Active thermal cloaking and mimicking.

Maxence Cassier,Trent Degiovanni,Fernando Guevara Vasquez,Sébastien Guenneau

doi:10.1098/rspa.2020.0941

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.

Highlights

The concept of invisibility cloaks was originally introduced in optics and electromagnetics [1,2,3,4] to illustrate a method to manipulate fields using passive anisotropic heterogeneous media deduced from a geometric transform of the governing equations
We proposed a strategy for active cloaking for the time-dependent parabolic heat equation
Similar to previous work for active cloaking for e.g. the Helmholtz or Laplace equation, our results rely on active sources coming from Green identities to reproduce solutions inside or outside a bounded domain

Summary

Introduction

The concept of invisibility cloaks was originally introduced in optics and electromagnetics [1,2,3,4] to illustrate a method to manipulate fields using passive anisotropic heterogeneous media deduced from a geometric transform of the governing equations. We consider a similar problem, but instead of using a passive medium for the cloak, we use specially designed heat sources and sinks distributed on a surface surrounding the object. Given a solution to the heat (or mass or light diffusion) equation in a homogeneous medium and with no sources inside of a domain, it is possible to reproduce it inside the domain with a distribution of sources on the surface of the domain, while giving a zero solution outside We call this the interior reproduction problem, see figure 2a. Apart from the active cloaking strategies for the steady-state heat equation in [7,9], there are passive cloaking methods for the heat equation that use carefully crafted materials to hide objects [5,29,33,34,35].

Integral representation of heat equation solutions

Cloaking

Mimicking

A simple numerical approach to potential theory for the heat equation

Findings

Summary and perspectives