Hybrid pattern-forming systems

The hybrid models combine short-scale Monte-Carlo computations of surface
structure with a mean-field treatment of rapidly diffusing species. They are
largely motivated by studies of patterns on catalytic surfaces. They are
observed at the scale of microns, but the pattern-forming mechanism lies in
surface phase transitions that involve nanoscale transport processes.

A down-to-earth hybrid model is the Ising model coupled with a long-range
diffusing inhibitor. It shows a variety of patterns resembling that of a
noisy FitzHugh-Nagumo model. More realistic computations, based on available
thermodynamic and kinetic data for Pt surfaces reproduce effects of
nanoscale surface restructuring and roughening, as well as of microscale
pattern formation.