Laboratory experiments and numerical simulations are used to study quasicrystal and superlattice patterns that arise when a fluid layer is both differentially heated and vertically oscillated. These complex-ordered states arise from interaction between two distinct classes of modes, each with a different temporal response and spatial scale. The formation of complex-ordered patterns in convection do not depend on three-wave interactions (resonant triads) that are responsible for similar patterns found in other non-equilibrium systems. Instead, four-wave interactions (resonant tetrads), which are consistent with the system symmetries, are found to play a central role. Onset of complex-ordered patterns from conduction, from pure harmonic, and from subharmonic convection is described. Experiments demonstrate the superlattices exist for a wide parameter range well away from the bicritical point; in this regime experiments and Boussinesq simulations are in good agreement.

J. L. Rogers, M. F. Schatz, W. Pesch, and O. Brausch, "Complex-ordered patterns in acceleration-modulated Rayleigh-Benard Convection, " in preparation (preprint to be posted by mid-September).