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Structures, Metamaterials, Scattering, and Inverse Problems

结构、超材料、散射和反演问题

基本信息

批准号：
1814854
负责人：
Graeme Milton
金额：
$ 38.8万
依托单位：
University of Utah
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1814854&HistoricalAwards=false
关键词：
Structures Metamaterials Scattering Inverse Problems

项目摘要

The significance of this project is multifold. It studies the forces that cable networks under tension can support, and this should be important to civil engineering, in particular to bridge or building design. It studies the possible elastic responses of 3-d printed metamaterials, and this could be helpful in designing structure that guide acoustic and elastic waves, for controlling vibrations and potentially for cloaking against sonar. It opens the field of boundary field equalities, that generalizes the notion of conservation laws, and which can be used for benchmarking numerical algorithms for calculating the response of inhomogeneous bodies. It develops a new approach to scattering of electromagnetic and elastic waves off an inclusion, that can help one understand the extent to which an arbitrarily shaped inclusion can scatter the waves. It develops new bounds that can be useful for predicting the electromagnetic response of two-phase composites even if one does not know the detailed microstructure. This should help in the identification of the most energy-absorbing composites and nano-particles. It explores what novel responses can be achieved in metamaterials, through coupled effects of electrical current flow, interaction with magnetic fields, and vibrations. This may lead to new types of magnetic field sensors and to novel devices coupling deformation and magnetic effects. For biomedical, engineering and counterterrorism applications it is vitally important to know what is inside a body from non-invasive testing, and it is better if one can say things with near certainty. The project will provide new methods of obtaining precise lower and upper limits on the volume occupied by an inclusion in a body. This may have applications to determining the size of certain tumors, or voids in a body, or the porosity in an osteoporotic bone. It studies new classes of theoretical inhomogeneous bodies for which there is an exact solution for the field and this may be useful for benchmarking numerical algorithms, and for gaining insight into how fields can be manipulated in inhomogeneous bodies. Finally, it trains two postdocs in interdisciplinary research.The project provides a cross-fertilization of ideas from the four areas of Structures, Metamaterials, Scattering, and Inverse Problems. Some of these ideas, developed in the theory of composites, will be applied for the first time to inverse problems where one seeks to determine what is inside a body from boundary measurements, and to scattering problems where one seeks to understand the range of possible scattering responses as the shape of the scatterer is varied. The work on boundary field equalities, that stems from the theory of exact relations in composites, seeks to explore generalizations of the classic conservation law that a field which is divergence-free inside a body has zero net flux through the surface. For bodies containing certain wide classes of inhomogeneous media these equalities provide exact identities that are satisfied by the Dirichlet to Neumann map, which plays a central role when one seeks to extract information about what is inside a body from boundary measurements. The work on elastic tensors of 3-d printed materials seeks to bring a close to the challenging question of what elastic tensors are possible in mixtures of one given material plus void. The proposal addresses the inverse problem of estimating the size of an inclusion in a body, through boundary measurements in the time (rather than frequency) domain.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.

这个项目的意义是多方面的。它研究张力下的索网可以支撑的力，这对土木工程，特别是桥梁或建筑设计很重要。它研究了3d打印超材料可能的弹性响应，这可能有助于设计引导声波和弹性波的结构，用于控制振动，并可能用于隐身声纳。它打开了领域的边界场等式，概括的概念，守恒定律，并可用于基准数值算法计算的非均匀体的响应。它发展了一种新的方法来散射电磁波和弹性波的夹杂物，可以帮助人们了解的程度，一个任意形状的夹杂物可以散射的波。它开发了新的边界，可以用于预测的电磁响应的两相复合材料，即使不知道详细的微观结构。这应该有助于识别最能吸收能量的复合材料和纳米颗粒。它探讨了通过电流流动、与磁场的相互作用和振动的耦合效应，在超材料中可以实现什么样的新颖响应。这可能会导致新类型的磁场传感器和耦合变形和磁效应的新设备。对于生物医学、工程和反恐应用来说，通过非侵入性测试了解人体内部是什么是至关重要的，如果人们能够近乎肯定地说出来，那就更好了。该项目将提供新的方法，以获得一个夹杂物在一个机构所占的体积的精确下限和上限。这可以应用于确定某些肿瘤的大小，或身体中的空隙，或骨质疏松骨中的孔隙度。它研究了新的理论上的非均匀体，有一个确切的解决方案，该领域，这可能是有用的基准数值算法，并获得洞察力如何领域可以操纵在非均匀体。最后，它培养了两名跨学科研究的博士后。该项目提供了结构，超材料，散射和逆问题四个领域的思想交叉。其中一些想法，在复合材料的理论，将首次应用到逆问题，其中一个试图确定什么是内部的一个机构从边界测量，并散射问题，其中一个试图了解的范围内可能的散射响应的散射体的形状是不同的。边界场等式的工作源于复合材料中的精确关系理论，旨在探索经典守恒定律的推广，即物体内部无发散的场通过表面的净通量为零。对于包含某些广泛类别的非均匀介质的物体，这些等式提供了由狄利克雷到诺依曼映射满足的精确恒等式，当人们试图从边界测量中提取关于物体内部的信息时，狄利克雷到诺依曼映射起着核心作用。关于3D打印材料弹性张量的工作旨在解决一个具有挑战性的问题：在一种给定材料加上空隙的混合物中可能存在哪些弹性张量。该提案解决了逆问题，即通过时间（而不是频率）域中的边界测量来估计物体中夹杂物的大小。该奖项反映了NSF的法定使命，并被认为值得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来支持。