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Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

  • C.M. Horowitz
  • E.V. Albano

Abstract:

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp2. It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models.

PACS. 68.35.Ct Interface structure and roughness – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 02.50.-r Probability theory, stochastic processes, and statistics – 81.15.Aa Theory and models of film growth 

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Copyright information

© EDP Sciences, Springer-Verlag 2003

Authors and Affiliations

  • C.M. Horowitz
    • 1
  • E.V. Albano
    • 1
  1. 1.Instituto de Investigaciones Fisicoquımicas Teóricas y Aplicadas, (INIFTA), CONICET, UNLP. Sucursal 4, Casilla de Correo 16, (1900) La Plata, ArgentinaAR

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