  In this work we perform a systematic analysis of various structural
parameters that have influence on the thermal rectification effect, i.e.
asymmetrical heat flow, and the negative differential thermal resistance --
reduction of the heat flux as the applied thermal bias is increased -- present
in a one-dimensional, segmented mass-graded system consisting of a coupled
nearest-neighbor harmonic oscillator lattice (ballistic spacer) and two
diffusive leads (modeled by a substrate potential) attached to the lattice at
both boundaries. At variance with previous works, we consider the size of the
spacer as smaller than that of the leads. Also considered is the case where the
leads are connected along the whole length of the oscillator lattice; that is,
in the absence of the ballistic spacer. Upon variation of the system's
parameters it was determined that the performance of the device, as quantified
by the spectral properties, is largely enhanced in the absence of the ballistic
spacer for the small system-size limit herein considered.
