Asymptotic and effective coarsening exponents in surface growth models

Abstract

We consider a class of unstable surface growth models, z_t = -\partial_x J, developing a mound structure of size lambda and displaying a perpetual coarsening process, i.e. an endless increase in time of lambda. The coarsening exponents n, defined by the growth law of the mound size lambda with time, lambda=t^n, were previously found by numerical integration of the growth equations [A. Torcini and P. Politi, Eur. Phys. J. B 25, 519 (2002)]. Recent analytical work now allows to interpret such findings as finite time effective exponents. The asymptotic exponents are shown to appear at so large time that cannot be reached by direct integration of the growth equations. The reason for the appearance of effective exponents is clearly identified.

6 pages. Several parts and conclusions have been rewritten. (Addendum to the article that can be found in http://www.arxiv.org/abs/cond-mat/0110058)

References in corpus (5)

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Cited by in corpus (2)

• Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation
• Universality classes for unstable crystal growth