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|a Oza, Anand Uttam
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Oza, Anand Uttam
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|a Harris, Daniel Martin
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|a Rosales, Rodolfo R.
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|a Bush, John W. M.
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|a Wind-Willassen, Øistein
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|a Harris, Daniel Martin
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|a Rosales, Rodolfo R.
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|a Bush, John W. M.
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|a Pilot-wave hydrodynamics in a rotating frame: Exotic orbits
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|b American Institute of Physics (AIP),
|c 2015-01-14T21:41:32Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/92872
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|a We present the results of a numerical investigation of droplets walking on a rotating vibrating fluid bath. The drop's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. As the forcing acceleration is progressively increased, stable circular orbits give way to wobbling orbits, which are succeeded in turn by instabilities of the orbital center characterized by steady drifting then discrete leaping. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but its statistical behavior reflects the influence of the unstable orbital solutions. The study results in a complete regime diagram that summarizes the dependence of the walker's behavior on the system parameters. Our predictions compare favorably to the experimental observations of Harris and Bush ["Droplets walking in a rotating frame: from quantized orbits to multimodal statistics," J. Fluid Mech.739, 444-464 (2014)].
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|a National Science Foundation (U.S.) (NSF Grant No. CBET-0966452)
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|a National Science Foundation (U.S.) (NSF Grant No. CMMI-1333242)
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|a National Science Foundation (U.S.) (Grant Nos. DMS-1007967)
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|a National Science Foundation (U.S.) (Grant No. DMS-1115278)
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|a National Science Foundation (U.S.) (Grant No. DMS-1318942)
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|a National Science Foundation (U.S.) (NSF Graduate Research Fellowship Program)
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|a Fannie and John Hertz Foundation
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|a Danish National Advanced Technology Foundation (NanoPlast project)
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|a en_US
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|a Article
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|t Physics of Fluids
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