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The Diffusion of Passive Tracers in Laminar Shear Flow
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Superdiffusion in the dissipative standard map.

G M Zaslavsky1, M Edelman

  • 1Department of Physics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.

Chaos (Woodbury, N.Y.)
|December 3, 2008
PubMed
Summary
This summary is machine-generated.

Transport properties of chaotic attractors were studied. Anomalous superdiffusion was observed near crises, driven by sticky trajectories interacting with invariant Cantor sets.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Chaotic (strange) attractors govern complex system dynamics.
  • Transport properties, like diffusion, are key to understanding system behavior.
  • The dissipative standard map is a model for chaotic dynamics.

Purpose of the Study:

  • Investigate transport properties along unfolded trajectories of the dissipative standard map.
  • Identify conditions leading to anomalous diffusion.
  • Understand the role of invariant sets in chaotic transport.

Main Methods:

  • Numerical simulations of the dissipative standard map.
  • Analysis of diffusion processes along trajectories.
  • Examination of trajectory behavior near special parameter values and crises.

Main Results:

  • Diffusion is generally normal, but becomes anomalous near specific control parameter values (crises).
  • Anomalous diffusion exhibits superdiffusive behavior and temporal non-uniformity.
  • Trajectory stickiness to invariant Cantor sets is identified as the cause of anomalous superdiffusion.

Conclusions:

  • Invariant Cantor sets significantly influence chaotic transport.
  • The observed anomalous superdiffusion is linked to sticky dynamics near these sets.
  • The distribution function on sticky sets closely matches the SRB measure of the chaotic attractor.