Links, Knots and Knotted Labyrinths in Bistable Systems

Abstract

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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References in corpus (4)

• From Labyrinthine Patterns to Spiral Turbulence
• Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
• A Nonlocal Contour Dynamics Model for Chemical Front Motion
• Dynamic Front Transitions and Spiral-Vortex Nucleation

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• Density and concentration field description of nonperiodic structures
• The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave