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Structural Spectra and Applications to Heterogeneous Media

结构谱及其在异质介质中的应用

基本信息

批准号：
1813698
负责人：
Robert Lipton
金额：
$ 30.55万
依托单位：
Louisiana State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-15 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1813698&HistoricalAwards=false
关键词：
Structural Spectra Applications Heterogeneous Media

项目摘要

Advancements in technology benefit from improvements in understanding heterogeneous materials and their ability to control electromagnetic, elastic, and acoustic phenomena. In this project the investigator and his collaborators develop three research areas that support these improvements by introducing and applying novel spectral problems associated with the geometry of material heterogeneity. In the first set of projects the theory of periodic and quasi periodic electrostatic spectra is developed for structured geometries enabling control of wave propagation in photonic, phononic, and metamaterial crystals. This theory will be applied to the systematic design of pass bands and band gaps for devices used in communication and energy transmission. In the second set of projects a novel spectral theory is developed for restriction operators acting on electromagnetic fields inside heterogeneous materials and applied to provide new efficient approaches to the fast numerical solution of multiscale problems for dielectric and magnetic media. A final research project develops a spectral formulation for energy concentration in heterogeneous media and applies it to identify the worst case loads for structures made from composite and polycrystalline media. This will give us a better understanding of why metallic and composite joints fail in infrastructure and aviation. These research projects are in line with the research interests of the the Materials and Manufacturing Directorate at Wright Patterson Air Force Base and a continuation of interaction between the PI and the labs initiated in the previous NSF award. It is anticipated that the graduate student supported by this award will benefit from the interaction with scientists at the Materials and Manufacturing Directorate at Wright Patterson Air Force Base. Earlier work on the theory of band gaps addresses the asymptotic theory of band gaps at infinite contrast. In this project the investigator will exploit new structural spectra associated with inclusion geometry and lattice parameters to develop new techniques for complex operator valued functions which deliver explicit formulas for band gaps at finite contrast. The approach proposed here is distinct from earlier ones and will provide new explicit formulas for the size of band gaps and pass bands given in terms of contrast, shape and configuration of scatters, and lattice parameters. In a second thrust of the project, the investigator and his collaborators will develop new spectral methods related to the restriction operator for the vector wave equation to deliver new and faster methods for the numerical solution of multiscale problems of electromagnetic wave propagation in heterogeneous media. A novel spectral formulation for energy concentration will be developed and applied to identify worst case loads for structures made from composite and polycrystalline media.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

技术的进步得益于对非均质材料及其控制电磁、弹性和声学现象的能力的改进。在这个项目中，研究者和他的合作者开发了三个研究领域，通过引入和应用与材料非均匀性几何相关的新光谱问题来支持这些改进。在第一组项目中，周期和准周期静电谱理论被发展为结构几何，使控制波在光子、声子和超材料晶体中的传播。该理论将应用于通信和能量传输设备的通带和带隙的系统设计。在第二组项目中，开发了一种新的谱理论，用于约束算子作用于非均质材料内部的电磁场，并将其应用于介质和磁性介质多尺度问题的快速数值求解中。最后的研究项目开发了一种异质介质中能量集中的光谱公式，并将其应用于确定由复合材料和多晶介质制成的结构的最坏情况载荷。这将使我们更好地理解金属和复合材料接头在基础设施和航空中失败的原因。这些研究项目符合赖特帕特森空军基地材料和制造理事会的研究兴趣，也是PI与之前NSF奖发起的实验室之间互动的延续。预计获得该奖项的研究生将受益于与赖特帕特森空军基地材料和制造理事会的科学家的互动。早先关于带隙理论的研究解决了无限反差下带隙的渐近理论。在这个项目中，研究者将利用与包体几何和晶格参数相关的新结构光谱来开发复杂算子值函数的新技术，这些函数可以提供有限对比度下带隙的明确公式。本文提出的方法不同于先前的方法，并将根据对比度、散射体的形状和配置以及晶格参数，为带隙和通带的大小提供新的显式公式。在该项目的第二个重点，研究者和他的合作者将开发与矢量波动方程的限制算子相关的新的频谱方法，为非均匀介质中电磁波传播的多尺度问题的数值解决提供新的和更快的方法。将开发一种新的能量浓度谱公式，并将其应用于确定由复合材料和多晶介质制成的结构的最坏情况载荷。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。