Dynamics of linked filaments in excitable media

TL;DR

This study explores the long-term behavior of linked vortex filaments in a 3D excitable medium, revealing regular spinning conformations, dependence on crossing number, boundary stabilization, and complex collision dynamics.

Contribution

It provides a comprehensive numerical analysis of linked vortex filaments, identifying stable configurations, boundary effects, and collision behaviors in excitable media.

Findings

Linked vortex filaments exhibit stable spinning conformations.

Boundary interactions can stabilize torus links and suppress instabilities.

Collision of links results in complex wrestling motions and dominance dynamics.

Abstract

In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh-Nagumo excitable medium. In particular, we study all torus links with no more than 12 crossings and identify a timescale over which the dynamics is regular in the sense that each link is well-described by a spinning rigid conformation of fixed size that propagates at constant speed along the axis of rotation. We compute the properties of these links and demonstrate that they have a simple dependence on the crossing number of the link for a fixed number of link components. Furthermore, we find that instabilities that exist over longer timescales in the bulk can be removed by boundary interactions that yield stable torus links which settle snugly at the medium boundary. The Borromean rings are used as an example of a non-torus link to demonstrate both the irregular tumbling dynamics that arises in the bulk and its suppression by a tight confining medium. Finally, we investigate the collision of torus links and reveal that this produces a complicated wrestling motion where one torus link can eventually dominate over the other by pushing it into the boundary of the medium.