Geoffrey Beck

Wave-turbulence manage to give a statistic description of the effective balance of the mean energy input from a source at low wave-numbers, transfer of energy through reversible non-linearities to higher and higher wave-numbers. The final goal is to derive a wave kinetic equation which describe this cascade from a random initial ocean. But catching the specfic asymtotic regime where the non-linearties are small and the time scale is sufficiently long to allow quasi-resonnance mechanism isn't an easy task. To check the physical relevance of wave-turbulence regime, one can imagine a laboratory experiment where the water surface becomes random with the help of a folationg object whch act as a random shaker. I'm also interseted to interactions of water-waves with a partially immersed body allowed to move freely in the vertical direction. In 2D fluid, the whole system of equations can be reduced to a transmission problem with transmission conditions given in terms of the displacement of the object and of the average horizontal discharge beneath it; these two quantities are in turn determined by two nonlinear ODEs with forcing terms coming from the exterior wave-field. One application of this prject is to recover wave energy by the the solid displacement. The wave energy are transferred to device by electrical cable. I also work on derivation of 1D models of electrical networks from 3D electromagnetic wave propagation by multi-sacle asymptotic analysis of 3D Maxwell equations. Important effortd are devoted to understand the skin-effect due to the high contrast of conductity inside a cable, to take into acconunt singular geometry such as defect on junctions, or comparaison beetween 1D models and 3D simulations. One motivation to reduced complex wave propagtion to simple 1D models is tu use the last ones for wire troubleshooting. One intersting inverse problem is how to recover underlying graph for unknows electrical networks by reflectometry.