A droplet may 'walk' across the surface of a vertically vibrating bath of the same fluid, due to the propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed to exist only in the quantum realm. Starting from first principles, we derive a discrete-time fluid model, whereby the bath-droplet interactions are modeled as instantaneous. By analysing the stability of the system's fixed points, we explain the dynamics of a walking droplet, and capture the quantizations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double-quantization of chaotic trajectories is obtained through systematic statistical analysis.
- Department of Mathematical Sciences - Head of Department
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Centre for Networks and Collective Behaviour
- Water Innovation and Research Centre (WIRC)
- Centre for Mathematical Biology
Person: Research & Teaching