  When a contaminant diffuses on the surface of a nanomechanical resonator, the
motions of the two become correlated. Despite being a high-order effect in the
resonator-particle coupling, such correlations affect the system dynamics by
inducing dissipation of the resonator energy. Here, we consider this
diffusion-induced dissipation in the cases of multiple particles adsorbed on
carbon nanotube and graphene resonators. By solving the stochastic equations of
motion, we simulate the ringdown of the resonator, in order to determine the
resonator energy decay rate. We find two different scalings with the number of
adsorbed particles $K$ and particle mass $m$. In the regime where the
adsorbates are inertially trapped at an antinode of vibration, the dissipation
rate $\Gamma$ scales with the total adsorbed mass $\Gamma\propto Km$. In
contrast, in the regime where particles diffuse freely over the resonator, the
dissipation rate scales as the product of the total adsorbed mass and the
individual particle mass: $\Gamma\propto Km^2$.
