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Related Experiment Videos

Spatial persistence and survival probabilities for fluctuating interfaces.

M Constantin1, S Das Sarma, C Dasgupta

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. mconstan@glue.umd.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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This study investigates spatial persistence in (1+1)-dimensional interfaces using the Kardar-Parisi-Zhang and Edwards-Wilkinson equations. Both steady-state and finite-initial-conditions probabilities show simple scaling with system size and sampling distance.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Investigating interface growth dynamics is crucial in statistical mechanics.
  • The Kardar-Parisi-Zhang (KPZ) and Edwards-Wilkinson (EW) equations model interface growth under different noise conditions.
  • Understanding spatial persistence and survival probabilities provides insights into interface behavior.

Purpose of the Study:

  • To numerically investigate steady-state (SS) and finite-initial-conditions (FIC) spatial persistence and survival probabilities.
  • To analyze the impact of finite sampling distance on measured spatial persistence.
  • To explore the effects of both white (uncorrelated) and colored (spatially correlated) noise on interface dynamics.

Main Methods:

  • Numerical simulations of (1+1)-dimensional interfaces governed by the KPZ and EW equations.

Related Experiment Videos

  • Analysis of spatial persistence and survival probabilities under varying noise types (white and colored).
  • Examination of scaling behavior with respect to system size and finite sampling distance.

    • Main Results:

    • Both SS and FIC persistence probabilities exhibit simple scaling behavior.
    • Scaling is dependent on system size and the finite sampling distance.
    • Analytical expressions for exponents in EW equation with power-law correlated noise were derived and numerically verified.

    Conclusions:

    • Spatial persistence probabilities of interfaces governed by KPZ and EW equations display predictable scaling.
    • Finite sampling distance significantly influences measured persistence probabilities.
    • The study provides validated analytical insights into interface dynamics with correlated noise.