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; 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.

研究人员及其同事研究了一些模仿大气/海洋动力学中更复杂，现实系统的行为的例子。 这里的主要重点是了解各种自由度的全部动力学中各种低维混沌结构的重要性，并得出了低维的随机模型，这些模型正确地捕获了与快速尺度的低维混乱的相互作用。 此外，在正交的准型地藻方程的背景下，分析了非高斯小规模过程的重要性。对于许多科学和工程中许多问题的重要性领域涉及有效方程的衍生，这些方程涉及少数合适的变量，这些变量捕获了许多未知数的大型系统的本质。 重要的例子包括耦合大气/海洋系统的演变，在分子动力学中折叠大蛋白，长时间的空气污染的分布等。首先需要有效的方程式，因为这些系统极大地压倒了直接的数值计算。此外，问题中通常只有几个变量提供了大多数所需的信息。 在上面的示例中，这些基本变量可能是美国的季节平均温度，一些角度描述了蛋白质的折叠变化，或者是从其来源传播空气污染物的主要方向。 这项工作的主要目的是进一步促进最初用于在大气/海洋动力学中推导有效方程的随机模式减少策略。检查了几个理想化的问题，以开发一种系统的方法，以实现更真实的系统，并验证该方法在各种设置中的适用性。