Active thermal cloaking and mimicking

Abstract

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.

Acoustic passive cloaking using thin outer resonators

“…One of such solutions is evident and is given by Y 0 = 1. Another solution, which is linearly independent with Y 0 , is the unique function satisfying (13) and which has the representation…”

“…(20)). Therefore our approach somehow has some connections with works on active cloaking [45,66,67,60,61,15,13].…”

“…Actually we do not use particular material but instead play with the geometry of the waveguide. Let us mention also that we do not add active sources in the system as people do in active cloaking [45,66,67,60,61,15,13]. No, what we realize is passive cloaking at infinity by perturbing the shape of the waveguide.…”

Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking

“…)) and satisfy also (7). This growth condition allows to make sense of the Fourier-Laplace transform for solutions that may grow exponentially in time 2 , as is the case of active media 3 .…”

“…Since we focus on the Laplacian, we use the H 1 norm on any bounded open set of interest (α, p, C could depend on the choice of the set). To summarize, in our situation we may assume that u satisfies the growth condition (7)…”