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From wave turbulence to wave energy by wave interaction


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.


Journal articles3 documents

  • Geoffrey Beck, David Lannes. Freely Floating Objects on a Fluid Governed by the Boussinesq Equations. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2022, 39 (3), https://ems.press/journals/aihpc/articles/5300753. ⟨10.4171/AIHPC/15⟩. ⟨hal-03122615v2⟩
  • Geoffrey Beck, Sébastien Imperiale, Patrick Joly. Asymptotic modelling of Skin-effects in coaxial cables. SN Partial Differential Equations and Applications, Springer, 2020. ⟨hal-02512156v2⟩
  • Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Mathematical modelling of multi conductor cables. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2014, pp.26. ⟨10.3934/dcdss.2015.8.521⟩. ⟨hal-01090481⟩

Conference papers6 documents

  • Geoffrey Beck, David Lannes, Lisl Weynans. Wave power farm made of many rigid floating structures in Boussinesq regime. WAVES 2022 — 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, France. ⟨hal-03628899⟩
  • Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Effective models for non-perfectly conducting thin coaxial cables. Waves 2019 - 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Aug 2019, Vienna, Austria. ⟨hal-02414849⟩
  • Geoffrey Beck, Maxime Bonnaud, Jaume Benoit. Recovering underlying graph for networks of 1D waveguides by reflectometry and transferometry. WAVES 2019 - 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Aug 2019, Vienna, Austria. ⟨hal-02414861⟩
  • Geoffrey Beck. Reconstruction of an unknown electrical network from their reflectogram by an iterative algorithm based on local identification of peaks and inverse scattering theory. 2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), May 2018, Houston, France. pp.1-6, ⟨10.1109/I2MTC.2018.8409731⟩. ⟨hal-02453477⟩
  • Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Matched asymptotics approach to the construction and justification of reduced graph models for 3D Maxwell's equations in networks of thin co-axial cables. 12th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2015), Department of Mathematics at Karlsruhe Institute of Technology (KIT), Jul 2015, Karlsruhe, Germany. ⟨hal-02088458⟩
  • Geoffrey Beck, Patrick Joly, Sébastien Imperiale. A rigorous approach to the propagation of electromagnetic waves in co-axial cables. 11th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2013), Jun 2013, Gamarth, Tunisia. ⟨hal-02453471⟩

Patents1 document

  • Geoffrey Beck. Computer-implemented method for reconstructing the topology of a network of cables: US20200363462A1. France, Patent n° : US Patent App. 16/638,451, 2020. 2017, https://patents.google.com/patent/US20200363462A1/en. ⟨hal-03115293⟩

Preprints, Working Papers, ...1 document

  • Akram Beni-Hamad, Geoffrey Beck, Sébastien Imperiale, Patrick Joly. An efficient numerical method for time domain electromagnetic wave propagation in co-axial cables. 2021. ⟨hal-03408400v2⟩