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We study thermal properties of one dimensional(1D) harmonic and anharmoniclattices with mass gradient. It is found that the temperature gradient can bebuilt up in the 1D harmonic lattice with mass gradient due to the existence ofgradons. The heat flow is asymmetric in the anharmonic lattices with massgradient. Moreover, in a certain temperature region the {\it negativedifferential thermal resistance} is observed. Possible applications inconstructing thermal rectifier and thermal transistor by using the gradedmaterial are discussed.

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