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Chaotic jets with multifractal space-time random walk.

Valerii V. Afanasiev1, Roald Z. Sagdeev, George M. Zaslavsky

  • 1Space Research Institute, Academy of Science of the USSR, Profsouznaya 84/32, Moscow 117810, USSRSpace Research Institute, Academy of Science of the USSR, Profsouznaya 84/32, Moscow 117810, USSRUniversity of Maryland, College Park, Maryland 20742.

Chaos (Woodbury, N.Y.)
|August 1, 1991
PubMed
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Particle diffusion in a 4-D map exhibits nonhomogeneous properties due to finite observation times. Long-lived "chaotic jets" influence transport, leading to a multifractal space-time random walk and generalized Levy laws.

Area of Science:

  • Statistical Physics
  • Dynamical Systems
  • Plasma Physics

Background:

  • Particle motion in combined magnetic and electrostatic fields is complex.
  • Understanding diffusion and transport is crucial in various physical systems.
  • The standard map and web map are fundamental models for chaotic dynamics.

Purpose of the Study:

  • To investigate normal and anomalous diffusion in a 4-D map model.
  • To analyze the impact of finite observation time on particle diffusion.
  • To explore the role of 'chaotic jets' in particle transport.

Main Methods:

  • Analysis of a four-dimensional (4-D) map derived from particle motion.
  • Consideration of weak chaos and coupled standard and web maps.
  • Application of Levy random walk theory and multifractal space-time concepts.

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Main Results:

  • Particle diffusion shows strong nonhomogeneous properties due to finite observation time.
  • Long-lived bundles of orbits, termed 'chaotic jets,' exhibit coherent propagation.
  • Chaotic jets influence asymptotic transport laws, leading to multifractal space-time behavior.

Conclusions:

  • Particle transport can be modeled as a random walk in a multifractal space-time.
  • The existence and properties of chaotic jets are linked to phase space topology.
  • Generalized Levy laws describe asymptotic displacement laws in this complex system.