We say a region of space is "cloaked" with respect to electromagnetic
measurements if its contents -- and even the existence of the cloak -- are
inaccessible to such measurements. One recent proposal for such cloaking
takes advantage of the coordinate-invariance of Maxwell's equations. As
usually presented, this scheme uses a singular change of variables. That
makes the mathematical analysis subtle, and the practical implementation
difficult. This talk examines the correctness and robustness of the
change-of-variable-based scheme, for scalar waves modelled by Helmholtz's
equation, drawing on joint work with Onofrei, Shen, Vogelius, and
Weinstein. The central idea is to use a less singular change of variables.
The quality of the resulting "approximate cloak" can be assessed by
studying the detectability of a small inclusion in an otherwise uniform
medium. We show that a small inclusion can be made nearly undetectable
(regardless of its contents) by surrounding it with a suitable lossy
layer.
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