Summary: We discuss the competition between the topological effect and the excluded volume effect on the average size of ring polymers with a fixed knot, reviewing some simulation results of the authors [Phys. Rev. E 64, 020801 (2001)]. Under a topological constraint, the average size of ring polymers can be much larger than that of no topological constraint. However, the effective expansion depends strongly on the excluded-volume parameter. We also discuss the radial distribution functions of segments of ring polymers with fixed knots. The numerical results of the radial distributions suggest that a topological constraint on ring polymers effectively leads to an entropic repulsion among polymer segments.
For the entire collection see [Zbl 1085.57002].