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

dc.contributor.authorBenguria, Rafael
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorMonneau, Régis
dc.date.accessioned2009-07-03T07:54:09Z
dc.date.available2009-07-03T07:54:09Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/714
dc.language.isoenen
dc.subjectTwo-body interactionsen
dc.subjectthermodynamic limit
dc.subjectHarnack inequality
dc.subjectCauchy-Born rule
dc.subjecterror estimates
dc.subjectdiscrete-continuum
dc.subjectnonlinear elasticity
dc.subject.ddc520en
dc.titleHarnack inequalities and discrete - continuum error estimates for a chain of atoms with two - body interactionsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherINRIA - Ecole Nationale des Ponts et Chaussées;France
dc.contributor.editoruniversityotherPontificia Universidad Catolica de Chile;Chili
dc.description.abstractenIn 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.en
dc.relation.isversionofjnlnameJournal of Statistical Physics
dc.relation.isversionofjnlvol134en
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages27-51en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10955-008-9662-4
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00267954/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelSciences connexes (physique, astrophysique)en


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