Driven flow with exclusion and transport in graphenelike structures

We study driven flow with exclusion in graphenelike structures. 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.