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| HAL : hal-00128444, version 2 |
| arXiv : math/0702017 |
| Fiche détaillée |  Récupérer au format |
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| Applied Mathematics & Optimization 57, 1 (2008) 1-17 |
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| Versions disponibles : | v1 (01-02-2007) | v2 (22-05-2007) |
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| Shape Minimization of Dendritic Attenuation |
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Antoine Henrot 1, 2Yannick Privat 1, 2 |
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| (2008) |
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| What is the optimal shape of a dendrite? Of course, optimality refers to some particular criterion. In this paper, we look at the case of a dendrite sealed at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the dendrite which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal. |
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| 1 : | 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 |
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| 2 : | CORIDA (INRIA Lorraine / IECN / MMAS) |
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INRIA – CNRS : UMR7122 – CNRS : UMR7502 – Université Paul Verlaine - Metz – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine |
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| Equations aux dérivées partielles |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Optimisation et contrôle Sciences du Vivant/Biologie du développement/Morphogenèse |
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| optimal shape – cable equation – dendrite – eigenvalue problem |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00128444, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00128444 | |
| oai:hal.archives-ouvertes.fr:hal-00128444 | |
| Contributeur : Antoine Henrot | |
| Soumis le : Mardi 22 Mai 2007, 12:25:57 | |
| Dernière modification le : Mardi 4 Novembre 2008, 16:23:07 | |
