Statistical properties of energy transport in a set of bending waves – SETBen

The aim of the SETBEn project is to develop original approaches on well identified questions, at the boundary between non-linear physics and non-equilibrium statistical physics (or “stochastic thermodynamics”). The specificity of the approach we have developed since a decade or so, is to evidence at human scale, phenomena that usually manifest themselves at microscopic scale. The experiment proposed consists of a set of bending waves generated in a thin elastic plate.

The first questions we want to address is the localization of the wave’s energy by defects randomly distributed on the plate. A macroscopic realization of a phenomenon similar to the ‘Anderson localization’ in a macroscopic dissipative system would, alone, be an eye-catching result. Such a system is a very good candidate for this study, because of its low dissipation. Moreover, being macroscopic, it allows access both to local quantities (deformation field, etc.) and to global quantities (transfer function, etc.). After identifying the localization, we want to characterize the influence of nonlinearity, by increasing the steepness (amplitude?) of the wave. Several question are still open in this direction.

Next, we want to trace back a signature of this resonance on the fluctuations of the power injected. This energy per time unit, which supplies the steady state, is called ‘house-keeping heat’ in the langage of stochastic thermodynamics. Such an observation would make a link between the fields of non-linear phenomena and statistical physics. We previously exhibited the analogy between forced granular gases and equilibrium thermostats, that allows the use of stochastic thermodynamics in such dissipative systems. An important question is how general such similitudes are? Is it also valid for non-equilibrium turbulent state of wave field? An additional advantage of this setup is that an effective temperature can be defined and measured in several independent ways, as already explored in previous studies. This could build new bridges between the turbulence and the out-of-equilibrium statistical physics.
questions, we plane to study the properties of transport two excited plates used as an out-of-equilibrium thermostat.