Creating materials in which heat propagates along a line: theory and numerical results

Abstract

In this paper the theory is developed for creating a material in which the heat is transmitted along a given line. This gives a possibility to transfer information using heat signals. This seems to be a novel idea. The technical part of the theory is the construction of the potential $q(x)$. This potential describes the heat equation $u_t=\Delta u-q(x)u$ in the limiting medium which is obtained after the small impedance particles are distributed in a given domain. A numerical method is also established to construct numerically such a potential.