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Clustering in randomly driven Hamiltonian systems.

D V Makarov1, M Yu Uleysky, M V Budyansky

  • 1Laboratory of Nonlinear Dynamical Systems, V.I. Il'ichev Pacific Oceanological Institute of the Russian Academy of Sciences, 690041 Vladivostok, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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Researchers developed a method to find stable regions in randomly driven Hamiltonian systems. This reveals coherent clusters, like sound rays in waveguides and particles in ocean mixing.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Fluid mechanics

Background:

  • Nonlinear Hamiltonian systems driven by noise exhibit complex behaviors.
  • Understanding stability regions in such systems is crucial for predicting long-term dynamics.
  • Coherent structures can emerge from random processes.

Purpose of the Study:

  • To develop a general method for identifying stability regions in randomly driven nonlinear Hamiltonian systems.
  • To demonstrate the physical manifestation of these stability regions as coherent clusters.
  • To validate the method using models from acoustics and oceanography.

Main Methods:

  • Utilizing a specific Poincaré map to analyze the phase space of randomly driven systems.
  • Developing a general method for finding stability regions.

Related Experiment Videos

  • Applying the method to two distinct physical models: waveguide sound propagation and Lagrangian mixing.

    • Main Results:

    • A general method for finding stability regions in randomly driven Hamiltonian systems was proposed and justified.
    • Coherent clusters were identified as physical manifestations of these stability regions.
    • Sound rays were observed to propagate coherently over long distances in a simulated random ocean waveguide.
    • Passive particles were found to be advected coherently for extended periods in a model of oceanic mixing.

    Conclusions:

    • The proposed Poincaré map-based method effectively identifies stability regions in randomly driven nonlinear Hamiltonian systems.
    • The formation of coherent clusters is a key phenomenon in these systems, with implications for wave propagation and mixing.
    • The findings have potential applications in understanding phenomena like long-range sound propagation in fluctuating environments and particle transport in turbulent flows.