  Inspired by some recent molecular dynamics (MD) simulations and experiments
on suspended graphene nanoribbons, we study a simplified model where the atoms
are disposed in a rectangular lattice coupled by nearest neighbor interactions
which are quadratic in the interatomic distance. The system has a mechanical
strain, and the border atoms are coupled to Langevin thermal baths. Atom masses
vary linearly in the longitudinal direction, modeling an isotope or doping
distribution. This asymmetry and tension modify thermal properties. Although
the atomic interaction is quadratic, the potential is anharmonic in the
coordinates. By direct MD simulations and solving Fokker--Planck equations at
low temperatures, we can better understand the role of anharmonicities in
thermal rectification. We observe an increasing thermal current with an
increasing applied mechanical tension. The temperatures and thermal currents
vary along the transverse direction. This effect can be useful to establish
which parts of the system are more sensitive to thermal damage. We also study
thermal rectification as a function of strain and system size.
