Thermal rectification and negative differential thermal resistance in lattices with mass gradient

We study thermal properties of one dimensional(1D) harmonic and anharmonic lattices with mass gradient. It is found that the temperature gradient can be built up in the 1D harmonic lattice with mass gradient due to the existence of gradons. The heat flow is asymmetric in the anharmonic lattices with mass gradient. Moreover, in a certain temperature region the {\it negative differential thermal resistance} is observed. Possible applications in constructing thermal rectifier and thermal transistor by using the graded material are discussed.