Harnack inequalities and discrete - continuum error estimates for a chain of atoms with two - body interactionsReportar como inadecuado




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1 Departamento de Fisica Santiago 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision 3 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

Abstract : 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.

Keywords : Two-body interactions nonlinear elasticity discrete-continuum error estimates Cauchy-Born rule Harnack inequality thermodynamic limit





Autor: Rafael Benguria - Jean Dolbeault - Régis Monneau -

Fuente: https://hal.archives-ouvertes.fr/



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