Modern Developments in Asymptotic Ray Theory

渐近射线理论的现代发展

• 批准号: 1982197
• 金额: --
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1982197
• 关键词: Modern; Developments; Asymptotic; Ray; Theory

Ray methods applied to the Helmholtz equation have been developed for, and applied to, high-frequency diffraction and scattering problems with unparalleled success. This theory underpins mathematical optics and is fundamental to the geometrical theory of diffraction. It relies upon describing waves in terms of an amplitude expansion and a single phase term, from which partial differential equations for these quantities follow.The lead investigator has identified a novel class of topical problems for which this approach does not work, and the plan is to modify substantially the existing theory by the inclusion of a generalised sum of terms in the phase, and then to apply the newly generalised theory to these problems.

射线方法应用于亥姆霍兹方程已经开发，并应用于高频衍射和散射问题，取得了空前的成功。这个理论是数学光学的基础，也是衍射几何理论的基础。它依赖于描述波的振幅扩展和一个单一的相位项，从这些量的偏微分方程如下。首席研究员已经确定了一类新的主题问题，这种方法不工作，计划是修改基本上现有的理论，包括一个广义总和的条款，在相位，然后将新的广义理论应用于这些问题。

项目成果

Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries

高频声波、电磁波和弹性波在一类特殊的不规则弯曲边界处的反射和传输

• DOI: 10.1093/imamat/hxz029
• 发表时间: 2019
• 期刊: IMA Journal of Applied Mathematics
• 影响因子: 1.2
• 作者: Radjen A