Electromagnetic Signatures of Inhomogeneities: Visibility vs. Invisibility

不均匀性的电磁特征：可见性与不可见性

基本信息

批准号：
2205912
负责人：
Michael Vogelius
金额：
$ 30万
依托单位：
Rutgers University New Brunswick
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-01 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2205912&HistoricalAwards=false
关键词：
Electromagnetic Signatures Inhomogeneities Visibility vs.

项目摘要

This mathematics research project aims to improve understanding of the relation between the regularity, the geometry, and the material contents of an inhomogeneity and its visibility/invisibility properties when probed by electromagnetic waves. The investigator plans to develop tools to enhance image resolution and to provide analysis that determines which geometric features are more visible or less visible. It is anticipated that the work will have direct implications for electromagnetic imaging techniques, whether they concern radar detection of unknown objects, nondestructive testing of material components, or biomedical imaging of live organs. The same tools and analysis will also be brought to bear on electromagnetic cloaking. The project will examine to what extent one may create approximate cloaks that work at broad bands of frequencies and at the same time use materials that are physically realistic. This will provide a better understanding of the limitations of passive cloaking devices and their physical realizability. The investigator will mentor a postdoctoral researcher as an integral part of the research. The research is intended to elucidate the relation between the regularity, the geometry, and the material contents of an inhomogeneity and its visibility/invisibility properties. Such understanding can be used to better detect inhomogeneities or hide them. The project also aims to develop novel asymptotic formulas for the effect of a change in boundary conditions on small boundary sets, a topic of importance for optimal design. The project investigates four sub-topics: (1) study of regularity of (the boundary of) inhomogeneities that exhibit non-scattering wave numbers, (2) study of geometry of (the boundary of) inhomogeneities that exhibit in finitely many non-scattering wave numbers, (3) comparison of recent results about the infeasibility of perfect cloaking and earlier results about the feasibility of approximate cloaking, and (4) development of uniformly valid asymptotic formulas for the field effects of "small" internal inhomogeneities and "small" boundary (condition) inhomogeneities. The mathematical techniques will include sharp estimates of the effects of small boundary condition inhomogeneities of extreme contrast and hodograph transform techniques with associated elliptic PDE estimates applied to examine the regularity properties of non-scattering inhomogeneities. To develop the relevant measure of the smallness of boundary condition inhomogeneities of extreme contrast, the investigator will introduce and examine various novel notions of capacity.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.

该数学研究项目旨在提高对规律性，几何形状和不均匀性的材料内容之间的关系及其可见性/隐形特性之间的关系。研究人员计划开发工具来增强图像分辨率，并提供分析，以确定哪些几何特征更可见或可见。可以预料，这项工作将直接对电磁成像技术产生影响，无论它们是否涉及对未知物体的雷达检测，材料成分的无损测试或活器官的生物医学成像。相同的工具和分析也将在电磁套上带来。该项目将检查一个可能在多大程度上创建近似斗篷，这些斗篷在广泛的频率频段中起作用，同时使用物理上现实的材料。这将更好地理解被动掩盖设备的局限性及其物理可靠性。研究人员将指导博士后研究人员作为研究的组成部分。该研究旨在阐明规律性，几何形状和不均匀性的材料内容及其可见性/隐形特性之间的关系。这种理解可用于更好地检测不均匀性或隐藏它们。该项目还旨在开发新型的渐近公式，以实现边界条件变化对小边界集的影响，这是最佳设计的重要性。该项目研究了四个子主题：（1）研究表现出非散波波数的不均匀性的（边界）的规律性，（（2）研究（2）对（）不均匀性的（边界）的几何形状有限地表现出许多非分散性波数，（3）与最新的杂物性和杂物性结果相比（3）相比，该结果的结合性和杂物性的差异为4，并且（4）杂乱无章的结果（4）五（4） “小”内部不均匀性和“小”边界（条件）不均匀性的渐近公式。数学技术将包括对极端对比度和Hodograph Transform技术的小边界条件不均匀性的影响的尖锐估计，并应用了相关的椭圆PDE估计，用于检查非散散制不均匀性的规律性特性。为了制定极端对比的边界条件不均匀性不均匀性的相关度量，研究人员将介绍和检查各种新颖的能力概念。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的评估来通过评估来支持的。