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Asikainen J, Majaniemi S, Dubé M, et al. Interface dynamics and kinetic roughening in fractals. Phys Rev E Stat Nonlin Soft Matter Phys. 2002;65(5):052104doi: 10.1103/PhysRevE.65.052104.
Asikainen, J., Majaniemi, S., Dubé, M., & Ala-Nissila, T. (2002). Interface dynamics and kinetic roughening in fractals. Physical review. E, Statistical, nonlinear, and soft matter physics, 65(5), 052104. https://doi.org/10.1103/PhysRevE.65.052104
Asikainen, J, et al. "Interface dynamics and kinetic roughening in fractals." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 65,5 (2002): 052104. doi: https://doi.org/10.1103/PhysRevE.65.052104
Asikainen J, Majaniemi S, Dubé M, Ala-Nissila T. Interface dynamics and kinetic roughening in fractals. Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5):052104. doi: 10.1103/PhysRevE.65.052104. Epub 2002 May 20. PMID: 12059616.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5):052104. doi: 10.1103/PhysRevE.65.052104. Epub 2002 May 20.

Interface dynamics and kinetic roughening in fractals.

Physical review. E, Statistical, nonlinear, and soft matter physics

J Asikainen, S Majaniemi, M Dubé, T Ala-Nissila

Affiliations

  1. Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Espoo, Finland.

PMID: 12059616 DOI: 10.1103/PhysRevE.65.052104

Abstract

We consider the dynamics and kinetic roughening of single-valued interfaces in two-dimensional fractal media. Assuming that the local height difference distribution function of the fronts obeys Levý statistics with a well-defined power-law decay exponent, we derive analytic expressions for the local scaling exponents. We also show that the kinetic roughening of the interfaces displays anomalous scaling and multiscaling in the relevant correlation functions. For invasion percolation models, the exponents can be obtained from the fractal geometry of percolation clusters. Our predictions are in excellent agreement with numerical simulations.

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