Long range height variations in surface growth
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This paper presents novel results obtained from numerical investigation of surfaces generated by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term and a single independent parameter. Surface roughness exhibits a certain dependence on the system size that indicates power-law shape of the surface spectrum for small wave numbers. This leads to a conclusion that although cellular surface patterns of definite scale dominate in the range of short distances, there are also scale-free long-range height variations present in large systems. The dependence of the spectral exponent on the equation parameter gives new insight into the influence of the additional term in the equation on the scaling behavior for large systems.
KeywordsStatistical and Nonlinear Physics
- 14.A.-L. Barabasi, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)Google Scholar