| 0:00:08 | a grand on the emperor is a container a cavity |
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| 0:00:12 | so i microscopic particles |
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| 0:00:14 | when agitated |
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| 0:00:15 | granted access dissipate energy you to invest conditions |
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| 0:00:19 | therefore the amplitude of harmonics bring with an attachment that damper the case in time |
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| 0:00:24 | when the influence of brevity is eliminated one observes a surprising characteristic behaviour |
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| 0:00:30 | unlike of is this temper |
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| 0:00:32 | i granted amber does not lead to an exponential decay |
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| 0:00:36 | in amplitude as a function of time |
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| 0:00:38 | instead |
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| 0:00:39 | if the case almost linearly |
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| 0:00:41 | this is true up to a certain residual amplitude |
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| 0:00:45 | after this point dedicate of the amplitude proceed much lower |
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| 0:00:51 | these characteristic features have been reported in a number of publications but remain unexplained |
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| 0:00:57 | the present paper aims to explain this behavior |
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| 0:01:02 | for large amplitudes we observe a collective motion of the particles synchronous to the motion |
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| 0:01:07 | of the box |
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| 0:01:08 | for small amplitudes a disordered gas like motion is observed |
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| 0:01:13 | we find the same dynamical behaviour in this they really driven going the temporal for |
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| 0:01:18 | small and q |
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| 0:01:19 | we see the cost like behavior |
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| 0:01:21 | a large amplitudes all particles collapsed in the lexically on the more twice the period |
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| 0:01:27 | and get released once the box starts this elaborate |
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| 0:01:31 | these two machines are separated by a threshold amplitude determined by the feeling ratio of |
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| 0:01:36 | the container |
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| 0:01:38 | dissimilarity suggest to consider the relaxation process as a sequence of statistics which is justified |
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| 0:01:44 | as long as the relaxation time is much larger than the period of the oscillation |
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| 0:01:50 | with this we can use the previously derived expressions what the energy dissipation in this |
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| 0:01:54 | day degree of the system to describe the relaxation |
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| 0:01:58 | the results of differential equation describing the decaying amplitude |
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| 0:02:02 | this prediction agrees very well with the experimental data |
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| 0:02:06 | the collect and collide damping process continues until the amplitude across a threshold where a |
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| 0:02:11 | transition to the gas like regime occurs and the damping is much weaker |
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| 0:02:17 | the initial slope of the amplitude and the residual amplitude whether rapidly near the case |
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| 0:02:21 | he says with a function of the feeling ratio of the country |
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| 0:02:26 | therefore |
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| 0:02:27 | when applying for another person |
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| 0:02:28 | one has to compromise between efficient dampening and final amplitude |
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