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Interface dynamics and kinetic roughening in fractals
J Asikainen1, S Majaniemi, M Dubé
1Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Espoo, Finland.
Summary
This study explores interface dynamics in fractal media, revealing anomalous scaling and multiscaling behaviors. Findings align with invasion percolation models and numerical simulations, offering insights into kinetic roughening.
Area of Science:
- Physics
- Complex Systems
- Statistical Mechanics
Background:
- Understanding the dynamics of interfaces in disordered media is crucial for various scientific fields.
- Kinetic roughening describes the growth of rough surfaces over time, often exhibiting complex scaling behaviors.
Purpose of the Study:
- To investigate the dynamics and kinetic roughening of single-valued interfaces in two-dimensional fractal media.
- To derive analytic expressions for local scaling exponents based on Levý statistics.
- To analyze anomalous scaling and multiscaling in interface correlation functions.
Main Methods:
- Theoretical analysis assuming Levý statistics for local height difference distribution.
- Derivation of analytic expressions for local scaling exponents.
- Investigation of kinetic roughening using correlation functions and invasion percolation models.
Main Results:
- Analytic expressions for local scaling exponents were derived.
- Anomalous scaling and multiscaling were observed in kinetic roughening.
- Exponents for invasion percolation models were linked to fractal geometry.
Conclusions:
- The study provides a theoretical framework for understanding interface dynamics in fractal media.
- Predictions show excellent agreement with numerical simulations.
- The findings contribute to the broader understanding of complex systems and statistical physics.