Mathematical Analysis and its Applications

数学分析及其应用

• 批准号: 1000230412-2014
• 负责人: Craig, Walter
• 金额: $ 14.57万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=648249
• 关键词: Mathematical; Analysis; its; Applications

Dr. Craig's research involves mathematical studies of the solutions of partial differential equations that describe wave evolution in physical phenomena, including ocean waves, fluid flows, quantum mechanics, and large scale features of space-time, covering a large spectrum of scales. His research program in this proposal includes problems of wave propagation and ocean dynamics, and techniques of Hamiltonian mechanics and their applications to vortex dynamics and other nonlinear wave propagation problems. He also will pursue collaborations with other physical scientists on a variety of problems involving wave phenomena. It is the nature of mathematical descriptions to possess properties of universality, which explains the effectiveness of descriptions in this large variety of situations and scales. Dr. Craig's research is theoretical, involving mathematical ideas and concepts. However these discoveries do lead to progress in other disciplines, where advances can lead to more efficient numerical simulations or to a conceptual understanding of experiments.

克雷格博士的研究涉及对偏微分方程解的数学研究，这些偏微分方程解描述了物理现象中的波动演变，包括海浪、流体流动、量子力学和覆盖大尺度范围的时空的大尺度特征。他的研究计划包括波传播和海洋动力学问题，以及哈密顿力学技术及其在涡旋动力学和其他非线性波传播问题中的应用。他还将在涉及波动现象的各种问题上寻求与其他物理学家的合作。数学描述的本质是具有普遍性的性质，这解释了描述在如此多的情况和规模中的有效性。克雷格博士的研究是理论性的，涉及到数学思想和概念。然而，这些发现确实导致了其他学科的进步，在这些学科中，进步可以导致更有效的数值模拟或对实验的概念性理解。