Geometric analysis of nonlinear systems

非线性系统的几何分析

• 批准号: DP200100210
• 负责人: Prof Nalini Joshi
• 金额: $ 29.91万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100210
• 关键词: Geometric; analysis; nonlinear; systems

Modern science derives its power from mathematics. The project aims to capture, identify and describe pivotal, transcendental solutions of nonlinear systems that are universal in science, in the sense that they always arise as mathematical models under certain physical limits. The project expects to produce new mathematical methods to describe such functions by using a newly discovered geometric framework. Expected outcomes include the description of elusive solutions of discrete and higher-dimensional nonlinear systems. This should provide significant benefits, such as new mathematical knowledge, innovative techniques, enhanced scientific capacity in Australia.

现代科学源于数学。该项目旨在捕获，识别和描述非线性系统的关键性，先验解决方案，这些解决方案在科学中是普遍的，从某种意义上说，它们总是在某些物理限制下以数学模型的形式出现。该项目希望通过使用新发现的几何框架来生成新的数学方法来描述此类功能。预期的结果包括对离散和高维非线性系统难以捉摸的解决方案的描述。这应该提供重大的好处，例如新的数学知识，创新技术，增强了澳大利亚的科学能力。