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

Wave-driven assembly of quasi periodic patterns of particles