| Abstract: | This paper presents novel results obtained from numerical investigation of surfacesgenerated by the two-dimensional isotropic Kuramoto-Sivashinsky equation with anadditional nonlinear term and a single independent parameter. Surface roughness exhibits acertain dependence on the system size that indicates power-law shape of the surfacespectrum for small wave numbers. This leads to a conclusion that although cellular surfacepatterns of definite scale dominate in the range of short distances, there are alsoscale-free long-range height variations present in large systems. The dependence of thespectral exponent on the equation parameter gives new insight into the influence of theadditional term in the equation on the scaling behavior for large systems. |
