Stability of knots in excitable media

Sutcliffe, Paul M. and Winfree, Arthur T. (2003) Stability of knots in excitable media. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 68 (1). 016218-1. ISSN 1063-651X. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Through extensive numerical simulations we investigate the evolution of knotted and linked vortices in the FitzHugh-Nagumo model. On medium time scales, of the order of a hundred times the vortex rotation period, knots simultaneously translate and precess with very little change of shape. However, on long time scales, we find that knots evolve in a more complicated manner, with particular arcs expanding and contracting, producing substantial variations in the total length. The topology of a knot is preserved during the evolution, and after several thousand vortex rotation periods the knot appears to approach an asymptotic state. Furthermore, this asymptotic state is dependent upon the initial conditions and suggests that, even within a given topology, a host of metastable configurations exists, rather than a unique stable solution. We discuss a possible mechanism for the observed evolution, associated with the impact of higher-frequency wavefronts emanating from parts of the knot which are more twisted than the expanding arcs.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Judith Broom
Date Deposited: 12 Sep 2008 12:18
Last Modified: 07 May 2014 10:46
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