Abstract
Nonequilibrium localized stationary structures of submicrometreand nanometre sizes can spontaneously develop under reactionconditions on a catalytic surface. These self-organizedstructures emerge because of the coupling between the reactionand a structural phase transition in the substrate. Depending onthe reaction conditions they can either correspond to denselycovered spots (islands), inside which the reaction predominantlyproceeds, or local depletions (holes) in a dense adsorbate layerwith a very small reactive output in comparison to thesurroundings. The stationary localized solutions are constructedusing the singular perturbation approximation. These results arecompared with numerical simulations, where special adaptive grid algorithms and numerical continuation of stationaryprofiles are used. Numerical investigations beyond the singularperturbation limit are also presented.
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