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Geoffrey Beck
14
Documents
Identifiants chercheurs
- geoffrey-beck
- 0000-0003-0967-213X
- IdRef : 197337767
- Google Scholar : https://scholar.google.fr/citations?user=4cRX_t8AAAAJ
Présentation
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.
Publications
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Freely Floating Objects on a Fluid Governed by the Boussinesq EquationsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2022, 39 (3), https://ems.press/journals/aihpc/articles/5300753. ⟨10.4171/AIHPC/15⟩
Article dans une revue
hal-03122615v2
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An efficient numerical method for time domain electromagnetic wave propagation in co-axial cablesComputational Methods in Applied Mathematics, 2022, ⟨10.1515/cmam-2021-0195⟩
Article dans une revue
hal-03408400v2
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Asymptotic modelling of Skin-effects in coaxial cablesSN Partial Differential Equations and Applications, 2020
Article dans une revue
hal-02512156v2
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Mathematical modelling of multi conductor cablesDiscrete and Continuous Dynamical Systems - Series S, 2014, pp.26. ⟨10.3934/dcdss.2015.8.521⟩
Article dans une revue
hal-01090481v1
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Wave power farm made of many rigid floating structures in Boussinesq regimeWAVES 2022 — 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jul 2022, Palaiseau, France
Communication dans un congrès
hal-03628899v1
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Effective models for non-perfectly conducting thin coaxial cablesWaves 2019 - 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Aug 2019, Vienna, Austria
Communication dans un congrès
hal-02414849v1
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Recovering underlying graph for networks of 1D waveguides by reflectometry and transferometryWAVES 2019 - 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Aug 2019, Vienna, Austria
Communication dans un congrès
hal-02414861v1
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Reconstruction of an unknown electrical network from their reflectogram by an iterative algorithm based on local identification of peaks and inverse scattering theory2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), May 2018, Houston, France. pp.1-6, ⟨10.1109/I2MTC.2018.8409731⟩
Communication dans un congrès
hal-02453477v1
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Matched asymptotics approach to the construction and justification of reduced graph models for 3D Maxwell's equations in networks of thin co-axial cables12th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2015), Department of Mathematics at Karlsruhe Institute of Technology (KIT), Jul 2015, Karlsruhe, Germany
Communication dans un congrès
hal-02088458v1
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A rigorous approach to the propagation of electromagnetic waves in co-axial cables11th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2013), Jun 2013, Gamarth, Tunisia
Communication dans un congrès
hal-02453471v1
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Computer-implemented method for reconstructing the topology of a network of cablesFrance, Patent n° : US Patent App. 16/638,451, 2020. 2017, https://patents.google.com/patent/US20200363462A1/en
Brevet
hal-03115293v1
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Electromagnetic waves propagation in thin heterogenous coaxial cables. Comparaison between 3D and 1D models2023
Pré-publication, Document de travail
hal-04147142v3
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A NUMERICAL METHOD FOR WAVE-STRUCTURE INTERACTIONS IN THE BOUSSINESQ REGIME2023
Pré-publication, Document de travail
hal-04151128v1
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A Linear Stochastic Model of Turbulent Cascades and Fractional Fields2023
Pré-publication, Document de travail
hal-03919233v2
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