Enhancement of Near Cloaking Using Generalized Polarization Tensors Vanishing Structures. Part I: The Conductivity Problem

Abstract

The aim of this paper is to provide an original method of constructing very effective nearcloaking structures for the conductivity problem. These new structures are such that their first Generalized Polarization Tensors vanish. We show that this in particular significantly enhances the cloaking effect. We then present some numerical examples of Generalized Polarization Tensors vanishing structures.

Invariance properties of generalized polarization tensors and design of shape descriptors in three dimensions

“…We refer to [6] and references therein for these applications. It is worth mentioning that the notion of GPTs has been used not only for imaging but also for invisibility cloaking [7].…”

Reconstruction of inhomogeneous conductivities via the concept of generalized polarization tensors

“…Expansion (2.14) is valid if |x| → ∞ and y ∈ ∂B. The contracted generalized polarization tensors are defined as follows (see [12]): …”

“…Recently the concept of GPTs finds another promising application to cloaking and electromagnetic and acoustic invisibility. It is shown that the near-cloaking effect of [29] can be dramatically improved by using multi-layered structures whose GPTs vanish up to a certain order [12].…”

Novel near-cloaking multicoated structures for screw dislocations

“…Along another seemingly unrelated research line, Ammari et al (2011) constructed very effective near-cloaking multicoated structures for conductivity problem (or mathematically equivalent anti-plane shear problem). The first generalized polarization tensors vanish in their designed near-cloaking structures, and thus these structures are made neutral to remote nonuniform loading of general type.…”