Title: The length of excitable knots,
Abstract: The FitzHugh-Nagumo equation provides a simple mathematical model of cardiac
tissue as an excitable medium hosting spiral wave vortices. Here we present
extensive numerical simulations studying long-term dynamics of knotted vortex
string solutions for all torus knots up to crossing number 11. We demonstrate
that FitzHugh-Nagumo evolution preserves the knot topology for all the examples
presented, thereby providing a novel field theory approach to the study of
knots. Furthermore, the evolution yields a well-defined minimal length for each
knot that is comparable to the ropelength of ideal knots. We highlight the role
of the medium boundary in stabilizing the length of the knot and discuss the
implications beyond torus knots. By applying Moffatt's test we are able to show
that there is not a unique attractor within a given knot topology.