Active wave-particle clusters

We investigate the collective dynamics of a class of inertial active particles, known as wave–particle entities (WPEs), inspired by the behavior of walking and superwalking droplets that couple self-generated waves with particle motion. Using a stroboscopic model, we numerically explore the interactions of multiple WPEs and find that they can self-organize into stable, bound clusters reminiscent of atomic nuclei. These active clusters display a rich variety of collective excitations, including shape oscillations and chiral rotational modes, whose characteristics depend on the spatial extent and temporal memory of the underlying waves. The resulting time-averaged collective wave-field potential shows qualitative parallels to the nuclear shell and bag models. At high memory or short wave decay lengths, the clusters destabilize or emit single WPEs with exponential decay statistics, akin to radioactive decay. Our findings reveal a diverse spectrum of emergent behaviors in active wave–particle systems, offering new pathways for studying hydrodynamic analogs of strongly interacting many-body quantum systems.