Eur. Phys. J. B 53, 401-404 (2006)
https://doi.org/10.1140/epjb/e2006-00380-9

Asymptotic and effective coarsening exponents in surface growth models

¹ Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via Sansone 1, 50019 Sesto Fiorentino, Italy

Corresponding author: ^a Paolo.Politi@isc.cnr.it

Received: 5 June 2006
Revised: 21 August 2006
Published online: 18 October 2006

Abstract

We consider a class of unstable surface growth models, , 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∼tⁿ, 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.