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.

我们对波动现象的理解是我们社会赖以生存的许多技术的基础，例如雷达、声纳、移动电话、超声波、光纤和结构中的裂纹检测。许多波动现象可以通过偏微分方程进行数学描述”（偏微分方程）；通过研究这些数学模型可以获得有关物理过程的信息。数学家有一套技术工具包来研究偏微分方程并提取有用的信息。该项目旨在强化研究人员在开发过程中发挥关键作用的两种工具，并将它们不仅相互结合，而且与不同数学领域的其他尖端技术结合起来。这种组合将增强这些技术的力量，并使数学家能够将它们应用到新的情况中，进一步增加我们对波的了解。该项目将研究的一些问题示例包括： - 声波和电磁波从带有尖角的障碍物和边缘。这些问题对于许多工程应用至关重要，因此多年来已得到广泛研究。然而，当前的数学工具仍然不够强大，不足以解决许多重要的实际问题。 - 波通过所谓的超材料、人工材料和周期性介质的传播，在光通信中使用的光子晶体中具有应用。- 材料表面裂纹的检测；这对于测试许多工程结构的完整性显然很重要，特别是核反应堆和化学反应堆。