Universality and self-similar behaviour of non-equilibrium systems with non-Fickian diffusion

Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial growth. Using the generalized kinetic approach we consider universality, scaling dynamics and fractal properties of pyramidal islands growth. In the framework of generalized kinetics, we propose a theoretical model to examine the numerically obtained data for averaged islands size, the number of islands and the corresponding universal distribution over the island size.