Discrete Time One-Dimensional Models for Faraday Pilot Waves

Abstract

We investigate a millimetric droplet bouncing on the surface of a vibrating bath, igniting a Faraday wave on each impact. As the magnitude of the vibrations increases, the resultant wavefield becomes more complex and a diverse range of droplet dynamics emerges. Arising from the Navier-Stokes equations, we present a one-dimensional discrete time model and preform an extensive numerical experiments on the system. We analyse the inherent characteristics of the droplet's chaotic trajectories and compare it to the widely known ``run and tumble'' model. This provides a platform to analyse the underlying probability structures in the chaotic regime. Furthermore, we present a reduced system of three maps and compare it to the Lorenz system. Finally, we consider our models under the influence of an external potential and examine the resultant dynamics.

Date of Award	29 Mar 2023
Original language	English
Awarding Institution	University of Bath
Supervisor	Paul Milewski (Supervisor) & Tim Rogers (Supervisor)