Borromean Hypergraph Formation in Dense Random Rectangles

Autor:	Klotz, Alexander R.
Rok vydání:	2024
Předmět:	Condensed Matter - Soft Condensed Matter Condensed Matter - Statistical Mechanics Mathematics - General Topology
Druh dokumentu:	Working Paper
Popis:	We develop a minimal system to study the stochastic formation of Borromean links within topologically entangled networks without requiring the use of knot invariants. Borromean linkages may form in entangled solutions of open polymer chains or in Olympic gel systems such as kinetoplast DNA, but it is challenging to investigate this due to the difficulty of computing three-body link invariants. Here, we investigate randomly oriented rectangles densely packed within a volume, and evaluate them for Hopf linking and Borromean link formation. We show that dense packings of rectangles can form Borromean triplets and larger clusters, and that in high enough density the combination of Hopf and Borromean linking can create a percolating hypergraph through the network. We present data for the percolation threshold of Borromean hypergraphs, and discuss implications for the existence of Borromean connectivity within kinetoplast DNA. Comment: 6 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.20874 Zobrazit plný text záznamu View this record from Arxiv