Geodesic
Numeric simulation of hexogonal nanoscale structure arrays formation in anodic aluminium oxide
Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 97-108

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In this article self-organization of nanoscale porous structure arrays in anodic metal oxide is considered. The mathematical model of the chemical reaction at the metal-oxide and oxide-electrolyte interfases is described. A weakly nonlinear analysis near the instability threshold result in two dimensional Kuramoto–Sivashinsky equation. Solution of this equation provides the same regular hexagonal pore arrays that are observed in physical experiments. In this work two stage complex Rosenbrock scheme, developed by author, is applied for numeric simulation of this problem. High accuracy $O(\tau^4)$ and L1-stability along with low complexity of this method allow to use conventional PC to perform calculations.
Keywords: Aluminium oxide, Hexagonal porous array, Kuramoto–Sivashinsky equation, numerical solution of ODE, stiff ODE, Rosenbrock method. 
@article{MM_2010_22_8_a7,
     author = {A. G. Limonov},
     title = {Numeric simulation of hexogonal nanoscale structure arrays formation in anodic aluminium oxide},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {97--108},
     publisher = {mathdoc},
     volume = {22},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_8_a7/}
}
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A. G. Limonov. Numeric simulation of hexogonal nanoscale structure arrays formation in anodic aluminium oxide. Matematičeskoe modelirovanie, Tome 22 (2010) no. 8, pp. 97-108. http://geodesic.mathdoc.fr/item/MM_2010_22_8_a7/