  Using numerical simulations, we examine the structure and diffusion of a
two-dimensional dusty plasma (2DDP) in the presence of a one-dimensional
periodic substrate (1DPS) as a function of increasing substrate strength. Both
the pair correlation function perpendicular to the substrate modulation and the
mean squared displacement (MSD) of dust particles are calculated. It is found
that both the structure and dynamics of 2DDP exhibit strong anisotropic
effects, due to the applied 1DPS. As the substrate strength increases from 0,
the structure order of dusty plasma along each potential well of 1DPS increases
first probably due to the competition between the inter-particle interactions
and the particle-substrate interactions, and then decreases gradually, which
may be due to the reduced dimensionality and the enhanced fluctuations. The
obtained MSD along potential wells of 1DPS clearly shows three processes of
diffusion in our studied 2DDP. Between the initial ballistic and finally
diffusive motion, there is the intermediate sub-diffusion discovered here,
which may result from the substrate-induced distortion of the caging dynamics.
