Dynamics of driven interfaces near isotropic percolation transition

M. P. Kuittu, M. Haataja, N. Provatas, T. Ala-Nissila

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete “forest fire” lattice models through Monte Carlo simulations in two and three spatial dimensions. An interface generated in the models is found to display complex behavior. Away from the percolation transition, the interface is self-affine with asymptotic dynamics consistent with the Kardar-Parisi-Zhang universality class. However, in the vicinity of the percolation transition, there is a different behavior at earlier times. By scaling arguments we show that the global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying percolation cluster. Our numerical results are in good agreement with theory. However, we demonstrate that at the depinning transition, the interface as defined in the models is no longer self-affine. Finally, we compare these results with those obtained from a more realistic reaction-diffusion model of slow combustion.

Original languageEnglish (US)
Pages (from-to)1514-1520
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number2
StatePublished - 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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