  We consider the one-dimensional totally asymmetric simple exclusion process
(TASEP) with position-dependent hopping rates. The problem is solved,in a mean
field/adiabatic approximation, for a general (smooth) form of spatial rate
variation. Numerical simulations of systems with hopping rates varying linearly
against position (constant rate gradient), for both periodic and open boundary
conditions, provide detailed confirmation of theoretical predictions,
concerning steady-state average density profiles and currents, as well as
open-system phase boundaries, to excellent numerical accuracy.
