Superlattice Patterns in Surface Waves

摘要: We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These are described most naturally in terms two interacting hexagonal sublattices. Two frequency forcing very large aspect ratio is utilized this work. A pattern ("superlattice-I") consisting lattices oriented relative angle 22^o obtained with 6:7 frequencies. Several theoretical approaches that may be useful understanding have been proposed. In another example, waves fully by superimposed wavelength sqrt(3), 30^o. The time dependence "superlattice-II" unusual. instantaneous reveal time-periodic stripe modulation breaks 6-fold symmetry any instant, but stripes absent average. not simply amplitude modulations primary standing wave. transition from superlattice-II state to 12-fold quasi-crystalline observed changing phase Phase diagrams (including superlattices, quasicrystalline patterns, ordinary hexagons, and squares) as function amplitudes phases driving accelerations.