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Spatial survival probability for one-dimensional fluctuating interfaces in the steady state.

Satya N Majumdar1, Chandan Dasgupta

  • 1Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, Bat. 100, 91405 ORSAY cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary

We studied spatial survival probability for fluctuating interfaces using Edwards-Wilkinson and Kardar-Parisi-Zhang dynamics. Results show scaling behavior dependent on system size and sampling interval.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Fluctuating interfaces are crucial in various physical phenomena.
  • Understanding their steady-state behavior is key to modeling complex systems.
  • Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) dynamics describe interface growth and fluctuations.

Purpose of the Study:

  • To investigate the spatial survival probability of fluctuating one-dimensional interfaces.
  • To analyze the scaling behavior of survival probability under EW and KPZ dynamics in the steady state.
  • To compare numerical findings with analytic predictions.

Main Methods:

  • Numerical integration of a discretized EW equation to long times.
  • Analysis of steady-state interface profiles.

Related Experiment Videos

  • Path-integral treatment of a 1D Brownian motion formulation.
  • Application of a deterministic approximation for analytic solutions.

    • Main Results:

    • Spatial survival probability exhibits scaling behavior with system size and sampling interval.
    • This scaling is observed for both steady-state and finite initial conditions.
    • Analytic results derived from Brownian motion and deterministic approximation show good agreement with numerical data.

    Conclusions:

    • The study provides a comprehensive analysis of spatial survival probability for fluctuating interfaces.
    • Scaling behavior is a robust feature of these systems under EW and KPZ dynamics.
    • The developed analytic approximations offer accurate predictions for numerical observations.