Heterogeneities and Topological Defects in Two-Dimensional Pinned   Liquids
  We simulate a model of repulsively interacting colloids on a commensurate two-dimensional triangular pinning substrate where the amount of heterogeneous motion that appears at melting can be controlled systematically by turning off a fraction of the pinning sites. We correlate the amount of heterogeneous motion with the average topological defect number, time dependent defect fluctuations, colloid diffusion, and the form of the van Hove correlation function. When the pinning sites are all off or all on, the melting occurs in a single step. When a fraction of the sites are turned off, the melting becomes considerably broadened and signatures of a two-step melting process appear. The noise power associated with fluctuations in the number of topological defects reaches a maximum when half of the pinning sites are removed, and the noise spectrum has a pronounced 1/f^\alpha structure in the heterogeneous regime. We find that regions of high mobility are associated with regions of high dislocation densities. 
J.-X. Lin, C. Reichhardt, Z. Nussinov, Leonid P. Pryadko, and C.J.   Olson Reichhardt