Reduced Stochastic Dynamics for Spatially Extended Systems

空间扩展系统的简化随机动力学

• 批准号: 0405944
• 负责人: Ilya Timofeyev
• 金额: $ 10.5万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405944&HistoricalAwards=false
• 关键词: Reduced; Stochastic; Dynamics; Spatially; Extended

The investigator and his colleagues study several examples mimicking the behavior of more complex, realistic systems in atmosphere/ocean dynamics. The main focus here is on understanding the importance of various low-dimensional chaotic structures in full dynamics with many degrees of freedom and deriving low-dimensional stochastic models which correctly capture the interaction of the low-dimensional chaos with fast scales. In addition, significance of non-Gaussian small-scale processes is analyzed in the context of the Barotropic Quasi-Geostrophic Equations.An area of great importance for many problems in science and engineering involves derivation of effective equations for a small number of suitable variables capturing the essence of large systems with many unknowns. Important examples include evolution of the coupled atmosphere/ocean systems, folding of large proteins in molecular dynamics, distribution of air-pollution over a long period of time, etc. Effective equations are required first because these systems vastly overwhelm direct numerical computations. In addition, often only a few variables in the problem provide most of the needed information. In the above examples, these essential variables might be the seasonal average temperature in the US, a few angles describing the folding changes in the protein, or the primary direction for the spread of an air-pollutant from its source. The main aim of this work is to further advance the stochastic mode-reduction strategy originally developed for derivation of the effective equations in the atmosphere/ocean dynamics. Several idealized problems are examined in order to develop a systematic approach for more realistic systems and validate the applicability of the method in various settings.

研究人员和他的同事研究了几个例子，模仿大气/海洋动力学中更复杂，更现实的系统的行为。 这里的主要重点是理解各种低维混沌结构在多自由度全动力学中的重要性，并推导出正确捕获低维混沌与快尺度相互作用的低维随机模型。 此外，非高斯小尺度过程的意义分析的正压准地转方程的背景下，在科学和工程中的许多问题的一个非常重要的领域涉及到的有效方程的推导，为少数合适的变量捕捉的本质大系统的许多未知数。 重要的例子包括演变的耦合大气/海洋系统，折叠的大蛋白质分子动力学，分布的空气污染在很长一段时间内，等有效的方程是必需的，因为这些系统大大压倒直接数值计算。此外，问题中通常只有少数变量提供了大部分所需的信息。 在上面的例子中，这些基本变量可能是美国的季节平均温度，描述蛋白质折叠变化的几个角度，或者空气污染物从其源头扩散的主要方向。 这项工作的主要目的是进一步推进的随机模式减少原来开发的大气/海洋动力学的有效方程的推导策略。几个理想化的问题进行检查，以制定一个系统的方法，更现实的系统，并验证该方法在各种设置中的适用性。