Spatial persistence and survival probabilities for fluctuating interfaces

Details Spatial persistence and survival probabilities for fluctuating interfaces Spatial persistence and survival probabilities for fluctuating interfaces

2003-12-18

arxiv.org/abs/cond-mat/0312461v2

Phys. Rev. E 69, 051603 (2004)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 5 figures

Scientific paper

10.1103/PhysRevE.69.051603

We report the results of numerical investigations of the steady-state (SS) and finite-initial-conditions (FIC) spatial persistence and survival probabilities for (1+1)--dimensional interfaces with dynamics governed by the nonlinear Kardar--Parisi--Zhang (KPZ) equation and the linear Edwards--Wilkinson (EW) equation with both white (uncorrelated) and colored (spatially correlated) noise. We study the effects of a finite sampling distance on the measured spatial persistence probability and show that both SS and FIC persistence probabilities exhibit simple scaling behavior as a function of the system size and the sampling distance. Analytical expressions for the exponents associated with the power-law decay of SS and FIC spatial persistence probabilities of the EW equation with power-law correlated noise are established and numerically verified.

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