LMA - Laboratoire de Mécanique et d’Acoustique

Research

I am interested in the study of nonlinear systems, in particular systems described by partial differential equations (PDE).

I am actually studying wind musical instruments which are oscillating nonlinear systems of infinite dimension with a hyperbolic PDE (wave equation). The challenge is to relate physical parameters of the instrument and the player to the sound produced. In order to obtain analytical formulae, I use the mathematical tools I have learnt during my PhD.

I have obtained a PhD in applied mathematics in October 2007. I studied mathematical models for quantum mechanics using spectral theory, functional analysis and perturbation theory.

CV

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List of publications

2009 Ricaud B., Guillemain P., Kergomard J., Silva F., Vergez C., Behavior of reed woodwind instruments around the oscillation threshold. Accepted for publication in Acta Acustica united with Acustica. Preprint version : http://hal.archives-ouvertes.fr/hal-00355058 .

2008 Cornean H., Duclos P., Ricaud B., On the skeleton method and an application to a quantum scissor, Proc. Symposia in Pure Math., vol 77, 657-672. Preprint version : http://hal.archives-ouvertes.fr/hal-00206274.

2007 Modelling and study of optical properties of carbon nanotubes. Thèse de doctorat. Accessible ici : http://tel.archives-ouvertes.fr/tel-00183627 .

2007 Cornean H. D., Pedersen T. G., Ricaud B., Perturbative vs. variational methods in the study of carbon nanotubes, Contemporary Mathematics, 447, 45-56, 2007. Preprint version : http://hal.archives-ouvertes.fr/hal-00023783.

2007 Cornean H., Duclos P., Ricaud B., Effective models for excitons in Carbon nanotubes, Ann. H. Poincaré 8 (2007), 135-163. Preprint : http://hal.archives-ouvertes.fr/hal-00166910.

2006 Cornean H., Duclos P., Ricaud B., On Critical Stability of Three Quantum Charges Interacting through Delta Potentials, Few-Body Systems 38, 2-4, 125-131 (2006). Preprint version : http://hal.archives-ouvertes.fr/hal-00022107.

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