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Persisting roughness when deposition stops.

Moshe Schwartz1, S F Edwards

  • 1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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This study modifies surface growth theories to fix an unphysical prediction. Modified theories show surfaces reach a stable, non-flat state after deposition stops, exhibiting history-dependent distributions.

Area of Science:

  • Physics
  • Materials Science
  • Surface Science

Background:

  • Surface growth under random deposition is modeled by Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) theories.
  • Both EW and KPZ theories predict unphysically flat surfaces after deposition ceases.

Purpose of the Study:

  • To modify EW and KPZ theories to accurately represent surface behavior after deposition stops.
  • To investigate the consequences of these modifications on surface evolution and steady-state properties.

Main Methods:

  • Modification of the EW and KPZ equations to incorporate physical constraints related to the angle of repose.
  • Analysis of the modified equations, focusing on a simpler system derived from the EW equation.
  • Investigation of surface evolution and steady-state distributions after deposition halts.

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Main Results:

  • The modified theories predict that surfaces do not become perfectly flat but reach a steady state with gradients limited by the angle of repose.
  • In the long-wavelength limit, the modified EW equation with noise shows behavior similar to the linear EW equation.
  • A significant finding is the emergence of history-dependent steady-state distributions after deposition stops.

Conclusions:

  • The modified theories provide a more physically realistic description of surface growth under random deposition.
  • Surface rearrangement ceases when the gradient reaches the angle of repose, leading to a stable, non-flat surface.
  • History-dependent steady-state distributions represent a novel characteristic of these modified surface growth models.