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Equilibrium-restricted solid-on-solid growth model on fractal substrates

Sang Bub Lee

Jin Min Kim*

  • Department of Physics, Kyungpook National University, Daegu 702-701, Korea

  • Department of Physics and Computer-aided Molecular Design Research Center, Soongsil University, Seoul 156-743, Korea

  • *Corresponding author; jmkim@ssu.ac.kr
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Phys. Rev. E 80, 021101 – Published 3 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021101

Abstract

The equilibrium-restricted solid-on-solid growth model on fractal substrates is studied by introducing a fractional Langevin equation. The growth exponent β and the roughness exponent α defined, respectively, by the surface width via W∼tβ and the saturated width via Wsat∼Lα, L being the system size, were obtained by a power-counting analysis, and the scaling relation 2α+df=zRW was found to hold. The numerical simulation data on Sierpinski gasket, checkerboard fractal, and critical percolation cluster were found to agree well with the analytical predictions of the fractional Langevin equation.

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Phys. Rev. E 80, 021101– Published 3 August, 2009
  • Received 4 May 2009

© 2009 American Physical Society

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