TIME-DISPERSIVE BEHAVIOR AS A FEATURE OF CRITICAL-CONTRAST MEDIA
TIME-DISPERSIVE BEHAVIOR AS A FEATURE OF CRITICAL-CONTRAST MEDIA
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DOI：
10.1137/18m1187167
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发表时间：
2019-01-01
影响因子：
1.9
通讯作者：
Kiselev, Alexander, V
中科院分区：
文献类型：
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作者：
Cherednichenko, Kirill;Ershova, Yulia;Kiselev, Alexander, V
出于对“超材料”一词赋予严格数学意义的需要，我们提出了一种新的方法来均匀化临界对比复合材料。这是基于介质的不同组件（“硬”和“软”）之间的界面上的狄利克雷到诺依曼映射的渐近分析，这导致本征模的渐近近似。这使我们看到，软组分的存在使硬组分表现为一类时间色散介质。通过这个论点的反转，我们还提供了一个配方，从周期性复合材料的规定色散特性的这种介质的建设。
Motivated by the need to attribute a rigorous mathematical meaning to the term "metamaterial," we propose a novel approach to the homogenization of critical-contrast composites. This is based on the asymptotic analysis of the Dirichlet-to-Neumann map on the interface between different components ("stiff" and "soft") of the medium, which leads to an asymptotic approximation of eigenmodes. This allows us to see that the presence of the soft component makes the stiff one behave as a class of time-dispersive media. By an inversion of this argument, we also offer a recipe for the construction of such media with prescribed dispersive properties from periodic composites.