Structure and Dynamics of Acoustically Levitated Granular Systems with Non-Conservative N-Body Interactions

Field-mediated interactions raise fundamental challenges for understanding particle structure, dynamics, and control because the effective forces between particles can be both multi-body and non-conservative. Here, we use acoustically levitated particle clusters to study these effects. Acoustic levitation provides a clean experimental platform in which particles interact through a surrounding acoustic field while remaining directly observable in real time.

In this thesis, we first explain how multi-body interactions arise in field-mediated systems and why pairwise additivity fails when both the field sources and the resulting force response depend on the full particle configuration. We then describe the acoustic levitation experiments, particle-tracking methods, finite-element force calculations, and molecular-dynamics simulations used throughout the thesis. Beginning with the minimal three-particle cluster, we show that non-conservative 3-body forces select a symmetry-broken trimer state rather than the equilateral triangle favored by conservative interactions. To explore a more extreme manifestation of non-reciprocity, we bind two particles into a dimer and demonstrate that its multi-body interaction with a third particle can drive persistent dynamics, including self-propulsion and limit-cycle motion, through a balance between energy injection and dissipation. For clusters of four to nine particles, we show that pair and 3-body forces select rings, centered stars, and symmetry-broken variants. For ten- and twelve-particle clusters, we show that the same interactions organize counter-rotating double-ring limit cycles and identify the pairwise and 3-body work channels that sustain this motion. Finally, we demonstrate that combining acoustic parametric pumping with quenching can reconfigure levitated clusters, providing a route to the active control of field-mediated matter.

Together, these results establish non-conservative multi-body interactions as a central organizing principle of acoustically levitated matter rather than a perturbative correction to an otherwise conservative, pairwise system. These interactions determine which structures form, which symmetries break, which modes become unstable, and how energy is injected and dissipated to sustain motion. More broadly, this work opens a path towards reconfigurable particle systems whose structures and dynamics can be selected through control of non-conservative multi-body interactions.