Modern mathematics to unravel the birth of coherence in dynamical systems

现代数学揭示动力系统相干性的诞生

• 批准号: DP210100357
• 负责人: Prof Gary Froyland
• 金额: $ 30.95万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP210100357
• 关键词: Modern; mathematics; unravel; birth; coherence

This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathematical theory and computational algorithms to anticipate the genesis and destruction of coherent objects, which are key organisers of complex geophysical flows. This breakthrough mathematics should provide significant benefits, such as improved prediction of eddy transport and persistence of weather and climate patterns.

该项目旨在揭示动态系统中长寿相似特征的出现和消失的确切数学机制。该项目希望使用创新的操作者理论方法在动态系统领域生成新的基本数学，以仔细嘲笑相干结构的生命周期。该项目的预期结果包括新的数学理论和计算算法，以预测相干对象的起源和破坏，这些对象是复杂地球物理流的关键组织者。这种突破性的数学应该带来重大的好处，例如改善对涡流运输的预测以及天气和气候模式的持久性。