Persistence homology of entangled rings

Topological constraints (TCs) between polymers determine the behavior of complex fluids such as creams, oils, and plastics. Most of the polymer solutions used in everyday life employ linear chains; their behavior is accurately captured by the reptation and tube theories which connect microscopic TCs to macroscopic viscoelasticity. On the other hand, polymers with nontrivial topology, such as rings, hold great promise for new technology but pose a challenging problem as they do not obey standard theories; additionally, topological invariance, i.e., the fact that rings must remain unknotted and unlinked if prepared so, precludes any serious analytical treatment.