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| HAL : hal-00267954, version 1 |
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| Journal of Statistical Physics 134 (2009) 27-51 |
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| Harnack inequalities and discrete - continuum error estimates for a chain of atoms with two - body interactions |
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| Rafael Benguria 1Jean Dolbeault 2 |
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| (2009) |
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| In the three-dimensional euclidean space, we consider deformations of an infinite linear chain of atoms where each atom interacts with all others through a two-body potential. We compute the effect of an external force applied to the chain. At equilibrium, the positions of the particles satisfy an Euler-Lagrange equation. For large classes of potentials, we prove that every solution is well approximated by the solution of a continuous model. We establish an error estimate between the discrete and the continuous solution based on a Harnack lemma of independent interest. Finally we apply our results to some Lennard-Jones potentials. |
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| 1 : | Departamento de Fisica |
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Pontificia Universidad Catolica de Chile |
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| 2 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 3 : | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Two-body interactions – nonlinear elasticity – discrete-continuum – error estimates – Cauchy-Born rule – Harnack inequality – thermodynamic limit |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00267954, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00267954 | |
| oai:hal.archives-ouvertes.fr:hal-00267954 | |
| Contributeur : Jean Dolbeault | |
| Soumis le : Vendredi 28 Mars 2008, 23:24:56 | |
| Dernière modification le : Samedi 7 Février 2009, 15:41:18 | |
