Size effects on thermal rectification in mass-graded anharmonic lattices
  In this work we study the thermal rectification efficiency of a one-dimensional mass-graded anharmonic oscillator lattice at large system sizes. A modest increase in rectification is observed. When the magnitude of the mass gradient scales with the system size, the aforementioned effect increases substantially. This result can be unmistakeably attributed to an asymmetry in the local temperature profile obtained for the employed parameter values. 
M. Romero-Bastida and Armando Gonzalez-Alarcon
cond-mat.stat-mech