dorsal/arxiv
View SchemaThe case of the trapped singularities
| Authors | R. Ball |
|---|---|
| Categories | |
| ArXiv ID | physics/0410160 |
| URL | https://arxiv.org/abs/physics/0410160 |
Abstract
A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of pathological and persistent degenerate singularities, is surveyed through the parameter space of a nonlinear dynamical model for a gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas. Along the route various obstacles and features are identified and treated appropriately. An organizing centre of low codimension is shown to be robust, several trapped singularities are found and released, and domains of hysteresis, threefold stable equilibria, and limit cycles are mapped. Characterization of this rich dynamical landscape achieves unification of previous disparate models for plasma confinement transitions, supplies valuable intelligence on the big issue of shear flow suppression of turbulence, and suggests targeted experimental design, control and optimization strategies.
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"abstract": "A case study in bifurcation and stability analysis is presented, in which\nreduced dynamical system modelling yields substantial new global and predictive\ninformation about the behaviour of a complex system. The first smooth pathway,\nfree of pathological and persistent degenerate singularities, is surveyed\nthrough the parameter space of a nonlinear dynamical model for a\ngradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas.\nAlong the route various obstacles and features are identified and treated\nappropriately. An organizing centre of low codimension is shown to be robust,\nseveral trapped singularities are found and released, and domains of\nhysteresis, threefold stable equilibria, and limit cycles are mapped.\nCharacterization of this rich dynamical landscape achieves unification of\nprevious disparate models for plasma confinement transitions, supplies valuable\nintelligence on the big issue of shear flow suppression of turbulence, and\nsuggests targeted experimental design, control and optimization strategies.",
"arxiv_id": "physics/0410160",
"authors": [
"R. Ball"
],
"categories": [
"physics.plasm-ph",
"math.DS",
"nlin.AO"
],
"title": "The case of the trapped singularities",
"url": "https://arxiv.org/abs/physics/0410160"
},
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