Pattern formation

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.

D.O.Kharchenko, V.O.Kharchenko, S.V.Kokhan. Universality and self-similar behaviour of non-equilibrium systems with non-Fickian diffusion, Condensed Matter Physics, 17(3), art. no. 33004 (2014)

Statistical properties of nanosized clusters on a surface in overdamped stochastic reaction-Cattaneo systems

In this work we study an overdamped stochastic reaction-Cattaneo model describing nanosized pattern formation on a surface at monolayer deposition. We study and compare an influence of both primary and secondary mechanisms onto pattern formation processes. The primary mechanisms relate to the rates of chemical reactions and interaction strength of adsorbate; the secondary mechanisms are related to finite atomic disturbance propagation speed and stochastic contribution satisfying fluctuation-dissipation relation. Considering statistical properties of surface structures we discuss transitions between homogeneous phases related to low and high density states. We illustrate that these transitions are accompanied by a formation of adsorbate or vacancy islands. It was found that spherical adsorbate and vacancy islands are characterized by different distribution functions over their sizes for different symmetry of substrate lattice. We have shown that depending on system control parameters island size distributions can change their modality. The size of localized nano-clusters can be controlled by both primary and secondary mechanisms of pattern formation.

V.O.Kharchenko, D.O.Kharchenko, A.V.Dvornichenko. Statistical properties of nanosized clusters on a surface in overdamped stochastic reaction-Cattaneo systems, Surface Science, 630, pp.158-167 (2014)

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