  The totally asymmetric simple exclusion process (TASEP), a well-known model
in its strictly one-dimensional (chain) version, is generalized to cylinder
(nanotube) and ribbon (nanoribbon) geometries. A mean-field theoretical
description is given for very narrow ribbons ("necklaces"), and nanotubes. For
specific configurations of bond transmissivity rates, and for a variety of
boundary conditions, theory predicts equivalent steady state behavior between
(sublattices on) these structures and chains. This is verified by numerical
simulations, to excellent accuracy, by evaluating steady-state currents. We
also numerically treat ribbons of general width. We examine the adequacy of
this model to the description of electronic transport in carbon nanotubes and
nanoribbons, or specifically-designed quantum dot arrays.
