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Crystallization kinetics and self-induced pinning in cellular patterns

Aranson1, Malomed, Pismen

  • 1Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Front propagation between states is driven by periodic nucleation events. These events are triggered by the explosive growth of a localized mode, determining front speed and exhibiting noise-induced creep.

Area of Science:

  • Nonlinear dynamics
  • Pattern formation physics
  • Mathematical modeling

Background:

  • The Swift-Hohenberg model describes pattern formation in various physical systems.
  • Understanding front propagation between different states is crucial in nonlinear science.
  • Localized modes can significantly influence system dynamics.

Purpose of the Study:

  • To numerically and analytically investigate front propagation between cellular and uniform states within the Swift-Hohenberg model.
  • To identify the underlying mechanism driving front propagation.
  • To analyze the role of localized modes and noise on front dynamics.

Main Methods:

  • Numerical simulations of the Swift-Hohenberg equation.
  • Analytical treatment using asymptotic analysis.

Related Experiment Videos

  • Derivation of an evolution equation for the zero-eigenvalue mode.
  • Investigation of noise effects on front propagation.

    • Main Results:

    • Front propagation is determined by periodic nucleation events.
    • These events are triggered by the explosive growth of a localized zero-eigenvalue mode.
    • An evolution equation for this mode was derived, enabling evaluation of nucleation time intervals and front speed.
    • In the presence of noise, "thermally activated" front propagation (creep) beyond the pinning threshold was observed.

    Conclusions:

    • Periodic nucleation events, driven by localized mode growth, are the key mechanism for front propagation.
    • The derived model accurately predicts front speed and noise-induced creep.
    • This study provides a deeper understanding of pattern formation and front dynamics in nonlinear systems.