Metamaterials and Inverse Problems

超材料和反问题

• 批准号: 1211359
• 负责人: Graeme Milton
• 金额: $ 86.18万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2018-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211359&HistoricalAwards=false
• 关键词: Metamaterials; Inverse; Problems

The research supported by this award will explore the range of electromagnetic properties that composite materials formed from constituent materials with extreme properties can exhibit, at a single frequency, and over a broad range of frequencies. Any interesting behavior that the exotic microstructures, introduced for the first time here, are found to exhibit should motivate the search for practical microstructures exhibiting similar interesting effects. The project also addresses the practically important problem of placing rigorous upper and lower limits (bounds) on the volume of an inclusion in a body using a small number of measurements of the electromagnetic or elastic fields at the surface of the body, focusing on the electromagnetic case in the quasistatic regime where the wavelength of the time harmonic fields is much larger than the microstructure and the moduli and fields are complex. Additionally, the project introduces a new approach for estimating the volume fractions of the phases in a two-phase composite, from measurements of the effective bulk modulus, and bulk and shear moduli of the phases at a set of real frequencies in the quasistatic regime. Finally the research project seeks to find corrections to the effective moduli of composites due to the imperfectness of the interfaces between phases, in the case where the imperfection is not too great. The formulae should facilitate the calculation of effective moduli with imperfect interfaces given numerical solutions for perfect interfaces.Metamaterials are man-made composite materials with properties that are unachievable in ordinary materials. A better understanding of the macroscopic response of such metamaterials has widespread technological importance. There is a constant need for new materials in the defense, automotive, aerospace, electronics and other manufacturing and telecommunication industries. The impact of such new materials is likely to be greatest when their properties are radically different from any material we know. This project will help shape a picture outlining what electromagnetic responses of materials are possible. In a second direction, for biomedical, engineering and counterterrorism applications it is vitally important to determine what is inside a body using non-invasive testing, and it is better if one can say things with near certainty. The project will give precise lower and upper limits on the volume occupied by an inclusion in a body, or by one phase in a two-phase composite. This may have future applications to determining the size of cancer tumors, or of voids in a body, or the porosity in an osteoporotic bone. In a third direction, new mathematical approximations for physical effects of imperfections at the interface between two different materials will be developed, which are expected to be of use in the practical design of new composite materials. The award will help train a postdoctoral associate and a graduate student in an interdisciplinary research area.

该奖项支持的研究将探索由具有极端特性的组成材料形成的复合材料在单一频率和广泛频率范围内可以表现出的电磁特性。任何有趣的行为，奇异的微观结构，介绍了第一次在这里，被发现表现出应激励实际的微观结构表现出类似的有趣的效果的搜索。该项目还解决了实际上重要的问题，严格的上限和下限（边界）的体积上的夹杂物在一个身体使用少量的测量电磁或弹性场在身体的表面，集中在准静态制度的时间谐波场的波长远大于微观结构和模量和字段是复杂的电磁情况。此外，该项目介绍了一种新的方法来估计两相复合材料中各相的体积分数，从测量的有效体积模量，体积和剪切模量的阶段在一组真实的频率在准静态政权。最后，研究项目旨在寻找修正的有效模量的复合材料，由于各相之间的界面的不规则性，在不完美的情况下，是不是太大。这些公式可以方便地计算非理想界面的有效模量，并给出理想界面的数值解。异向介质是一种人造复合材料，具有普通材料无法达到的特性。更好地理解这种超材料的宏观响应具有广泛的技术重要性。 国防、汽车、航空航天、电子和其他制造业和电信行业对新材料的需求不断增加。当这些新材料的性质与我们已知的任何材料都截然不同时，它们的影响可能是最大的。这个项目将有助于形成一个概述材料的电磁响应是可能的图片。在第二个方向上，对于生物医学，工程和反恐应用，使用非侵入性测试来确定体内的东西是至关重要的，如果人们可以近乎肯定地说，那就更好了。该项目将给出物体中夹杂物或两相复合物中一相所占体积的精确下限和上限。这可能有未来的应用程序，以确定癌症肿瘤的大小，或在一个机构的空隙，或在骨质疏松症的骨孔隙度。在第三个方向，将开发新的数学近似的两种不同的材料之间的界面处的缺陷的物理效应，这是预期将在新的复合材料的实际设计中使用。该奖项将帮助培养博士后助理和研究生在跨学科研究领域。