New Methods and Analysis for Wave Propagation Problems

波传播问题的新方法和分析

• 批准号: EP/I025995/1
• 负责人: Euan Spence
• 金额: $ 26.34万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI025995%2F1
• 关键词: New; Methods; Analysis; Wave; Propagation

Our understanding of wave phenomena underpins many technologies upon which our society depends, for example, radar, sonar, mobile phones, ultrasound, optical fibres, and crack-detection in structures.Many wave phenomena can be described mathematically by Partial Differential Equations'' (PDEs); and information about the physical processes can be obtained by studying these mathematical models. Mathematicians have a toolkit of techniques to study PDEs and extract useful information. This project seeks both to sharpen'' two tools, which the investigator has played a key role in developing, and to combine them, not only with each other, but also with other cutting-edge techniques from different areas of mathematics. This combination will increase the power of these techniques and allow mathematicians to apply them in new situations, further increasing our knowledge of waves.Some examples of problems this project will investigate are:- The scattering of sound and electromagnetic waves from obstacles with sharp corners and edges. These problems are of fundamental importance to many engineering applications, and hence have been extensively studied for many years. However, the current mathematical tools are still not powerful enough to solve many important practical problems.- The propagation of waves through so-called meta-materials'', artificial materials engineered to produce properties not found in nature, and periodic media'', which have applications in photonic crystals used in optical communication.- The detection of cracks in the surface of materials; this is obviously important for testing the integrity of many engineering structures, but in particular nuclear and chemical reactors.

我们对波浪现象的理解为许多技术所依赖的许多技术，例如雷达，声纳，手机，超声，超声，光纤和结构中的裂纹。可以通过部分微分方程数学地描述许多波浪现象''（pdes）；可以通过研究这些数学模型来获得有关物理过程的信息。数学家拥有研究PDE和提取有用信息的技术工具包。该项目既试图增强”两种工具，研究人员在开发中发挥了关键作用，不仅将它们相互结合，还可以与来自不同数学领域的其他尖端技术相结合。这种组合将增加这些技术的力量，并使数学家能够在新情况下应用它们，进一步增加了我们对波浪的了解。该项目将研究的一些示例是： - 声音和电磁波从尖锐的角落和边缘的障碍物中散射。这些问题对于许多工程应用至关重要，因此已经进行了多年的广泛研究。但是，当前的数学工具仍然不足以解决许多重要的实际问题。-通过所谓的元材料传播波浪的传播，“人工材料”设计为生产自然界中发现的特性和定期介质的'，它们在光子晶体中使用的光子晶体中应用。这对于测试许多工程结构（尤其是核和化学反应器）的完整性显然很重要。