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== Pilot-wave hydrodynamics ==
{{attachment:HaileyZackUofC.jpg|HaileyZackUofC|width="300"}} {{attachment:DuncanBrett.jpg|DuncanBrett|width="300"}} 

(Haily Hultquist and Zach Taebel visiting Stéphane Perrard, a graduate student studying under Sidney Nagel, U of Chicago lab Sep 2016)

A project to explore drops suspended by sub-Faraday wave threshold vertical fluid oscillations and then interacting with Faraday waves (surface gravity waves) exhibit a kind of wave-particle duality. This project shares much with the study of antibubbles as the bounce of a drop off the liquid surface is mediated via a think layer of viscous air.

See
http://math.mit.edu/~bush/?page_id=484 and review article http://www.annualreviews.org.ezproxy.library.wisc.edu/doi/abs/10.1146/annurev-fluid-010814-014506?journalCode=fluid
and playing with Faraday waves:

http://www.nbi.dk/CATS/theses/Jacob_Sparre_Andersen/node12.html#SECTION00310000000000000000

www.physics.utoronto.ca/~phy326/far/far.pdf

https://www.youtube.com/watch?v=nq3ZjY0Uf-g

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References:

Faraday waves in a BEC: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.095301

2015 Faraday waves http://journals.aps.org.ezproxy.library.wisc.edu/pre/abstract/10.1103/PhysRevE.92.033014

Faraday waves at a liquid liquid interface to which you could add a drop of a third fluid
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0ahUKEwjxhbDmrKjPAhXJ24MKHSyXBXQQFghZMAY&url=https%3A%2F%2Fpure.tue.nl%2Fws%2Ffiles%2F3309842%2FMetis240218.pdf&usg=AFQjCNGnbYg32P4t77iuW1gQsNyeI-0Afw&sig2=kkCIxhhT1TZCLZvlU4Y9gw

Masters thesis with the theory:

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&ved=0ahUKEwjxhbDmrKjPAhXJ24MKHSyXBXQQFghwMAk&url=https%3A%2F%2Fwww.utwente.nl%2Fewi%2Faa%2Feducation%2FThesis%2Fon-faraday-waves-and-jets.pdf&usg=AFQjCNFTCwpQZPu25Tt2iaNEstWHGL2KLQ&sig2=pUHZA_HFbBMLadV8Uwcb_Q

Parametric oscillations: see wiki and https://wiki.physics.wisc.edu/garage/Active%20mechanical%20stablization%20of%20structures. The vertically shaken beaker is like a pendulum with its point of support moved harmonically up and down. The fluid has a resonance for each a standing gravity surface wave (exponentially damped with depth, and damped via viscosity).

Invisid theory and experiment with water: Benjamin, T.B. & Ursell, F. (1954). “ On the stability of the plane free surface of a liquid in vertical periodic motion.” Proceedings of the Royal Society of London, 225, 505-515. http://rspa.royalsocietypublishing.org/content/225/1163/505.short

Faraday wave chaos and changing patterns: Kudrolli, A. & Gollub, J.P. (1996). “Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio.” Physica D, 97,133-154. http://www.sciencedirect.com/science/article/pii/0167278996000991
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Haily Hultquist and Zach Taebel