Perfect cloaking of ellipsoidal regions
Perfect cloaking of ellipsoidal regions
复制标题
椭圆体区域的完美隐形
DOI：
10.1090/s0033-569x-2014-01348-2
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发表时间：
2014
影响因子：
0.8
通讯作者：
G. Dassios
中科院分区：
文献类型：
--
作者：
G. Dassios
.大多数现有的隐形装置的显式形式涉及表现出以下行为的球形区域。如果隐形区域来自于炸毁一个点，我们就实现了完美的隐形，但电导率张量变得奇异，因此很难实现。非奇异的电导率张量可以通过炸毁一个小球来实现，但这样的隐身并不完美，因为内场由初始小球半径的平方控制。这种行为反映了球面系统的高度聚焦效应，其中当半径减小到零时，球面的2-D流形退化到其中心的0-D流形。在目前的工作中，我们展示了一个椭圆形的隐形区域，它实现了完美的内部隐形，同时保持了电导率张量的规律性。这是可能的，因为共焦椭球体系统在椭球体塌缩到其焦椭圆时不表现出任何维数损失。这是另一个高度对称性要付出高昂代价的例子。此外，从实用的角度来看，对于三维物体来说，最“经济”的隐身结构是由具有三个自由度的椭球体提供的，因此可以最好地适应任何合理的几何物体。长球形或扁球形、近似圆盘形、近似针状以及球形的斗篷都是椭球简并的情况。
. Most of the existing explicit forms of cloaking devices concern spherical regions which exhibit the following behavior. If the cloaking region comes from blowing up a point we achieve perfect cloaking, but the conductivity tensor becomes singular and therefore hard to realize. A nonsingular conductivity tensor can be achieved by blowing up a small sphere, but then the cloaking is not perfect, since the interior field is controlled by the square of the radius of the initial small sphere. This behavior reflects the highly focusing effect of the spherical system where the 2-D manifold of a sphere degenerates to the 0-D manifold of its center as the radius diminishes to zero. In the present work, we demonstrate a cloaking region in the shape of an ellipsoid which achieves perfect interior cloaking and at the same time preserves the regularity of the conductivity tensor. This is possible since the confocal ellipsoidal system does not exhibit any loss of dimensionality as the ellipsoid collapses down to its focal ellipse. This is another example where high symmetry has a high price to pay. Furthermore, from the practical point of view, the most “economical” cloaking structure, for three dimensional objects, is provided by the ellipsoid which has three degrees of freedom and therefore can best fit any reasonable geometrical object. Cloaks in the shape of a prolate or an oblate spheroid, an almost disk, an almost needle, as well as a sphere are all cases of ellipsoidal degeneracies.
DOI：
10.1103/physreve.83.016603
发表时间：
2009-12
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
A. Greenleaf;Y. Kurylev;M. Lassas;G. Uhlmann
通讯作者：
A. Greenleaf;Y. Kurylev;M. Lassas;G. Uhlmann