Links, Knots and Knotted Labyrinths in Bistable Systems

Details Links, Knots and Knotted Labyrinths in Bistable Systems Links, Knots and Knotted Labyrinths in Bistable Systems

1996-06-17

arxiv.org/abs/patt-sol/9606003v2

Phys. Rev. Lett. 77(4) 767-770, 1996

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, typeset by REVTeX

Scientific paper

10.1103/PhysRevLett.77.767

The existence of stable links and knots is demonstrated in three-dimensional, bistable, chemical media. The reaction-diffusion medium segregates into regions of high and low concentration separated by sharp interfaces. The interfaces repel at short distances so that domains with various topologies are possible depending on the initial conditions and system parameters. Front instabilities can give rise to knotted labyrinthine patterns. A lattice-gas model whose mean-field limit is the FitzHugh-Nagumo equation is described and implemented to carry out the simulations.

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