Cloaking via change of variables in electric impedance tomography

@article{citeulike:2358235, abstract = {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.}, author = {Kohn, R. V. and Shen, H. and Vogelius, M. S. and Weinstein, M. I. }, citeulike-article-id = {2358235}, doi = {10.1088/0266-5611/24/1/015016}, journal = {Inverse Problems}, keywords = {cloaking, metamaterial}, number = {1}, pages = {015016+}, posted-at = {2008-02-09 17:39:31}, priority = {2}, title = {Cloaking via change of variables in electric impedance tomography}, url = {http://dx.doi.org/10.1088/0266-5611/24/1/015016}, volume = {24}, year = {2008} }

TY - JOUR ID - citeulike:2358235 TI - Cloaking via change of variables in electric impedance tomography JF - Inverse Problems VL - 24 IS - 1 SP - 015016 N2 - 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. KW - cloaking KW - metamaterial AU - Kohn, RV AU - Shen, H AU - Vogelius, MS AU - Weinstein, MI PY - 2008/// UR - http://dx.doi.org/10.1088/0266-5611/24/1/015016 ER -