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|
|Supervisor||Paul Milewski (Supervisor) & Tim Rogers (Supervisor)|
Discrete Time One-Dimensional Models for Faraday Pilot Waves
Russell, E. (Author). 29 Mar 2023
Student thesis: Doctoral Thesis › PhD