective models against the original full dynamics. With these statistical insights, the research further focuses on the study of coarse-grained dynamics and invariant measures for two possible situations --- namely, dynamics with and without separation of scales. The projects also address important aspects of dispersive wave turbulence: clarification of the derivation of kinetic equations and their validation; and detailed characterization of resonance conditions, flux dynamics, and spatially localized, coherent structures.A multitude of spatiotemporal scales may arise in modeling problems in modern science, ranging from molecular dynamics simulation of protein folding to short term climate prediction for coupled atmosphere-ocean dynamics --- the study of which has great impact on our daily world. This project investigates mathematical methods that can be used to understand and predict the complicated behavior of systems of this type.

NSF奖摘要- DMS-0206679数学科学：非线性色散波的统计建模和可预测性摘要0206679蔡本研究的中心主题是统计可预测性和空间扩展的有效动力学的发展，一般的多尺度非线性系统，特别是非线性色散波。对多尺度非线性动力学所表现出的复杂行为进行建模通常需要对大尺度、粗粒度的动力学进行有效的描述。它们的分辨率需要对系统中存在的所有空间和时间激励进行精确的数学表征。将在一个近可积的设置和在一个系统中，尺度的分离，以及不稳定性，可以精确地调整和控制的统计特性的量化的时空混沌的长时间，大规模的动态的问题。一旦获得良好的统计特性，它不仅可以提供指导，在建模粗粒度的动态，但也对原始的完整动态这些有效的模型的统计校准。有了这些统计的见解，研究进一步集中在两种可能的情况下-即，动态和不分离的尺度的粗粒度的动态和不变的措施的研究。这些项目还涉及色散波湍流的重要方面：澄清动力学方程的推导及其验证;以及共振条件、通量动力学和空间局部化的相干结构的详细表征。在现代科学中的建模问题中可能出现大量的时空尺度，从蛋白质折叠的分子动力学模拟到耦合大气-海洋动力学的短期气候预测-对它的研究对我们的日常生活产生了很大的影响。该项目研究可用于理解和预测此类系统复杂行为的数学方法。