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Maximal height scaling of kinetically growing surfaces
S Raychaudhuri1, M Cranston, C Przybyla
1Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
Physical Review Letters
|October 3, 2001
Summary
This study explores the maximal height of growing self-affine surfaces. We found its scaling properties in early and late times, revealing universal behaviors in surface growth dynamics.
Area of Science:
- Surface growth dynamics
- Statistical physics
- Self-affine surfaces
Background:
- Understanding the statistical properties of growing surfaces is crucial in various scientific fields.
- Self-affine surfaces exhibit scale invariance, a common characteristic in natural phenomena and complex systems.
Purpose of the Study:
- To investigate the scaling properties of the maximal height of growing self-affine surfaces.
- To analyze the distribution of maximal heights in both early-time and late-time regimes.
- To establish theoretical frameworks supported by numerical and exact results.
Main Methods:
- Employing scaling arguments to analyze the maximal height relative to the average height.
- Utilizing extreme-value statistics to determine the distribution of maximal heights.
- Conducting numerical simulations and referencing exact results for 1D surfaces.
Main Results:
- In the late-time regime, maximal height scales with lateral extent L as h*(L) ~ L^alpha.
- The distribution of maximal heights follows logP(h*(L)) ~ -A(h*(L)/L^alpha)^a for large values.
- In the early-time regime, maximal height scales as h*(L) ~ t^beta [lnL - (beta/alpha)lnt + C]^(1/b).
Conclusions:
- The maximal height of growing self-affine surfaces exhibits distinct scaling behaviors in different time regimes.
- Theoretical predictions derived from scaling and extreme-value arguments are validated by simulations and exact results.
- These findings contribute to a deeper understanding of universal properties in surface growth phenomena.