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Topological instability along filamented invariant surfaces.
B A Carreras1, V E Lynch, L Garcia
1Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA.
Chaos (Woodbury, N.Y.)
|November 8, 2003
Summary
Weak mixing in dynamical systems is linked to the topology of invariant surfaces. Higher genus surfaces exhibit weak mixing and fractional kinetics, demonstrated in plasma turbulence models.
Area of Science:
- Plasma Physics
- Dynamical Systems Theory
- Turbulence Modeling
Background:
- Weak mixing in dynamical systems with zero Lyapunov exponents is often governed by invariant surface topology.
- Surfaces with genus greater than one can exhibit weak mixing and fractional kinetics.
Purpose of the Study:
- To demonstrate how invariant surface topology influences weak mixing and fractional kinetics.
- To analyze a plasma physics model exhibiting quasicoherent structures and topological instability.
Main Methods:
- Investigated a 3D resistive pressure-gradient-driven turbulence model in toroidal geometry.
- Analyzed the topological structure of velocity stream function isosurfaces.
- Examined particle transport mechanisms under specific plasma conditions.
Main Results:
- Identified quasicoherent structures and a web-like topology of filamentary invariant surfaces.
- Demonstrated that these filamentary surfaces can lead to stochastic jets and topological instability.
- Observed anomalous superdiffusion-type particle transport along these surfaces.
Conclusions:
- The topological structure of invariant surfaces plays a crucial role in weak mixing and fractional kinetics.
- Plasma turbulence models can exhibit complex topological features leading to anomalous particle transport.
- Findings have implications for understanding transport phenomena in magnetized plasmas.