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

TL;DR

This paper presents analytical methods to understand non-Fickian diffusion in complex systems, focusing on the universality, scaling, and fractal properties of pyramidal island growth during epitaxial processes.

Contribution

It introduces a generalized kinetic model to analyze non-Fickian diffusion and describes the universal behavior and fractal characteristics of island formation.

Findings

Identification of universal scaling laws in island growth

Development of a theoretical model matching numerical data

Insights into fractal and self-similar properties of non-equilibrium systems

Abstract

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.