We study pattern formation processes in anisotropic system governed by the Kuramoto-Sivashinsky equation with multiplicative noise as a generalization of the Bradley-Harper model for ripple formation induced by ion bombardment. For both linear and nonlinear systems we study noise-induced effects at ripple formation and discuss scaling behavior of the surface growth and roughness characteristics. It was found that the secondary parameters of the ion beam (beam profile and variations of an incidence angle) can crucially change the topology of patterns and the corresponding dynamics.
We study the epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of the phase-field approach based on the Burton-Cabrera-Frank model. Considering the statistical criteria of pattern formation, it is shown that the system dynamics is governed by the interaction strength of adatoms and the noise intensity of the total flux fluctuations. We have shown that the noise action can crucially change the processes of pyramidal pattern formation. The scaling behavior of the height-height correlation function is discussed.
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