Approximate Cloaking for The Heat Equation via Transformation Optics

TL;DR

This paper demonstrates how transformation optics can be used to achieve approximate cloaking for the heat equation, with the effectiveness depending on the regularization parameter and spatial dimension.

Contribution

It introduces a method for approximate cloaking of heat conduction using transformation optics, quantifying the cloaking effectiveness in different dimensions.

Findings

Degree of visibility is proportional to ε in 3D

Visibility is proportional to 1/|ln ε| in 2D

Provides theoretical bounds for cloaking effectiveness

Abstract

In this paper, we establish approximate cloaking for the heat equation via transformation optics. We show that the degree of visibility is of the order $\epsilon$ in three dimensions and $|\ln\epsilon|^{-1}$ in two dimensions, where $\epsilon$ is the regularization parameter.