How to efficiently extract a filament from a topological tangle (Part 2)

Tangled filamentary matter plays an important role across a range a physical and biological systems, from packed DNA and worm collectives to fabrics and yarn. Understanding the relationship between mechanics, elasticity and topology in such a system continues to present challenges, limiting our ability to control these complex tangled structures. In particular, the question of how to extract a single filament from a tangle represents a fundamental problem of tangle control. Here, we theoretically explore filament oscillation as a dynamical protocol for solving this extraction problem. By combining statistical mechanics with elasticity and topology, we demonstrate that this oscillation protocol affects tangle structure, enabling the driven filament to escape the tangle in certain cases. We further exhibit a relationship between tangle structure, filament oscillation and escape time. Our results represent a first step towards the design of algorithms for controlling and manipulating complex tangled matter.