  We have developed HiNTS, the {\bf Hi}erarchical {\bf N}anoparticle {\bf
T}ransport {\bf S}imulator, and adapted it to study commensuration effects in
two classes of Nanoparticle (NP) solids: (1) a bilayer NP solid (BNS) with an
energy offset, and (2) a BNS as part of a Field-Effect Transistor (FET). HiNTS
integrates the ab initio characterization of single NPs with the
phonon-assisted tunneling transition model of the NP-NP transitions into a
Kinetic Monte Carlo based simulation of the charge transport in NP solids.
First, we studied a BNS with an inter-layer energy offset $\Delta$, possibly
caused by a fixed electric field. Our results include the following. (1) In the
independent energy-offset model, we observed the emergence of commensuration
effects when scanning the electron filling factor $FF$ across integer values.
These commensuration effects were profound as they reduced the mobility by
several orders of magnitude. We analyzed these commensuration effects in a five
dimensional parameter space, as a function of the on-site charging energy
$E_C$, energy offset $\Delta$, the disorder $D$, the electron filling factor
$FF$, and the temperature $k_{B}T$. We demonstrated the complexity of our model
by showing that at integer filling factors $FF$ commensuration effects are
present in some regions of the parameter space, while they vanish in other
regions, thus defining distinct dynamical phases of the model. We determined
the phase boundaries between these dynamical phases. (2) Using these results as
a foundation, we shifted our focus to the experimentally much-studied NP-FETs.
NP-FETs are also characterized by an inter-layer energy offset $\Delta$, which,
in contrast to our first model, is set by the gate voltage $V_G$ and thereby
related to the electron filling $FF$. We demonstrated the emergence of
commensuration effects and distinct dynamical phases in these NP-FETs.
