  We study of the dynamics of ring polymers confined to diffuse in a background
gel at low concentrations. We do this in order to probe the inter-play between
topology and dynamics in ring polymers. We develop an algorithm that takes into
account the possibility that the rings hinder their own motion by passing
through themselves, i.e. "self-threading". Our results suggest that the number
of self-threadings scales extensively with the length of the rings and that
this is substantially independent of the details of the model. The slowing down
of the rings' dynamics is found to be related to the fraction of segments that
can contribute to the motion. Our results give a novel perspective on the
motion of ring polymers in gel, for which a complete theory is still lacking,
and may help us to understand the irreversible trapping of ring polymers in gel
electrophoresis experiments.
