Eur. Phys. J. B (2016) 89: 32
https://doi.org/10.1140/epjb/e2016-60830-3

Regular Article

Long range height variations in surface growth

Institute of Theoretical Physics and Astronomy, Vilnius University, Goštauto st. 12, 01108 Vilnius, Lithuania

^a e-mail: vaidas.juknevicius@tfai.stud.vu.lt

Received: 19 October 2015
Received in final form: 23 December 2015
Published online: 3 February 2016

Abstract

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.