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

TL;DR

This study compares different arc closure schemes to analyze entanglement and locate knots in ring polymers, introducing a new minimally-interfering closure method that improves robustness and efficiency.

Contribution

The paper introduces a novel minimally-interfering closure scheme for better topological analysis of ring polymers and applies it to knot localization problems.

Findings

The minimally-interfering closure method is more robust and computationally efficient.

Different closure schemes can influence the perceived entanglement in ring polymers.

The new method effectively localizes knots in various polymer configurations.

Abstract

The interplay between the topological and geometrical properties of a polymer ring 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, and the resulting topological state may depend on the specific closure scheme that is followed. To understand the impact of this ambiguity in contexts of practical interest, such as knot localization in a ring with non trivial topology, we apply various closure schemes to model ring polymers. The rings have the same length and topological state (a trefoil knot) but have different degree of compactness. The comparison suggests that a novel method, termed the minimally-interfering closure, can be profitably used to characterize the arc entanglement in a robust and computationally-efficient way. This closure method is finally applied to the knot localization problem which is tackled using two different localization schemes based on top-down or bottom-up searches.