Wave-Driven Assembly of Quasiperiodic Patterns of Particles.

We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three-dimensional patterns. We experimentally demonstrate this theory by using ultrasound waves to assemble quasiperiodic patterns of carbon nanoparticles in water using an octagonal arrangement of ultrasound transducers, and we document good agreement between theory and experiments. The theory also applies to obtaining quasiperiodic patterns in other situations where particles move with linear waves, such as optical lattices.