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Related Experiment Videos

Diffusion coefficient of propagating fronts with multiplicative noise.

Andrea Rocco1, Jaume Casademunt, Ute Ebert

  • 1Dipartimento di Fisica, Università di Roma "La Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

Fronts in unstable or metastable states exhibit diffusive wandering due to noise. This study derives an effective diffusion coefficient for these fronts, providing a new analytical expression for their noisy behavior.

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Area of Science:

  • Physics
  • Chemical Kinetics
  • Statistical Mechanics

Background:

  • Front propagation in reaction-diffusion systems is influenced by noise.
  • Both fronts in metastable and pushed fronts in unstable states show diffusive wandering.
  • Previous work suggested a multiple scale ansatz for effective diffusion.

Purpose of the Study:

  • To derive an expression for the effective diffusion coefficient of fronts in the presence of noise.
  • To provide a systematic theoretical framework for understanding front dynamics under fluctuating conditions.
  • To analyze the nature of front position fluctuations and their relaxation dynamics.

Main Methods:

  • Decomposition of the fluctuating front into an average profile and fluctuating eigenmodes.
  • Analysis of stability operators and their eigenmodes.

Related Experiment Videos

  • Mathematical derivation of the effective diffusion coefficient.

    • Main Results:

    • An expression for the effective diffusion coefficient of fronts was derived.
    • Front position fluctuations were shown to follow a Wiener process.
    • Fluctuations around the time-averaged front profile exhibit exponential relaxation.

    Conclusions:

    • The derived expression quantifies the effective diffusion of fronts in noisy environments.
    • The study clarifies the distinct temporal behaviors of front position and profile fluctuations.
    • This work offers a rigorous approach to modeling front propagation with noise.