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We study of the dynamics of ring polymers confined to diffuse in a backgroundgel at low concentrations. We do this in order to probe the inter-play betweentopology and dynamics in ring polymers. We develop an algorithm that takes intoaccount the possibility that the rings hinder their own motion by passingthrough themselves, i.e. "self-threading". Our results suggest that the numberof self-threadings scales extensively with the length of the rings and thatthis is substantially independent of the details of the model. The slowing downof the rings' dynamics is found to be related to the fraction of segments thatcan contribute to the motion. Our results give a novel perspective on themotion 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 gelelectrophoresis experiments.

Dynamics of Self-Threading Ring Polymers in a Gel