Optimal unravelling of tangled filaments

Tangled fibers represent an important class of disordered, strongly interacting systems, with relevance across length scales, from tangled DNA to human-scale materials such as yarn and rope. Despite recent work demonstrating the functionality of amorphous tangles, the problem of controlling tangle topology continues to present profound challenges. In particular, the question of how to extract a single filament from a tangle remains poorly understood. Here, we combine detangling experiments and numerical simulations with a topological analysis of tangle mechanics to understand the fiber extraction problem. Our results indicate the existence of optimal fiber extraction protocols, demonstrating that the topological state of disordered filamentary matter can be robustly manipulated.