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Noise-driven interfaces and their macroscopic representation.

Marco Dentz1, Insa Neuweiler2, Yves Méheust3

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We developed macroscopic models for stochastic interface growth, linking mesoscopic mass transfer to macroscopic interface dynamics. This work provides a framework for upscaling complex interface behaviors in models like Edwards-Wilkinson and Kadar-Paris-Zhang.

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Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Stochastic interface growth models are crucial for understanding phenomena from thin-film deposition to biological pattern formation.
  • Macroscopic representations are needed to bridge the gap between microscopic dynamics and observable large-scale behaviors.
  • Existing models often struggle to connect mesoscopic processes with macroscopic interface properties.

Purpose of the Study:

  • To develop a macroscopic representation of noise-driven interfaces in (1+1) dimensional stochastic growth models.
  • To derive deterministic equations for phase saturation in the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models.
  • To establish a link between mesoscopic mass transfer and macroscopic interface dynamics.

Main Methods:

  • Characterization of the interface using a phase field with values between 0 and 1.
  • Determination of one-point interface height statistics for EW and KPZ models.
  • Development of a Gaussian closure approximation for the KPZ model.

Main Results:

  • Exact results for the EW model's phase saturation.
  • A Gaussian closure approximation yielding deterministic equations for the KPZ model.
  • Identification of an interface compression term and a diffusion term influencing interface width.

Conclusions:

  • The interface compression rate connects mesoscopic mass transfer to macroscopic interface dynamics.
  • The study provides a systematic framework for upscaling stochastic interface dynamics.
  • These findings elucidate the relationship between mesoscale and macroscale interface models.