Cloaking via change of variables in electric impedance tomography
Cloaking via change of variables in electric impedance tomography
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DOI：
10.1088/0266-5611/24/1/015016
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发表时间：
2008-02-01
期刊：
影响因子：
2.1
通讯作者：
Weinstein, M. I.
中科院分区：
文献类型：
--
作者：
Kohn, R. V.;Shen, H.;Weinstein, M. I.
Pendry等人最近的一篇论文(2006 Science 312 1780-2)利用麦克斯韦方程的坐标不变性来展示如何将一个空间区域‘隐身’--换句话说，通过用合适的(各向异性和非均匀的)介质屏蔽层包围该区域，使其无法被电磁传感所访问。从本质上讲，格林利夫等人早在几年前(2003年Math.莱特资源。10685-93,2003 Physiol。米斯。24413-9)在与电阻抗断层成像密切相关的环境中。这些论文虽然很出色，但有两个缺点：(A)他们认为的斗篷相当独特；(B)GreenLeft、Lassas和Uhlmann的分析不适用于n=2维的空间。本论文提供了一种新的方法，在电阻抗断层成像的背景下弥补了这些缺点。特别地，我们展示了如何利用变量的非奇异变换来获得正则的近斗篷，并证明了基于变量变换的方案在任意维n>；=2上都能实现完美的斗篷。
A recent paper by Pendry et al ( 2006 Science 312 1780 - 2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked' - in other words, made inaccessible to electromagnetic sensing by surrounding it with a suitable ( anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Greenleaf et al ( 2003 Math. Res. Lett. 10 685 - 93, 2003 Physiol. Meas. 24 413 - 9) in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: ( a) the cloaks they consider are rather singular; and ( b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near- cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n >= 2.