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| HAL : hal-00015299, version 2 |
| Fiche détaillée |  Récupérer au format |
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| ESAIM - Control Optimisation and Calculus of Variations 14 (2008) 657-677 |
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| Versions disponibles : | v1 (06-12-2005) | v2 (27-03-2007) |
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| Eliciting Harmonics on Strings |
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| Steven J. Cox 1Antoine Henrot 2, 3 |
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| (2008) |
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| One may produce the $q$th harmonic of a string of length $\pi$ by applying the 'correct touch' at the node $\pi/q$ during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude $b$ concentrated at $\pi/q$. The 'correct touch' is that $b$ for which the modes, that do not vanish at $\pi/q$, are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree $q-1$. We establish lower and upper bounds on the spectral abscissa and show that the set of associated root vectors constitutes a Riesz basis and so identify 'correct touch' with the $b$ that minimizes the spectral abscissa. |
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| 1 : | Computational & Applied Mathematics |
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Rice University |
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| 2 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 3 : | CORIDA (INRIA Nancy - Grand Est / IECN / LMAM) |
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INRIA – CNRS : UMR7502 – Université de Lorraine |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Point-wise damping – spectral abscissa – Riesz basis |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00015299, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00015299 | |
| oai:hal.archives-ouvertes.fr:hal-00015299 | |
| Contributeur : Antoine Henrot | |
| Soumis le : Mardi 27 Mars 2007, 08:23:45 | |
| Dernière modification le : Lundi 3 Novembre 2008, 18:06:16 | |
