Mathematics of Metamaterials

点击翻译按钮获取中文摘要

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.