We study computational aspects of modeling reaction-diffusion patterns on microdesigned and microcomposite catalysts in one and two spatial dimensions. Special emphasis is placed on the numerical bifurcations of pulse-type solutions (possibly involving the continuous spectrum of the pulses) as well as the computation of modulated travelling waves for the full PDEs. We also discuss the transition to "effective behavior" of composite catalysts with fine-grained component geometry. The computations are presented along with comparable experimental results from our collaboration with the Fritz-Haber-Institut in Berlin.

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