Abstract
Formation of hexagonal periodic nanoscale structures at the surface of aluminum oxide is considered in the present paper. The mathematical model of chemical reactions at metal-oxide and oxide/electrolyte interfaces is described. A weak nonlinear approximation near the instability threshold results in the two-dimensional Kuramoto-Sivashinsky equation. The solution of this equation provides the same regular hexagonal nanoscale structure arrays that are observed in physical experiments. The two-stage complex Rosenbrock scheme developed by the author is applied for the numerical simulation of this problem in the present paper. The high accuracy O(τ4) and L1 stability, along with the relative simplicity of the method, make it possible to use a conventional PC to perform the calculations.
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