Analytical and numerical study of the unstable limit cycles of walking droplets

Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation.

Name thesis:degree_name

Bachelor

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mechanical Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Kurzban, Benjamin(Benjamin A.)

Advisor dc:contributor.advisor

• Matthew Durey

• Mechanical Engineering.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/131013

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/131013