https://doi.org/10.1140/epjb/e2016-70132-5
Regular Article
On the origin of multiscaling in stochastic-field models of surface growth
1 Departamento de Matemáticas,
Universidad de Oviedo, Campus de
Gijón, 33203
Gijón,
Spain
2 Grupo Interdisciplinar de Sistemas
Complejos (GISC) and Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de
Ingeniería (ICAI), Universidad Pontificia Comillas, 28015
Madrid,
Spain
3 Instituto de Física de Cantabria
(IFCA), CSIC–UC,
39005
Santander,
Spain
a e-mail: rgallego@uniovi.es
Received:
3
March
2016
Received in final form:
9
June
2016
Published online:
5
September
2016
Multiscaling appears in some non-equilibrium systems when different moments of a bulk averaged state variable scale with different and nontrivial exponents. This multiexponent scaling behaviour is highly nontrivial and is associated with different fractal properties at different observation scales. It is unclear what kind of generic mechanisms could make multiscaling to emerge in continuous hydrodynamic descriptions of dynamical systems with only local interactions, governed by partial-differential equations, in the continuum. Here we present an extensive numerical study of a continuous model of epitaxial thin-film growth, which main characteristic is that it includes infinitely many nonlinearities. For strong enough nonlinearity, the model shows effective multiscaling over a range of time/length scales, while normal monoscaling is actually recovered at long wavelengths. We conjecture that the existence of infinitely many weakly relevant nonlinear terms may lead to this nontrivial scaling behaviour in a generic way.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016