论文标题
带有复杂波数的2D Helmholtz方程的主动外部覆盖物，并应用于热套
Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking
论文作者
论文摘要
我们设计了二维Helmholtz方程的来源，该方程可以通过取消区域中的入射场来掩盖对象，而没有完全围绕对象隐藏的源。与以前的实际正伴象作品一样，来源也取决于绿色身份。新颖性是我们证明了同样的方法适用于复杂的波数，这使其适用于各种媒体，包括具有分散，损失和增益的媒体。此外，通过通过复杂的论点来推导Graf的添加公式的界限，我们获得了允许量化掩护效果质量的新估计值。我们通过应用它们来实现热量方程式的主动外部覆盖来说明我们的结果。
We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation.
