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Bouncing droplets on a billiard table
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17.We remark that another natural (Faraday) length scale is set using the linear dispersion relation in combination with the period T. Such a choice, however, leads to a more complicated form for the coefficients in the dimensionless equation.
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/content/aip/journal/chaos/23/1/10.1063/1.4790840
2013-02-11
2015-04-19

Abstract

In a set of experiments, Couder et al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. I present a dynamical systems model, in the form of an iterative map, for a droplet on an oscillating bath. I examine the droplet bifurcation from bouncing to walking, and prescribe general requirements for the surface wave to support stable walking states. I show that in addition to walking, there is a region of large forcing that may support the chaotic motion of the droplet. Using the map, I then investigate the droplet trajectories in a square (billiard ball) domain. I show that in large domains, the long time trajectories are either non-periodic dense curves or approach a quasiperiodic orbit. In contrast, in small domains, at low forcing, trajectories tend to approach an array of circular attracting sets. As the forcing increases, the attracting sets break down and the droplet travels throughout space.

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Scitation: Bouncing droplets on a billiard table
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4790840
10.1063/1.4790840
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