We discuss steady states and domain growth properties of two species of particles diffusing on a ring, or two coupled rings. Driven in opposite directions by a bias, the particles form clusters, due to an excluded volume interaction. Remarkably, the "one-lane" system remains disordered, displaying numerous small clusters while the "two-lane" system continues to coarsen until only a single macroscopic cluster survives. In the coarsening regime, the average cluster size increases significantly faster than in a purely diffusion-limited mechanism, even though the scaling form of the cluster size distribution remains consistent with such growth. Recent conjectures, suggesting that the two-lane system should revert to disorder in the thermodynamic limit, will be reviewed.
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