Mathematics of Metamaterials

Milton0707978超透镜实现了比普通透镜更精细的分辨率，并具有一些惊人的特性，例如，如果可偏振偶极子位于透镜的临界距离内，则它们基本上是不可见的。这个项目提高了我们对超透镜和不可见性的理解，特别是对球面超透镜，这不仅是超分辨率的，而且是放大的。它还试图刻画由具有极端性能的组成材料组成的复合材料在准静态极限下表现出的奇异电磁行为，其中时间谐波辐射的波长远远大于微结构。这位研究人员还研究了一种名为“质量材料”的新材料。在它们的微观结构中，有旋转的顶部集合，每个旋转的顶部都位于身体的凹陷中，每个旋转顶部的一侧都有一个质量，允许人们通过适当地摆动身体来增加或减少每个顶部的旋转。这些材料应该能够在微尺度上储存和释放能量。研究人员还探索了新的弹性动力学方程，并研究了具有特殊性质的新微结构，即它们的平均动量不仅取决于它们的总速度，而且还取决于它们是如何变形的，即它们的应变。超材料，即具有普通材料无法实现的性能的复合材料，引起了人们的极大兴趣，并开始革命性地改变我们对材料及其可以展示的性能的理解。由于我们定制物质微结构的能力的进步，例如通过纳米技术，这些材料的更多技术应用现在是可能的。该项目研究如何从高对比度材料构建复合材料，以显示比现有材料更丰富的弹性和电磁性能。在国防、汽车、航空航天、电子以及其他制造和电信行业，对新材料的需求一直不断。当这些新材料的性能与我们已知的任何材料完全不同时，它们的影响可能会最大。该项目可能导致开发出一系列完全不同、具有新特性的新材料。这也将为彭德里在球面超透镜方面的工作提供一个迫切需要的坚实的理论基础，并加深我们对不可见性的理解。

Milton0707978 Superlenses achieve resolution finer than convential lenses,and have some startling properties, such as making polarizabledipoles essentially invisible if they lie within a criticaldistance of the lens. This project improves our understanding ofsuperlenses and invisibility, particularly for sphericalsuperlenses, which not only superresolve but also magnify. Italso seeks to characterize exotic electromagnetic behaviors thatcomposite materials formed from constituent materials withextreme properties can exhibit in the quasistatic limit, wherethe wavelength of the time-harmonic radiation is much larger thanthe microstructure. The investigator also studies a new class ofmaterial named "massnetic materials." These have in theirmicrostructure collections of spinning tops, each situated in acavity in the body, and each weighted on one side by a mass thatallows one to increase or decrease the spin of each top byappropriately oscillating the body. These materials should beable to store and release energy on the microscale. Theinvestigator also explores new equations of elastodynamics, andstudies novel microstructures with the unusual property thattheir average momentum depends not just on their overallvelocity, but also on how they are deformed, i.e. on theirstrain. Metamaterials, i.e. composite materials with propertiesunachievable in ordinary materials, have attracted a great dealof interest and are beginning to revolutionize our understandingof materials and the properties they can exhibit. Moretechnogical applications of these materials are now possible dueto advances in our ability to tailor the microstructure ofsubstances, for instance through nanotechnology. This projectstudies how composites can be constructed from high contrastmaterials to exhibit elastic and electromagnetic properties farricher than existing materials. In the defence, automotive,aerospace, electronics, and other manufacturing andtelecommunication industries there is a constant need for newmaterials. The impact of such new materials is likely to begreatest when their properties are radically different from anymaterial we know. The project could lead to the development ofwhole classes of radically different new materials with novelproperties. Also it should give a much needed firm theoreticalfoundation to Pendry's work on spherical superlenses, and enhanceour understanding of invisibility.