Constantin, M and Dasgupta, C and Chatraphorn, Punyindu P and Majumdar, Satya N and Sarma, Das S (2004) Persistence in nonequilibrium surface growth. In: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 69 . 061608/122.

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Abstract
Persistence probabilities of the interface height in (1 + 1) and (2 + 1)dimensional atomistic, solidonsolid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the longtime steadystate regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steadystate regimes. For the MBE universality class, the positive and negative persistence exponents in the steadystate are found to be = 0.66Â±0.02 and = 0.78Â±0.02, respectively, in (1 + 1) dimensions, and = 0.76Â±0.02 and = 0.85Â±0.02, respectively, in (2 + 1) dimensions. The noise reduction technique is applied on some of the (1 + 1)dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steadystate persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steadystate persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steadystate persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.
Item Type:  Journal Article 

Publication:  Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 
Publisher:  American Physical Society (APS) 
Additional Information:  Copyright for this article belongs to American Physical Society (APS). 
Department/Centre:  Division of Physical & Mathematical Sciences > Physics 
Date Deposited:  10 Dec 2004 
Last Modified:  19 Sep 2010 04:13 
URI:  http://eprints.iisc.ac.in/id/eprint/456 
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