Statistics of power injection in a plate set into chaotic vibration

TL;DR

This study investigates the statistical properties of power injection in a chaotic vibrating plate, comparing experimental results with models and examining the fluctuation theorem's applicability.

Contribution

It provides experimental data and statistical models for power injection in chaotic vibrations, and evaluates the fluctuation theorem's validity under different forcing conditions.

Findings

Logarithmic cusp at zero power in distributions

Gaussian tails for periodic forcing

Exponential tails for random forcing

Abstract

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.