Thermal rectification in three-dimensional mass-graded anharmonic oscillator lattices

In this work we study the thermal rectification efficiency, i.e., asymmetric heat flow, of a three-dimensional mass-graded anharmonic lattice of length $N$ and width $W$ by means of nonequilibrium molecular dynamics simulations. The obtained rectification, which is of the same order of magnitude as that of the corresponding one-dimensional lattice, saturates at low values of the aspect ratio $W/N$, consistent with the already known behavior of the corresponding heat fluxes of the homogeneous system under analogous conditions. The maximum rectification is obtained in the temperature range wherein no rectification could be obtained in other one-dimensional systems, as well as in the corresponding one-dimensional instance of the model studied herein.