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Related Experiment Videos

Stellar oscillons.

O M Umurhan1, L Tao, E A Spiegel

  • 1Department of Astronomy, Columbia University, New York, New York 10027, USA.

Annals of the New York Academy of Sciences
|June 29, 2002
PubMed
Summary
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This study investigates acoustic instability in polytropes, revealing localized oscillating structures. These findings, derived from a complex Ginzburg-Landau equation, may explain oscillons in vibrated granular materials.

Area of Science:

  • Physics
  • Fluid Dynamics
  • Nonlinear Dynamics

Background:

  • Acoustic instability in plane-parallel polytropes is a complex phenomenon.
  • Thermal dissipation, modeled by Newton's law of cooling, influences instability evolution.
  • Understanding nonlinear pattern formation is crucial in various physical systems.

Purpose of the Study:

  • To analyze the weakly nonlinear evolution of acoustic instability in a polytrope with thermal dissipation.
  • To develop a nonlinear pattern theory based on unstable horizontal wavenumbers.
  • To compare numerical solutions with experimental observations of localized structures.

Main Methods:

  • Weakly nonlinear analysis of acoustic instability.
  • Application of Newton's law of cooling for thermal dissipation.

Related Experiment Videos

  • Derivation and numerical solution of a quintic complex Ginzburg-Landau equation (CGLE).

    • Main Results:

    • The most unstable horizontal wavenumbers form a band around zero.
    • Numerical solutions of the CGLE yield vertically oscillating, localized structures.
    • These structures exhibit characteristics similar to experimentally observed oscillons.

    Conclusions:

    • The complex Ginzburg-Landau equation effectively models the nonlinear behavior of acoustic instability.
    • The study provides a theoretical framework for understanding oscillon formation in granular materials.
    • Weakly nonlinear analysis is a powerful tool for studying pattern formation in dissipative systems.