Crossover Collision of Scroll Wave Filaments

Scroll waves are three-dimensional stacks of rotating spiral waves, with spiral tips aligned along filament curves. Such spatio-temporal patterns arise, for example, in reaction diffusion systems of excitable media type.

We introduce and explore the crossover collision as the only generic possibility for scroll wave filaments to change their topological knot or linking structure. Our analysis is based on elementary singularity theory, Thom transversality, and abackwards uniqueness property of reaction diffusion systems.

All phenomena are illustrated numerically by six mpeg movies downloadable at http://www.mathematik.uni-bielefeld.de/documenta/vol-05/21.html(see below) and, in the printed version, with six snapshots from each sequence.

2000 Mathematics Subject Classification: 35B05, 35B30, 35K40, 35K55, 35K57, 37C20

Keywords and Phrases: Parabolic systems, scroll wave patterns, scroll wave filaments, spirals, excitable media, crossover collision, singularity theory, Thom transversality, backwards uniqueness, video.

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Full text: dvi.gz 58 k, dvi 160 k, ps.gz 8144 k, pdf 1946 k.

MPeg Videos, compressed by gzip:

Figure 7 (p.718): twodim.mpg.gz 25.2 MB Figure 8 (p.720): ring.mpg.gz 10.9 MB Figure 9 (p.721): scrolls.mpg.gz 10.8 MB Figure 10 (p.723): scrollzoom.mpg.gz 10.9 MB Figure 11 (p.725): rings.mpg.gz 3.4 MB Figure 13 (p.727): knot.mpg.gz 9.1 MB

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