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Effect of Electrostriction on the Self-organization of Porous Nanostructures in Anodized Aluminum Oxide

L. G. Stanton, A. A. Golovin (2008)

Mathematical Modelling of Natural Phenomena

The self-organization of porous nanostructures in anodic metal oxide is considered. A mathematical model which incorporates the chemical reactions at the metal-oxide and oxide-electrolyte interfaces and elastic stress caused by the electrostrictive effects is developed. It is shown through linear stability analysis, that a short-wave instability exists in certain parameter regimes which can lead to the formation of hexagonally ordered pores observed in anodized aluminum oxide.

Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²

Agnieszka Herczak, Michał Olech (2009)

Banach Center Publications

We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.

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