A Variational Perspective on Cloaking by Anomalous Localized Resonance
A Variational Perspective on Cloaking by Anomalous Localized Resonance
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DOI：
10.1007/s00220-014-1943-y
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发表时间：
2012-10
影响因子：
2.4
通讯作者：
R. Kohn;Jianfeng Lu;B. Schweizer;M. Weinstein
中科院分区：
文献类型：
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作者：
R. Kohn;Jianfeng Lu;B. Schweizer;M. Weinstein
关于“反常局域共振隐身”的文献已经有了很多。问题的数学核心涉及散度形式的椭圆型方程在平面上的行为。复值系数具有矩阵-壳-核的几何结构，在矩阵和核中的实部等于1，在壳中的−等于1；人们有兴趣了解当a(X)的虚部减少到零(从而椭圆性丢失)时解的共振行为。这一领域的大多数分析工作都依赖于变量分离，因此仅限于径向几何。我们介绍了一种基于对偶变分原理的新方法，并将其应用于一些非径向算例。在我们的例子中，就像在径向设置中一样，震源的空间位置在决定是否发生共振方面起着至关重要的作用。
A body of literature has developed concerning “cloaking by anomalous localized resonance.” The mathematical heart of the matter involves the behavior of a divergence-form elliptic equation in the plane,. The complex-valued coefficient has a matrix-shell-core geometry, with real part equal to 1 in the matrix and the core, and −1 in the shell; one is interested in understanding the resonant behavior of the solution as the imaginary part ofa(x) decreases to zero (so that ellipticity is lost). Most analytical work in this area has relied on separation of variables, and has therefore been restricted to radial geometries. We introduce a new approach based on a pair of dual variational principles, and apply it to some non-radial examples. In our examples, as in the radial setting, the spatial location of the sourcefplays a crucial role in determining whether or not resonance occurs.