Dynamics of driven interfaces near isotropic percolation transition

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Journal Title
Journal ISSN
Volume Title
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
1998
Major/Subject
Mcode
Degree programme
Language
en
Pages
1514-1520
Series
Physical Review E, Volume 58, Issue 2
Abstract
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.
Description
Keywords
interfaces, dynamics, kinetic roughening, lattice models, Monte Carlo simulations
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Citation
Kuittu, M.-P. & Haataja, M. & Provatas, N. & Ala-Nissilä, Tapio. 1998. Dynamics of driven interfaces near isotropic percolation transition. Physical Review E. Volume 58, Issue 2. P. 1514-1520. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.58.1514.