CAREER: Efficient Ray-Based Methods for Modeling Wave Propagation

职业：基于射线的高效波传播建模方法

• 批准号: 0449708
• 负责人: Miguel Alonso
• 金额: --
• 依托单位: University of Rochester
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-01-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0449708&HistoricalAwards=false
• 关键词: CAREER; Efficient; Ray; Based; Methods

Wave phenomena are central to physics and engineering. Modeling the propagation of waves, however, can be an analytical or computational challenge when the system, medium, or potential in which they propagate is complex. In these cases, the ray model is often used to obtain approximate solutions. For quantum mechanical wave functions, the "rays" correspond to classical particle trajectories. When ray information is used properly, it can give a very accurate description of wave propagation phenomena. While several ray-based methods for modeling the propagation of waves have been proposed, they often have problems and do not incorporate measures of their own accuracy The scientific goals of the work proposed here are to achieve a profound understanding of the validity of the ray model within wave theory, and to generate all-purpose ray-based methods that describe the propagation of waves in complex media with unprecedented accuracy and computational efficiency. This work will rely on two different and complementary frameworks. The first one, particularly suited for problems of wave propagation through inhomogeneous media for the case of small wavelengths, is based on assigning flexible, interconnected field contributions to the rays, such that their sum gives accurate field estimates that are asymptotically independent of the contributions' width. In preliminary studies, this framework has been shown to be free of the problems that plague other techniques, and to give estimates of great accuracy. Furthermore, a simple measure of the estimates' error is accessible. So far, this formalism has been applied only to test cases involving propagation of scalar waves in two-dimensional inhomogeneous media. In this project, the framework will be extended to describe realistic situations involving three (and higher) dimensional fields in complicated media presenting, for example, absorption, gain, and anisotropies. The application of the method to the solution of differential equations not related to wave phenomena will also be explored. The second framework relates to wave propagation in piecewise homogeneous media, and is particularly suited to the study of partially coherent fields. It is based on representations of wave fields that behave exactly as ray weights, obeying the free radiative transfer equation. These representations can reduce significantly the computation times needed for estimating the intensity, flux, or polarization of partially coherent fields in regions away from their sources. Analogous representations can be defined to describe waves in anisotropic, optically active, absorptive or gain media. These representations can also be used in the description of systems involving refraction and reflection at interfaces and of propagation through scattering media, although this might require some assumptions about the coherence properties of the field. The understanding of such assumptions will give insight into the applicability of the ray-based radiative transfer model. The principal investigator and graduate students will participate in technical conferences organized by minority societies, as well as in outreach events for the promotion of science to the general public, particularly to underrepresented groups. Collaboration with national and foreign researchers in several different areas will be instrumental in the achievement of the goals of this project. These links will be strengthened not only through joint projects but also through participation in the organization of crossdisciplinary workshops and conferences.

波动现象是物理学和工程学的核心问题。然而，当波在其中传播的系统、介质或势很复杂时，对波的传播进行建模可能是一个分析或计算挑战。在这些情况下，通常使用射线模型来获得近似解。对于量子力学波函数，“射线”对应于经典的粒子轨迹。当射线信息被正确利用时，它可以非常准确地描述波的传播现象。虽然已经提出了几种基于射线的方法来模拟波的传播，但它们经常存在问题，并且没有包含它们自己的精度测量。本文提出的工作的科学目标是在波动理论中深刻地理解射线模型的有效性，并产生以前所未有的精度和计算效率描述复杂介质中波的通用的基于射线的方法。这项工作将依赖于两个不同和互补的框架。第一种方法特别适用于小波长情况下波在非均匀介质中的传播问题，它的基础是给射线分配灵活的、相互关联的场贡献，这样它们的总和就给出了与贡献宽度渐近无关的精确场估计。在初步研究中，这个框架被证明没有困扰其他技术的问题，并给出了非常准确的估计。此外，估计误差的一个简单测量是可以获得的。到目前为止，这种形式只适用于标量波在二维非均匀介质中传播的测试情况。在这个项目中，框架将被扩展到描述涉及复杂介质中的三维(和更高)维场的现实情况，例如，吸收、增益和各向异性。文中还将探讨该方法在求解与波动现象无关的微分方程组中的应用。第二个框架涉及波在分段均匀介质中的传播，特别适用于部分相干场的研究。它基于波场的表示，波场的行为与射线权重完全相同，遵守自由辐射传输方程。这些表示法可以显著减少估计远离其源区域的部分相干场的强度、通量或极化所需的计算时间。可以定义类似的表示法来描述各向异性、光学活性、吸收或增益介质中的波。这些表示也可用于描述在界面处涉及折射和反射的系统以及通过散射介质的传播，尽管这可能需要对场的相干属性进行一些假设。对这些假设的理解将使我们深入了解基于射线的辐射传输模型的适用性。首席调查员和研究生将参加由少数群体组织的技术会议，以及向公众，特别是代表人数不足的群体宣传科学的外联活动。与国内和外国研究人员在几个不同领域的合作将有助于实现该项目的目标。这些联系不仅将通过联合项目得到加强，而且还将通过参与组织跨学科讲习班和会议得到加强。