dorsal/arxiv
View SchemaComplex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
| Authors | Aric Hagberg, Ehud Meron |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9405001 |
| URL | https://arxiv.org/abs/patt-sol/9405001 |
| DOI | 10.1063/1.166047 |
| Journal | Chaos 4, 477 (1994) |
Abstract
Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.
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"abstract": "Two front instabilities in a reaction-diffusion system are shown to lead to\nthe formation of complex patterns. The first is an instability to transverse\nmodulations that drives the formation of labyrinthine patterns. The second is a\nNonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar\nfront unstable and gives rise to a pair of counterpropagating fronts. Near the\nNIB bifurcation the relation of the front velocity to curvature is highly\nnonlinear and transitions between counterpropagating fronts become feasible.\nNonuniformly curved fronts may undergo local front transitions that nucleate\nspiral-vortex pairs. These nucleation events provide the ingredient needed to\ninitiate spot splitting and spiral turbulence. Similar spatio-temporal\nprocesses have been observed recently in the ferrocyanide-iodate-sulfite\nreaction.",
"arxiv_id": "patt-sol/9405001",
"authors": [
"Aric Hagberg",
"Ehud Meron"
],
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"patt-sol",
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],
"doi": "10.1063/1.166047",
"journal_ref": "Chaos 4, 477 (1994)",
"title": "Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities",
"url": "https://arxiv.org/abs/patt-sol/9405001"
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