Harmonic analysis of rough oscillations

粗振动的谐波分析

• 批准号: DP160100941
• 负责人: A/Prof Pierre Portal
• 金额: $ 30.56万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-05-25 至 2021-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160100941
• 关键词: Harmonic; analysis; rough; oscillations

This project intends to explore new perspectives in harmonic analysis. Harmonic analysis is a set of mathematical techniques used in many branches of science and engineering to analyse complex signals (functions). It is highly effective in modelling phenomena such as the propagation of electromagnetic waves, but it is currently limited to propagation occurring in a simple-enough medium. An intense international research effort in harmonic analysis is currently under way to lift this limitation. This project is part of that effort, and aims to unite two of its fundamental directions of development: one focusing on the roughness of the medium; and one focusing on the interaction between highly oscillatory aspects of the function and the geometry of the medium.

这个项目旨在探索谐波分析的新视角。谐波分析是一组数学技术，用于科学和工程的许多分支，以分析复杂的信号（函数）。它在模拟电磁波传播等现象方面非常有效，但目前仅限于在足够简单的介质中进行传播。目前，国际上正在进行谐波分析方面的密集研究，以消除这一限制。该项目是这一努力的一部分，旨在统一其两个基本发展方向：一个侧重于介质的粗糙度;另一个侧重于功能的高度振荡方面与介质的几何形状之间的相互作用。