(a) uniform bouncing (Γ=1.45, State 0) | ¡@(b) dominance by two ends (Γ=1.80) | ¡@(c) chaos (Γ=2.20) | ¡@
¡@ | ¡@ | ¡@ |
State 0 | ¡@¡@ |
State 1 | ¡@¡@ |
State 2 | ¡@¡@ |
¡@ |
More movies cited by Y.-C. Sun, Master Thesis, National Taiwan Normal University, June 2015, Taipei, Taiwan.
Figures from previous manuscript [pdf]
Distance of individual particles from the substrate, as
functions of time t, for different values of £F. 25Hz, N = 8, in
periods of State 0. (a) Sample trajectories, with the end particles
displayed by two different colors and others in gray. The
phase of the substrate and the hypothetical parabolic flight
are also displayed above each sub-panels. (b) Trajectory of
one particle accumulated from 18 vibration cycles, projected
onto one single period. The thick line shows the average,
with the hypothetical parabolic flight displayed by the thin
line. (c) The variance among the trajectories shown in (b),
£_Z12, normalized by the mean separation with the substrate
over the entire cycle, as a function of Γ
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Image-based definition of states ¡V (a) Sample images
and tracking results, with small crosses indicating the center
of the first and last segments, the large cross showing the
center of the middle particles. The long dashed line indicates
the threshold height hc = d/4 above the center of the middle
particles, for defining the states. (b) The time fraction of each
state for an accumulation of 2500 vibrations, using different
choice of hc. The results are insensitive to the change of hc
within the range marked by stripe. (c) Sample of an blurred
frame and its result.
|
Durations of events defined by the switch of states.
N = 8, 25Hz, hc = d/4, based on about 40 minutes of recording
in setup β. (a) Histogram of the durations for State 0
and State 2, 0 and 2, with the bin width indicated by the
vertical grid lines, at three different vibration intensity. (b)
Mean values of τ0, τ2, and the average time for either end of
the chain staying active τ(1).
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