Asymptotic and effective coarsening exponents in surface growth models

P. Politi () and A. Torcini

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 53, issue 3, 401-404

Abstract: We consider a class of unstable surface growth models, $\partial_t z=-\partial_x {\cal J}$ , developing a mound structure of size λ and displaying a perpetual coarsening process, i.e. an endless increase in time of λ. The coarsening exponents n, defined by the growth law of the mound size λ with time, λ∼t n , were previously found by numerical integration of the growth equations [A. Torcini, 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology, and orientation, 02.30.Jr Partial differential equations, (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00380-9

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