在柏拉图式的关系中，沉默是福
Silence is bliss in a Platonic relationship
摘要：
我们描述了一种有效的主动隐身策略的标量亥姆霍兹方程在三维多极有源源位于顶点的柏拉图固体。在假想的柏拉图固体内部创建一个“无声区”，并且只有入射场保留在无声区和有源源配置外部的限定区域中。这种源的分布确保了隐身策略的实施非常有效。特别地，一旦确定了在单个源位置处所需的多极源幅度，则可以通过简单的后处理来计算其他源幅度，该简单的后处理涉及多极源矢量与旋转矩阵的相乘。问题的一般性质意味着该技术与任何标量波场有关，包括声学和电磁学。
英文摘要：
We describe an effective active cloaking strategy for the scalar Helmholtz equation in three dimensions where multipole active sources are located at the vertices of the Platonic solids. A "silent zone" is created interior to the imaginary Platonic solid and only the incident field remains in a defined region exterior to the silent zone and active source configuration. This distribution of the sources ensures that the implementation of the cloaking strategy is extremely efficient. In particular, once the multipole source amplitudes required at a single source location are determined, the other source amplitudes can be calculated by simple post-processing involving multiplication of the multipole source vector by a rotation matrix. The general nature of the problem means that the technique is relevant to any scalar wave field, including both acoustics and electromagnetism.
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