Probing the entanglement and locating knots in ring polymers: a comparative study of different arc closure schemes

摘要

The interplay between the topological and geometrical properties of a polymerring can be clarified by establishing the entanglement trapped in any portion(arc) of the ring. The task requires to close the open arcs into a ring, andthe resulting topological state may depend on the specific closure scheme thatis followed. To understand the impact of this ambiguity in contexts ofpractical interest, such as knot localization in a ring with non trivialtopology, we apply various closure schemes to model ring polymers. The ringshave the same length and topological state (a trefoil knot) but have differentdegree of compactness. The comparison suggests that a novel method, termed theminimally-interfering closure, can be profitably used to characterize the arcentanglement in a robust and computationally-efficient way. This closure methodis finally applied to the knot localization problem which is tackled using twodifferent localization schemes based on top-down or bottom-up searches.