平板混沌振动中的功率注入统计
Statistics of power injection in a plate set into chaotic vibration
摘要：
在周期性或随机局部强迫作用下，振动板进入波动湍流的混沌状态。研究了强迫点处板的局部速度响应与强迫之间的相关性。统计模型与实验相当好的协议，提出了每一个强迫。两种注入功率分布在零功率时都有对数尖点，而在周期驱动时则是高斯分布，而在随机驱动时则是指数分布。在涨落定理（也称为Gallavotti-Cohen定理）的框架下，研究了长时间间隔内注入工作的分布。看来该定理的结论仅针对周期性的、确定性的强迫得到验证。使用独立的相空间收缩的估计，这一结果进行了讨论，在现有的理论框架。
英文摘要：
A vibrating plate is set into a chaotic state of wave turbulence by either a periodic or a random local forcing. Correlations between the forcing and the local velocity response of the plate at the forcing point are studied. Statistical models with fairly good agreement with the experiments are proposed for each forcing. Both distributions of injected power have a logarithmic cusp for zero power, while the tails are Gaussian for the periodic driving and exponential for the random one. The distributions of injected work over long time intervals are investigated in the framework of the fluctuation theorem, also known as the Gallavotti-Cohen theorem. It appears that the conclusions of the theorem are verified only for the periodic, deterministic forcing. Using independent estimates of the phase space contraction, this result is discussed in the light of available theoretical framework.
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