Topological dynamics of knotted and tangled matter

CDSNS Colloquium
Friday, September 29, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 249
Vishal Patil – Stanford – vppatil@stanford.edu
Alex Blumenthal
Knots and tangles play a fundamental role in the dynamics of biological and physical systems, from DNA and root networks to surgical sutures and shoelaces. Despite having been studied for centuries, the subtle interplay between topology and mechanics in tangled elastic filaments remains poorly understood. Here we investigate the dynamical rules governing the behavior of knotted and tangled matter. We first study the human-designed knots used to tie ropes together. By developing an analogy with long-range ferromagnetic spin systems, we identify simple topological counting rules to predict the relative mechanical stability of commonly used climbing and sailing knots. Secondly, we examine the complex tangling dynamics exhibited by California blackworms, which form living tangled structures in minutes but can rapidly untangle in milliseconds. Using ultrasound imaging datasets, we construct a minimal model that explains how the kinematics of individual active filaments determines their emergent collective topological dynamics. By identifying generic dynamical principles of topological transformations, our results can provide guidance for designing classes of self-adaptive topological metamaterials.