Localized nonequilibrium nanostructures in surface chemical reactions

Nonequilibrium localized stationary structures of submicrometre and nanometre sizes can spontaneously develop under reaction conditions on a catalytic surface. These self-organized structures emerge because of the coupling between the reaction and a structural phase transition in the substrate. Depending on the reaction conditions they can either correspond to densely covered spots (islands), inside which the reaction predominantly proceeds, or local depletions (holes) in a dense adsorbate layer with a very small reactive output in comparison to the surroundings. The stationary localized solutions are constructed using the singular perturbation approximation. These results are compared with numerical simulations, where special adaptive grid algorithms and numerical continuation of stationary profiles are used. Numerical investigations beyond the singular perturbation limit are also presented.