Mathematics of Metamaterials

Milton0707978 超级透镜的分辨率比传统透镜更高，并且具有一些惊人的特性，比如说，如果极化偶极子位于透镜的临界距离内，那么它们基本上是不可见的。 这个项目提高了我们对超透镜和隐形的理解，特别是球形超透镜，它不仅能超分辨，而且能放大。 它还试图表征奇异的电磁行为，复合材料形成的组成材料具有极端的性能可以表现在准静态极限，其中的时间谐波辐射的波长远大于微观结构。 研究人员还研究了一种名为“massnetic材料”的新材料。“这些在他们的微观结构中有旋转陀螺的集合，每个陀螺位于身体的一个空腔中，每个陀螺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陀螺的旋转。 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，并研究了具有不寻常性质的新型微结构，即它们的平均动量不仅取决于它们的总体速度，而且还取决于它们如何变形，即它们的应变。 超材料，即具有普通材料无法实现的特性的复合材料，引起了人们极大的兴趣，并开始彻底改变我们对材料及其特性的理解。 这些材料的更多技术应用现在是可能的，因为我们在调整物质微观结构方面的能力有所提高，例如通过纳米技术。 该项目研究如何用高对比度材料制造复合材料，使其表现出比现有材料更好的弹性和电磁性能。 在国防、汽车、航空航天、电子以及其他制造和电信行业，对新材料的需求不断增加。 当这些新材料的性质与我们所知的任何材料完全不同时，它们的影响可能是最大的。 该项目可能会导致开发具有新颖特性的完全不同的新材料。 它也应该给Pendry的球面超透镜工作提供一个非常需要的坚实的理论基础，并增强我们对隐形的理解。

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.