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.

该项目旨在揭示动力系统中长寿命相干特征出现和消失的精确数学机制。该项目希望在动力系统领域产生新的基础数学，使用创新的算子理论方法仔细梳理相干结构的生命周期。该项目的预期成果包括新的数学理论和计算算法，以预测相干物体的起源和毁灭，这些物体是复杂地球物理流动的关键组织者。这一突破性的数学应该提供显着的好处，如改善预测的涡流传输和天气和气候模式的持久性。