As an instructor at MIT, I developed an experiment exploring the collective dynamics of droplets bouncing on the surface of a vertically vibrating fluid bath. Each time the droplets bounce, they produce a wave field which both propels the droplets and binds them to their neighbours, creating lattices with highly regular structure. As the vibrational forcing of the bath is increased, these hydrodynamic lattices can destabilize to self-sustaining, out-of-oscillations or a striking solitary-like wave, depending on the number of droplets. We also uncovered a rich bifurcation structure underpinning the experimentally observed instabilities In a broader context, the role of inertia differentiates the walking droplet system from prevailing active and driven matter systems (for example, bacterial and colloidal suspensions) wherein the dynamics are typically overdamped. Indeed, that solitary-like waves are supported by the hydrodynamic lattice points to the existence of a wider class of self-sustaining, nonlinear waves in inertial, underdamped active systems.

Collective vibrations of confined levitating droplets, SJT, M. M. P. Couchman, J. W. M. Bush, Physical Review Fluids (2020)

Collective vibrations of a hydrodynamic active lattice, SJT, M. Durey, R. R. Rosales, Proceedings of the Royal Society A (2020)

A discrete complex Ginzburg-Landau equation for a hydrodynamic active lattice, SJT, M. Durey, R. R. Rosales, arXiv:2010.12655 (2020)